re: Physicists Find Fiber's LimitClearly you need to read Agrawal Second Ed Ch 7, in particaluar the first paragraph on page 305 and ask yourself 1) What would the noise spectrum of AM/PM noise look like for complex modulated signals, and having figured that out, 2) could would it interfere with the detected signals, and 3) could it be filtered out 4) how much and how?

The proof I supplied for applying the central limit theorem is perfectly valid at any given time. Having different carriers makes no difference. Adding a separate phase to each of N random phases still leaves those phases random. Proof: If phi_n are uniformly i.i.d. distributed, so are phi_n+n*omega*t.

As for the NLS, it does not require quasimonochromatic fields. The E^2 term in the dielectric constant is the total field intensity, not any spectral density.

Gosh, too many textbooks will now have to be rewritten ... or maybe not (!)

re: Physicists Find Fiber's LimitExactly! That equation is only accurate under the assumption of quasi-monochromatic waves, or if you like: pair-wise between individual tones of two complex signals. Consider it this way: when the individual tone powers of the complex multi-tone signal are reduced (spread spectrum), the nonlinear tones (cross products) are reduced proportionate to the square of spread. In simple terms, cut the signal tone powers by 3db by doubling the number of tones, the power of each cross tone drops by 6db. Therefore, spectral density, not total power, is the issue.

re: Physicists Find Fiber's Limit"Even if you did, most fiber NL effects scale non-linearly with power spectral density of the source (not total optical power)..."

Where did you get that idea? Have you ever seen n(w) = n0(w) + n1 * (E*conj(E)) ?

re: Physicists Find Fiber's LimitGentlemen, a reminder:

WDM implies frequency differences in the base carriers. So you cannot make the assertion that WDM with phase modulation tends to Gaussian anything. FDM is ultra-WDM. You cannot ignore the frequency differences of the subchannels, even for a single wavelength.

Even if you did, most fiber NL effects scale non-linearly with power spectral density of the source (not total optical power)...so when the effective spectral density is greatly reduced, as is the case here, the NL effects are also significantly reduced...

re: Physicists Find Fiber's LimitI wouldn't worry too much about Ito calculus if I were you. Following Mark Kac in his famous adage, "be wise and discretize", and you don't have to worry too much about those mathematical subtleties, it is taken care of automatically for you ...

re: Physicists Find Fiber's LimitThanks for reiterating the point about adding phase only signals producing amplitude noise. I would have thought that was elementary. Oh well.

About solitons, I agree with you that spectral efficiencies of soliton systems are actually pretty low, significantly less than 1bit/s/Hz, because you have to keep the solitons apart by a sufficiently long time slot. I presume that at least theoretically one could use so called multi-solitons to get the spectral efficiencies up and get closer to a bit - but then with the complexities of a WDM system to deal with, I have my suspicions that even multi-solitons won't go very high with spectral efficiencies either. I think solitons may have other merits, but they are not the road to very high spectral efficiencies.

re: Physicists Find Fiber's LimitHere's the point: I am sure if you take a sufficiently * narrow * total bandwidth, you can get spectral efficiencies close to a linear channel, because it is the interplay between nonlinearities and dispersion that causes problems. One way of looking at the problem is, compute the nonlinear length and the dispersion length. If one of these is much longer than the other one, then you are either in the pure SPM or pure dispersion limit: in either of those cases, you'll be back to the linear channel formula for spectral efficiencies.

To take an extreme example just for pedagogical purposes, if you stuck a bunch of audio bandwidth channels side by side, in fiber, covering a * small * total bandwidth, say 1GHz, I have no doubt that you can get spectral efficiencies predicted by the linear SNR, as long as you are not killed by the phase noise generated by nonlinear mixing of amplifier ASE and signal (which will happen for long enough systems and will take away a factor of two).

* However * the spectral efficiency when a very broad bandwidth is being used, in a WDM system, it is a very different story. That is where the paper applies: to consider theoretical limits to the fiber, you really have to excite the whole allowable bandwidth.

Of the systems you refer to, please quote: (1) total data rate (2) total bandwidth (*including channel spacing*)

If (1)/(2) is significantly large, my prediction is that (2) is comparatively small to the total optical bandwidth.

Finally, here is a simple proof for you that what the Kahn and Ho say about getting rid of CPM using phase modulation is not really correct for WDM systems: ubwdm has by now pointed this out multiple times: suppose you * did * produce a number of phase only signals exp[i phi_n(t)] which carry information. Now consider any instant of time, and consider the total complex amplitude at a given time:

A(t) = Sum_n exp[i phi_n(t)]

Since the signals are information bearing, at any instant of time phi_n(t) are random. Therefore, by applying the law of large numbers, A(t) tends to a complex Gaussian distribution with amplitude and phase fluctuations as the number of WDM channels grow large.

This leads to CPM, and for large enough total bandwidths, long enough fibers, etc, will destroy the spectral efficiency compared to the linear channel. As far as I am concerned, that is the message of this paper ...

Note that you do not escape the problems by dividing a very wide band into very narrow channels, because the CPM seen by a given channel will not depend on its own bandwidth. Therefore, it is sort of irrelevant whether you have sharp filters at your output or not. you may need that to * get * to the allowed (nonlinear) limit because that will require coherent detection (otherwise you lose phase). Unless, as ubwdm points out, you use tdm.

re: Physicists Find Fiber's LimitPhase error variance of OPLL inpresence of GVD and fiber-nonlinearity can not be simply determined by the use of common theoretical techniques in wireless..like assumimg Tikanov distrivution of phase error etc.. ..Interestingly, no good dynamic theory exists for OPLL in presence of ISI due to GVD and non-linearity..( I mean starting from the fundamental assumptions of Eto calculus etc ..)except a few standard old papers by L.G.Kazovsky.. I guess, PPM and UBWDM will do us a favor, by providing a very good dynmic theory of OPLL locking, in presence of phase noise due to GVD and non-linearity..Let do complete cooking than a half-baked potatos.. ..Since, I am not that good theory, I couldn't solve the problem, I hope PPM will take the challenge..I swear it's an amazingly good problem on eto calculus..

re: Physicists Find Fiber's LimitSince it was mentioned elsewhere, I would suggest you look into CenterPoint and Kestrel's technology. It is essentially FDM analog, with complex modulation on each channel, not as you suspect, simple plain-FM. But even plain FM is pretty good.

The channels (as seen pre-PLL) do overlap due to some spectral spreading, even after filtering, but this is perfectly allowable, so long as the data that emerges out of the subchannel in-lock has an acceptable error rate, and the time to achieve lock is also acceptable. Note the filtering is electrical, not optical, so can be very sharp and narrow.

Since each of the channels can be treated almost independently (save for some channel spacing), they can easily be tailored for the local dispersion slope. This can be done using adaptive algorithms commonly found in low cost MODEM (signal processing) chips.

Although the overall spectral density of the commercial equipment from each of these companies is not 10 bps/Hz, it can be significantly above 3 bps/Hz.

The fact that this type of system was not even discussed is the reason they had to go to Nature to get press...the general approach (to high spectral density data) is fairly common knowledge, and has been done (some might say over done!) in the relevant journals...

re: Physicists Find Fiber's LimitFrom "A Study in Scarlet" by Arthur Conan Doyle - Sherlock Holmes would not care about the theoretical bandwidth in a fiber. He would care about how to effectively bring bandwidth to users and how to put products and services on it that they want.

His ignorance was as remarkable as his knowledge. Of contemporary literature, philosophy and politics he appeared to know next to nothing. Upon my quoting Thomas Carlyle, he inquired in the naivest way who he might be and what he had done. My surprise reached a climax, however, when I found incidentally that he was ignorant of the Copernican Theory and of the composition of the Solar System. That any civilized human being in this nineteenth century should not be aware that the earth travelled round the sun appeared to me to be such an extraordinary fact that I could hardly realize it.

"You appear to be astonished," he said, smiling at my expression of surprise. "Now that I do know it I shall do my best to forget it."

"To forget it!"

"You see," he explained, I consider that a man's brain originally is like a little empty attic, and you have to stock it with such furniture as you choose. A fool takes in all the lumber of every sort that he comes across, so that the knowledge which might be useful to him gets crowded out, or at best is jumbled up with a lot of other things, so that he has a difficulty in laying his hands upon it. Now the skillful workman is very careful indeed as to what he takes into his brain-attic. He will have nothing but the tools which may help him in doing his work, but of these he has a large assortment, and all in the most perfect order. It is a mistake to think that that little room has elastic walls and can distend to any extent. Depend upon it there comes a time when for every addition of knowledge you forget something that you knew before. It is of the highest importance, therefore, not to have useless facts elbowing out the useful ones."

"But the Solar System!" I protested.

"What the deuce is it to me?" he interrupted impatiently: "you say that we go round the sun. If we went round the moon it would not make a pennyworth of difference to me or to my work."

re: Physicists Find Fiber's Limitdoes anyone think this technology is dead for the foreseeable future??? what do you think of CORV products in the area?? thanks in advance. km

re: Physicists Find Fiber's LimitOkay, it's time to finish this FM, angle modulation business.

1). FM has nothing to do with phase modulation in question. The phase modulation in question as raised by reviewers is a modulation on E field, or a phasor as called in Goodman's. The intensity of a phasor (E*conj(E)) is then always constant. Take a phasor into NLS, you will see SPM and XPM does not set a limit for its propagation, as the reviewers pointed out. Now let's talk about more realistic multi channel systems since capacity is the question. This is what the reviewers should go further. We can have two type of systems: Multiplicative or additive. DWDM is additive. So everything about "a phasor" is now totaly off, now we have a lot of cross terms, each representing the inter channel crosstalk and the results are much worse than OOK systems since phase is more sensitive to everything. For a multiplicative (modulated) system, you can have bandwidth limited multichannels. You can do that by cascading multiple MZ modulators (as Centerpoint, Kestrel are doing). So now we are essentially similiar to OTDM business when capacity is the question: Will nonlinear SPM and XPM set a limit for capacity. The answer is now not so obvious but still yes! Because now the nonlinearity and dispersion will broaden or compress each channel differently also it varies along the fiber for each channel, which limit how close the channel can be placed. But,you may ask, what about soliton? The answer is: Well, the soliton efficiency has not changed compared to DWDM case. We still cannot do better than the NON-Shannon conforming limit.

Now, back to the FM confusion. FM modulates carrier frequency on the RF power. The instanous intensity is not constant. In optics, the equivalent carrier frequency is the wavelength. The confusion is actually quite consistent with other stuff being said, again due to lack of basic training.

re: Physicists Find Fiber's LimitI think I can safely say I have a working as well as theoretical knowledge of FM, having worked on wireless communication systems. In any case, FM signals do not violate my statement about band limitation: a pure phase signal is guaranteed to have out of band power. FM is no exception. One can try to suppress out of band power but cannot get rid of it. For a refresher, see Proakis P.215-217.

Adding together independent FM signals which are spaced close enough together to have high spectral efficiency (ie no interchannel spacings) is also guaranteed to generate large amplitude modulations.

I think I don't need to respond to the bizzare statement about needing square law detectors to obtain amplitude fluctuations from a beating signal. Adding nontrivial phase only signals together produce non-phase-only signals, namely signals with amplitude fluctuations. As these propagate down the fiber, these will generate CPM in the usual way.

The coherent subband systems that I have seen touted don't have anywhere near the spectral efficiencies corresponding to the constellations used. Spectral efficiency = bit rate /total bandwidth (*including* interchannel spacings). The large constellations are meaningless - you simply have to look at the delivered total data rates and the total bandwidths counting channel spacing. One can put arbitrary complicated signals on channels spaced far apart - that will do nothing to improve the true spectral efficiency.

re: Physicists Find Fiber's LimitAt this point, your posting seems to have turned into gobbleydegook, so I find it hard to respond. The capacity estimate in the paper is obtained as usual by bounding mutual entropies, following general statement of Shannon capacity for the channel. Strictly speaking, a bound is computed based on a WGN process at the input, which inherently contains amplitude and phase fluctuations.

re: Physicists Find Fiber's LimitIn other word, meaningless results. None of sources you mentioned are updated and are for a single channel only. Without considering chirp it is meaningless.

re: Physicists Find Fiber's LimitYou said: The comments in the Kahn and Ho article about phase modulation schemes getting rid of amplitude fluctuations (and hence CPM) are not quite accurate. The reason is somewhat subtle: to do that with a WDM system, you would have to do two things: (1) build a *bandlimited* phase only signal. This cannot be done (except for the trivial case of a constant tone).

Answer: Wrong, it is done every day, all day long: it is called the FM band on your radio...each of the signals on the radio is band limited...wonder how they overcame your math problem? Think a bit...

You also said: Further, one * cannot * enforce the phase only behaviour by designing individual channels to be phase only - ever hear of beating? adding two phase only signals in general will produce amplitude fluctuations.

Answer: Wrong again. Well, first, to be accurate, two phase only signals would generate a sum and difference signal (beating) on a square law detector, but there is no square law detector (at least in the fiber) here.

Next, even if there was, you assume a coherent relation between the modulation signal sources. Don't.

You are correct in that nonlinearity can cause PM to AM conversion...but less PM means less AM, so that is the approach: multiple subchannels: just like on the FM radio.

So in summary, multiple FDM complex modulated signals, each with independent coding, independent sources of modulation, on each of multiple wavelengths, none of which are coherent to each other, but each of which is detected coherently, through an optical filter, on a balanced detector. Subchannels filtered and processed digitally on low cost ICs.

It's in field trials with a major telecom customer today...I guess they forgot to see if it was working...

re: Physicists Find Fiber's LimitThe result is not by me,.. standard results publsihed by Elraife et al in JLT '91 Jan {?] I guess on limitation of transmission distance by GVD etc....I verified it. Also you can verify the same from 'Optical Networking" by Bonnoni, where there is a contribution from Enrico Forestari, on it with a different method. No chirp is assumed. Also you can see "Coherent Communication" by Betti etal, that book conatins a lot of results proving the superiority of IMDD system in transmission related impairment.

re: Physicists Find Fiber's LimitWell, in your last posting, there are many mistakes which I don't want to point out.

But if you were true [ which is not true either], then you have used Shanon's theorem wrongly. Your SNR has to be with respect to based-band signal in this case. Which means, your SNR calculation assumes amplitude modulation if I go by your formula!!! And you are finding amplitude fluctuation from beating!!!! You have to calculate its magnitude after filtering the respective channel..

Secondly, \eta calculation assumes the separation of dispersion and non-linearity operator. No matter whatever be the approach, either by analytical IST method or numerical SSF , that is always the inherent assumption and so is your calculation. I hope this point is pretty clear. Non-commutation of both the operator is the starting point.. .. .. Further, as far the paper go, I have strong feeling that Authors may be good theoretician but surely venturing this field for a recent time. Otherwise, they would have thought of more meaningful way of getting amplitude fluctuation to fit into the Shanon's formula. -Calpole

re: Physicists Find Fiber's LimitTo be more specific, GVD is there. But that's not what calpole is complaining.

Back to the phase modulation simulation results, do you include negative chirp in you simulation, calpole? The numbers do not look realistic to me. Could you be more specific about the conditions you used? Any consideration as to channel bandwidth etc?

re: Physicists Find Fiber's LimitVacuum Polarization (Physics) A process in which an electromagnetic field gives rise to virtual electron-positron pairs that effectively alter the distribution of charges and currents that generated the original electromagnetic field. (Human Biology) A process in which a childishly trivial posting on an electronic bulletin board generates a virtual intellectual gradient, lowering the average IQ of the board, resulting in a waste of time for everyone.

re: Physicists Find Fiber's LimitYour questions have already been answered, if you had chosen to read my post carefully.

The NLS has both dispersion and nonlinearity in it simultaneously. I have no idea what you mean by decoupling dispersion and nonlinearity. If there were only nonlinearity, or only dispersion, the evolution equations are trivial. I would have thought that this was adequately elementary.

I think that the basic misunderstanding that you have stems from a fictional notion of a phase only (you call it angle only) signal in a WDM context. I will include below the passage from my last post that explains why this is in error. I suggest you perform the following exercise for yourself. Construct your favourite signal source (has to be WDM, and has to be information-bearing). If one allows for real time cooperation between channels, it should be mathematically possible (though of no practical interest) to construct an *approximately* phase only (or angle only) electric field even with many channels. Propagate your equation beyond a dispersion length. Lo and behold! You will find that amplitude fluctuations have appeared. For system lengths significantly longer than the dispersion length, which is what is treated in the paper, one can pretty much neglect these initial transients.

-------------------

From before:

The comments in the Kahn and Ho article about phase modulation schemes getting rid of amplitude fluctuations (and hence CPM) are not quite accurate. The reason is somewhat subtle: to do that with a WDM system, you would have to do two things: (1) build a *bandlimited* phase only signal. This cannot be done (except for the trivial case of a constant tone). I won't burden you with the necessary math - try it our for yourself; you'll find that trying to twist the phase of a sine wave to make it carry information will inevitably put power out of band. (2) Further, one * cannot * enforce the phase only behaviour by designing individual channels to be phase only - ever hear of beating? adding two phase only signals in general will produce amplitude fluctuations. In principle, one could make all the WDM channels cooperate so that the * joint * signal had a constant phase (up to a small out of band leakage) initially. However, that would require electronic bandwidths of THz (if we had that we wouldn't be discussing WDM in the first case. Finally, even if you started with a phase only signal, dispersion would eventually convert phase fluctuations to amplitude fluctuations. For these reasons, you cannot escape amplitude fluctuations and hence CPM. Therefore the comment about eliminating CPM is rather glib. However, assuming that they were the paper reviewers, they voted with their feet by recommending publication of the paper.

re: Physicists Find Fiber's Limit Let me try to help you out a little: You worked with four Nobel Laureates. You have won it five times. You have started six startups, and built seven DWDM systems covered everything from components to costomer care. You have used eight optical PLLs with nine commercial LOs for every ten Terabits. It shows.

Now please get lost in your communication classes, at least until you figure out vacuum polarization in copper.

OT: First, in reality, the Nobel prize is only as good as the person that receives it...the prize by itself does not bestow nobility nor super-intelligence nor ethics. Like most awards, it is half technical and half political.

I have worked for/with several Nobel laureats (four to be exact) in my career, and they ranged from very smart and honorable (earned it and deserved it, poor politicians) to average smart and sneaky (stole their colleagues or students work and called it their own, great politicians).

Sorry, but getting the Nobel prize is not the be-all, and end-all proof of intelligence. LU is a loser company, period. If they are still at LU, they are losers...all the more because they are there with all their great credentials, etc. Probably what we call "walking dead", or "retired-in-place (RIP)". I know one Nobel prize winner (one of the ones I worked for many years ago) pimping a start-up for options and cash...letting his name (and the prize) be associated with a flakey VC-run spin-flip operation.

Now, as to nobody having done a good optical LO, you only confirm my assertion that you do not read.

re: Physicists Find Fiber's LimitThanks for your posting, I guess we must continue to debate without attacking personally..But, there are many things with which, I can not agree on the article...

""" First, you have this discussion about bit rates at fixed eye opening penalties. You probably won't take this well, but the quantity discussed in the article is the channel capacity. This is the maximal possible rate of error free transmission. Using some particular modulation and ECC scheme, one can talk about bit rates and the corresponding BER or other penalty measure. That is more ad hoc than the capacity. Admittedly, the capacity is a theoretical limit than a practical quantity; however, that is the quantity in the paper, not the quantities you want to discuss. It provides a wall that the bit rates for fixed penalties cannot cross (and if you have a good enough coding scheme, like a turbo code, you can make the (bit rate) vs (SNR per bit (EbNo)) curves approximate the capacity limit. Almost by definition, the quantities you are interested in are more derivative (and therefore need transformation) before being compared to channel capacity. """"

>>>>>>Your above assessment is correct. No problem in converging in opinian.

It is true that CPM, FWM build up with system length. This is in fact the effect that leads to the capacity limits discussed in the paper (specifically from CPM). It is just that the buildup is different from that of amplifier noise or other additive forms of noise. In fact, the length dependence is specifically present in the formula for the peak capacity if you care to look (through I0). The peak capacity goes to zero at infinite length. However, the dependence is not a simple inverse relation to distance, and therefore peak rate times length is not a good metric. In fact, the results show that the bit-rate times length metric needs revision for the nonlinear effects to be treated properly.

>>>>>>> Well, here is the problem. The formula of \eta that you have used to assess the SNR due to CPM either in IMDD or coherent system defies the reality. If you talk about angle-modulated systems, CPM affects via following way [1] PM-AM conversion of Modulated Phase generates RIN

[2] This RIN is transferred as CPM to other channel and cause SNR degradation of base-band signal in phase.

Problem with the treatment is that if I consider IMDD system then also your \eta is wrong and if I consider angle-modulated system then also the assessment of \eta is wrong even analytically.

>>>>>>>>>>>>>>>>>>>>>.. >>>>>>>>>>>>>>>>>>.....

I don't know where you got the idea that dispersion is being neglected - the NLS has both dispersion and nonlinearity in it. The dispersion coefficient appears explicitly in the different formulae. The *relevant* bandwidth is in the GHz rather than the THz range, since the discussion is about WDM systems. For the same reason, higher order dispersion can be neglected. Dispersion between channels leads to suppression of distant channels, as also discussed.

>>>>>>>>>>.Here is the problem. You have decoupled Dispersion and Non-linearity . \Detlta \E_{field} term in your expression should be term that depends on dispersion. I don't see it.

Also, even if individual channels are in GHz, since you are considering so many of them, third order dispersion is definietly the most important parameters as \beta_2 will vary accross the channel depending on \beta_3. You have assumed all the channels have equal \beta_2 parameters.

*********************

Also, I don't see where you get the bit about intensity noise: the paper deals explicitly with the E field, which means it deals with coherent communication (amplitude and phase).

>>>>>>>If there is no-Intensity noise how could get an effect of SNR degradation in baseband due to CPM in Angle-modulated systems???

A discussion of Q values in this context is misleading because the noise in question is not Gaussian. If it were, there would not be any discussion. We'd be back to the linear channel case. >>>> OK, though there are some points, I am not diverting the attension ..>>>

The comments in the Kahn and Ho article about phase modulation schemes getting rid of amplitude fluctuations (and hence CPM) are not quite accurate. The reason is somewhat subtle: to do that with a WDM system, you would have to do two things: (1) build a *bandlimited* phase only signal. This cannot be done (except for the trivial case of a constant tone). I won't burden you with the necessary math - try it our for yourself; you'll find that trying to twist the phase of a sine wave to make it carry information will inevitably put power out of band. (2) Further, one * cannot * enforce the phase only behaviour by designing individual channels to be phase only - ever hear of beating? adding two phase only signals in general will produce amplitude fluctuations. In principle, one could make all the WDM channels cooperate so that the * joint * signal had a constant phase (up to a small out of band leakage) initially. However, that would require electronic bandwidths of THz (if we had that we wouldn't be discussing WDM in the first case. Finally, even if you started with a phase only signal, dispersion would eventually convert phase fluctuations to amplitude fluctuations. For these reasons, you cannot escape amplitude fluctuations and hence CPM. Therefore the comment about eliminating CPM is rather glib. However, assuming that they were the paper reviewers, they voted with their feet by recommending publication of the paper.

As for estimating the quantity \eta - (I presume that is that you mean by \eta_c) - analytical estimates are always different from numerical ones. They are approximate, but they are in closed form and give insight that is difficult and inefficient to derive from numerics.

re: Physicists Find Fiber's LimitThanks for your posting, I guess we must continue to debate without attacking personally..But, there are many things with which, I can not agree on the article...

""" First, you have this discussion about bit rates at fixed eye opening penalties. You probably won't take this well, but the quantity discussed in the article is the channel capacity. This is the maximal possible rate of error free transmission. Using some particular modulation and ECC scheme, one can talk about bit rates and the corresponding BER or other penalty measure. That is more ad hoc than the capacity. Admittedly, the capacity is a theoretical limit than a practical quantity; however, that is the quantity in the paper, not the quantities you want to discuss. It provides a wall that the bit rates for fixed penalties cannot cross (and if you have a good enough coding scheme, like a turbo code, you can make the (bit rate) vs (SNR per bit (EbNo)) curves approximate the capacity limit. Almost by definition, the quantities you are interested in are more derivative (and therefore need transformation) before being compared to channel capacity. """"

>>>>>>Your above assessment is correct. No problem in converging in opinian.

It is true that CPM, FWM build up with system length. This is in fact the effect that leads to the capacity limits discussed in the paper (specifically from CPM). It is just that the buildup is different from that of amplifier noise or other additive forms of noise. In fact, the length dependence is specifically present in the formula for the peak capacity if you care to look (through I0). The peak capacity goes to zero at infinite length. However, the dependence is not a simple inverse relation to distance, and therefore peak rate times length is not a good metric. In fact, the results show that the bit-rate times length metric needs revision for the nonlinear effects to be treated properly.

>>>>>>> Well, here is the problem. The formula of \eta that you have used to assess the SNR due to CPM either in IMDD or coherent system defies the reality. If you talk about angle-modulated systems, CPM affects via following way [1] PM-AM conversion of Modulated Phase generates RIN

[2] This RIN is transferred as CPM to other channel and cause SNR degradation of base-band signal in phase.

Problem with the treatment is that if I consider IMDD system then also your \eta is wrong and if I consider angle-modulated system then also the assessment of \eta is wrong even analytically.

>>>>>>>>>>>>>>>>>>>>>.. >>>>>>>>>>>>>>>>>>.....

I don't know where you got the idea that dispersion is being neglected - the NLS has both dispersion and nonlinearity in it. The dispersion coefficient appears explicitly in the different formulae. The *relevant* bandwidth is in the GHz rather than the THz range, since the discussion is about WDM systems. For the same reason, higher order dispersion can be neglected. Dispersion between channels leads to suppression of distant channels, as also discussed.

>>>>>>>>>>.Here is the problem. You have decoupled Dispersion and Non-linearity . \Detlta \E_{field} term in your expression should be term that depends on dispersion. I don't see it.

Also, even if individual channels are in GHz, since you are considering so many of them, third order dispersion is definietly the most important parameters as \beta_2 will vary accross the channel depending on \beta_3. You have assumed all the channels have equal \beta_2 parameters.

*********************

Also, I don't see where you get the bit about intensity noise: the paper deals explicitly with the E field, which means it deals with coherent communication (amplitude and phase).

>>>>>>>If there is no-Intensity noise how could get an effect of SNR degradation in baseband due to CPM in Angle-modulated systems???

A discussion of Q values in this context is misleading because the noise in question is not Gaussian. If it were, there would not be any discussion. We'd be back to the linear channel case. >>>> OK, though there are some points, I am not diverting the attension ..>>>

The comments in the Kahn and Ho article about phase modulation schemes getting rid of amplitude fluctuations (and hence CPM) are not quite accurate. The reason is somewhat subtle: to do that with a WDM system, you would have to do two things: (1) build a *bandlimited* phase only signal. This cannot be done (except for the trivial case of a constant tone). I won't burden you with the necessary math - try it our for yourself; you'll find that trying to twist the phase of a sine wave to make it carry information will inevitably put power out of band. (2) Further, one * cannot * enforce the phase only behaviour by designing individual channels to be phase only - ever hear of beating? adding two phase only signals in general will produce amplitude fluctuations. In principle, one could make all the WDM channels cooperate so that the * joint * signal had a constant phase (up to a small out of band leakage) initially. However, that would require electronic bandwidths of THz (if we had that we wouldn't be discussing WDM in the first case. Finally, even if you started with a phase only signal, dispersion would eventually convert phase fluctuations to amplitude fluctuations. For these reasons, you cannot escape amplitude fluctuations and hence CPM. Therefore the comment about eliminating CPM is rather glib. However, assuming that they were the paper reviewers, they voted with their feet by recommending publication of the paper.

As for estimating the quantity \eta - (I presume that is that you mean by \eta_c) - analytical estimates are always different from numerical ones. They are approximate, but they are in closed form and give insight that is difficult and inefficient to derive from numerics.

re: Physicists Find Fiber's LimitI have read the article already, thank you. I have not read your thesis, however, I have this strange feeling that it wouldn't help me advance my knowledge about the issues at hand.

About your post: let me point out a few things.

First, you have this discussion about bit rates at fixed eye opening penalties. You probably won't take this well, but the quantity discussed in the article is the channel capacity. This is the maximal possible rate of error free transmission. Using some particular modulation and ECC scheme, one can talk about bit rates and the corresponding BER or other penalty measure. That is more ad hoc than the capacity. Admittedly, the capacity is a theoretical limit than a practical quantity; however, that is the quantity in the paper, not the quantities you want to discuss. It provides a wall that the bit rates for fixed penalties cannot cross (and if you have a good enough coding scheme, like a turbo code, you can make the (bit rate) vs (SNR per bit (EbNo)) curves approximate the capacity limit. Almost by definition, the quantities you are interested in are more derivative (and therefore need transformation) before being compared to channel capacity.

It is true that CPM, FWM build up with system length. This is in fact the effect that leads to the capacity limits discussed in the paper (specifically from CPM). It is just that the buildup is different from that of amplifier noise or other additive forms of noise. In fact, the length dependence is specifically present in the formula for the peak capacity if you care to look (through I0). The peak capacity goes to zero at infinite length. However, the dependence is not a simple inverse relation to distance, and therefore peak rate times length is not a good metric. In fact, the results show that the bit-rate times length metric needs revision for the nonlinear effects to be treated properly.

I don't know where you got the idea that dispersion is being neglected - the NLS has both dispersion and nonlinearity in it. The dispersion coefficient appears explicitly in the different formulae. The *relevant* bandwidth is in the GHz rather than the THz range, since the discussion is about WDM systems. For the same reason, higher order dispersion can be neglected. Dispersion between channels leads to suppression of distant channels, as also discussed.

Also, I don't see where you get the bit about intensity noise: the paper deals explicitly with the E field, which means it deals with coherent communication (amplitude and phase).

A discussion of Q values in this context is misleading because the noise in question is not Gaussian. If it were, there would not be any discussion. We'd be back to the linear channel case.

The comments in the Kahn and Ho article about phase modulation schemes getting rid of amplitude fluctuations (and hence CPM) are not quite accurate. The reason is somewhat subtle: to do that with a WDM system, you would have to do two things: (1) build a *bandlimited* phase only signal. This cannot be done (except for the trivial case of a constant tone). I won't burden you with the necessary math - try it our for yourself; you'll find that trying to twist the phase of a sine wave to make it carry information will inevitably put power out of band. (2) Further, one * cannot * enforce the phase only behaviour by designing individual channels to be phase only - ever hear of beating? adding two phase only signals in general will produce amplitude fluctuations. In principle, one could make all the WDM channels cooperate so that the * joint * signal had a constant phase (up to a small out of band leakage) initially. However, that would require electronic bandwidths of THz (if we had that we wouldn't be discussing WDM in the first case. Finally, even if you started with a phase only signal, dispersion would eventually convert phase fluctuations to amplitude fluctuations. For these reasons, you cannot escape amplitude fluctuations and hence CPM. Therefore the comment about eliminating CPM is rather glib. However, assuming that they were the paper reviewers, they voted with their feet by recommending publication of the paper.

As for estimating the quantity \eta - (I presume that is that you mean by \eta_c) - analytical estimates are always different from numerical ones. They are approximate, but they are in closed form and give insight that is difficult and inefficient to derive from numerics.

re: Physicists Find Fiber's LimitWell, I have decided to stop my attack on the article. Let switch over to the new topic as pointed out by ubwdm: Wheather coherent systems hold the key to enhance the capacity in future..

Actually, I started my research on coherent systems as it was very hot till the middle of the last decade. As far as my simulation results reveal, angle-modulated systems suffer much more severely from dispersion and non-linearity. So, bitrate-distance product is always much less for angle-modulated systems. Here is a table of maximum transmission distance at 10Gb/s over SMF-28 with only dispersion. by taking 1dB eye-penalty as the requirement.

NRZ-IMDD----67 Km PSK--------53 Km MSK------47 Km CPFSK---- 40 Km

So, definitely for long-haul and even for medium haul, angle-modulated systems don't seem to have a future simply because of its poorer performance against dispersion and non-linearity.

Howerever, in Fiber-wireless systems, in future, Coherent systems have a bright future for a seamless communication.

re: Physicists Find Fiber's Limit1). I mentioned Nobel prize winner because the other guy claims that only losers are left in Bell Labs. Decent people don't call them losers. Many losers are left in Lucent,true,but it takes a true loser to make a statement such as "only people left there are losers". Please read it again.

2). Look, I am not here to defend the paper. There are actually a few loose connections and I agree with you that some aspects are treated not well in the paper, but the merit of the paper is clear to me. It shows from NLS that nonlinearity sets a capacity limit for a typical fiber(as we knew it for a while) and it actually shows relationship between many variables, some are system metric and some are not. It does not mean you cannot work around the limitations. For example, what if one builds new fibers with alternating linearity coefficient (similiar to alternating dispersion in truewave fiber) or new hollow fibers with exotic cladding? No, the paper does not build real systems for you, nor does it claim to.

[1] How valid is the estimation of \eta_c? It is not as accurate as some of simulations I've seen (maybe you did some of them?) for a given problem, but what's important here are the concepts and qualitative behaviors.

[2]How wise it is to calculate the RIN due to non-linearity without considering dispersion [ Mind it they have used it only for useless pupose ] when author is talking about Tb/s???

The authors assume that dispersion won't help the fiber capacity, which sounds reasonable to me. I will address the phase modulation separately bellow. In case of soliton, it is possible to balance them out, but as I said before, the result is lower than their cases. No, they have not mathematically proven it is true.

[3] @50 Tb/s, third and fourth order dispersion will be very crucial. How can they neglect it in their calculation???

Again, they are under same assumption.

Now, points raised by reviewers: 1) Will coherent phase modulation (I could tell everything about the original concept and the patent, but it is a different story) improve the capacity? Maybe, I am not sure. Would it change discussions in the paper? It centainly would. Why it is ignored? Because coherent modulation is not practical in at least forseable future, not until optical PLL is practical. Lasers work because of coherency, holographic-anything does not work because of the required coherence.

So, the conclusion: the paper presented one of better analysis that relates to today's understanding. It proves one thing for sure: The capacity of a fiber as we know it today has a capacity limit that's much lower than that of Shannon's theory and increasing power would not help. You may not appreciate it because you are just out of school or whatever, but don't attack Nature because it published it. And I don't think you have any evidence that it is pure political.

re: Physicists Find Fiber's LimitI guess we are fighting over an article and even if it is written by a Nobel Lauriet does not gurantee the fact that he will talk sense all time.

Now, look at this: I have pointed out only a few crucial mistakes in the paper. So, far none of you has been able to defend that article, because it has been a sloppy article and now you are defending saying that it has been written by a Nobel Lauriet???? One of the authors of the article should be more ashamed because Nobel Commitee trusted him and now he is out to encash it by throwing any trash that he likes?

Defend the arcticle technically ubwdm. I have just finished my PhD in this field and I know no matter whether that crab is written by a Nobel Lauriet or a big 'Ass', can not be defended technically. If you have courage, answer following questions: [1] How valid is the estimation of \eta_c? [2]How wise it is to calculate the RIN due to non-linearity without considering dispersion [ Mind it they have used it only for useless pupose ] when author is talking about Tb/s??? [3] @50 Tb/s, third and fourth order dispersion will be very crucial. How can they neglect it in their calculation???

Please, don't defend it by saying it is from a Nobel Lauriet. Defend it technically so that I can learn something from the erudite person like you. Again, I will be happy to find that I am mistaken if you can prove it.

re: Physicists Find Fiber's Limit"At least you had the good sense to leave Bell Labs...how long did it take to figure out the only people left there are losers?"

Quite a few Nobel prize winners would be losers because they would all lose to nameless on the net... Just like the authors of this paper.

"If that article was in your honest technical opinion "one of the best" on WDM you have ever read, I can only conclude that you must not read very much!"

That's hardly surprising to anyone here. My statement is "The paper is one of best among tens of thousands published every year".

" Apparently you have not published much either. Kahn and Ho's review called it: "a contribution", after they completely trashed their assumptions and therefore the conclusions based on them. "

And the paper gets published on Nature.

" Oh, by the way...the nonlinearity in Copper comes from several sources..."

As ppm pointed out, you forgot about vacuum polarization, if you ever learned it in your communication classes.

"Guess none of those successful start-ups paid for you...I can guess why..."

You must be really interested in that... Sorry, I won't tell you anything. It is not part of this discussion...

re: Physicists Find Fiber's LimitAt least you had the good sense to leave Bell Labs...how long did it take to figure out the only people left there are losers?

If that article was in your honest technical opinion "one of the best" on WDM you have ever read, I can only conclude that you must not read very much!

Apparently you have not published much either. Kahn and Ho's review called it: "a contribution", after they completely trashed their assumptions and therefore the conclusions based on them.

Hint: That's what we call damnation by feigned praise!

Oh, by the way...the nonlinearity in Copper comes from several sources...point diodes due from poor contacts and twisted wires...line amplifiers...inadequate power supplies...but we managed to find ways around the problems...one at a time...

Finally, most of what we are discussing is not taught in EM class, it is taught in Communication Theory, or Communications Systems Analysis, which you would realize if you had taken any of the courses.

Hint: That's what we call: inadequate education!

Guess none of those successful start-ups paid for you...I can guess why...

re: Physicists Find Fiber's Limit>>>>>>>>>>>>>> 2. " They even don't know, without dispersion, non-linearity can do no harm to either IMDD or Angle modulated system!!!!!"

Comment: Huh, graduated from a graduate course, but need to improve problem solving skills. Why? a). Fiber or waveguide without dispersion for whole spectrum, when the capacity is the question? b). The phase shift of the second order SPM/XPM indeed "does no harm" to an angle or pure phase modulated SIGNAL. But it will HARM an angle modulated SYSTEM because the SYSTEM in question has >>>>>>>>>>>>> Well, I have commented purely on fiber transmission assuming it to be infinite bandwidth system to treat and simplify the problem of non-linearity. Most of the finite-bandwidth system can be modelded as a filter and filters can also cause PM-IM or IM-PM conversion and that way non-linearity can affect the signal quality even if dispersion is absent. But I have made comment pertaining to the assumptions used in the 'Nature's paper. There is no point bringing an well known obvious issue.

3. "With proper dispersion compensation, we can reduce the first order RIN due to non-linear phase , ..."

Comment: Get a clue.

>>>>>Well, this has been estblished in a paper in IEEE-JLT, April-2000 issue.. .. I guess that was a paper on CPFSK system and the impact of fiber non-linearity on it.

>>>>>>>> Sad part of the story about the article in Nature is that its treatment of RIN through \eta parameter is extremely vague. It's too crude to be even 1% truth, and I know it from my past long experince of simulation of NLS and other RIN related stuff. So, I can never digest that story. It was published because it was from Bel-lab, and I can ensure you without the kind politics from the reviewer, such kind of crab can never be published. Since, I had a good respect for Nature, I was disheartened to see a paper which even does not fit into the standard of 3rd graded journal like 'Journal of Optical Communication" from Germany.

re: Physicists Find Fiber's LimitOkey, Okey, you got to love all these half-baked potatoes on the net.

It is impossible to argue on this board. I am not going to correct every statements, but a couple are enough to show their true colors...

1) "Let me teach you something...a Copper wire system is far, far from linear...to get that kind of density (10bps/Hz) requires some real hard work in equalization and FEC...and it is all done with less than 20 dB SNR and in the presence of echo and crosstalk...makes the non-linearities in fiber look like child play..."

Comment: Need better basic training in graduate level EM theory.

2. " They even don't know, without dispersion, non-linearity can do no harm to either IMDD or Angle modulated system!!!!!"

Comment: Huh, graduated from a graduate course, but need to improve problem solving skills. Why? a). Fiber or waveguide without dispersion for whole spectrum, when the capacity is the question? b). The phase shift of the second order SPM/XPM indeed "does no harm" to an angle or pure phase modulated SIGNAL. But it will HARM an angle modulated SYSTEM because the SYSTEM in question has finite bandwidth and has multiple channels. 3. "With proper dispersion compensation, we can reduce the first order RIN due to non-linear phase , ..."

Comment: Get a clue.

It is apparent that many are confused by the paper. The paper is one of best among tens of thousands published every year, most of which indeed are useless. To attack the quality of "Nature" sounds more like sour grape than anything else. The paper gives a good analysis about nonlinear nature of fiber, but not for transmission with electrical or optical regeneration. It is very valuable esp. to those of us who are building long haul, ultra long haul/submarine systems who learned many issues with expensive and time consuming experiments. Those who have done it understand that they are not "fundamental limits" for the SYSTEM, as only a few clueless here claim so.

It's obvious that the paper does not cover the case when DCM used along the fiber reconditions the signal just like it does not cover systems with 2R/3R every 100KM. In real systems signals could be demuxed and optically reshaped to overcome some nonlinear effects. But again, the paper helps us to analyse these issues.

BTW, I left Bell Labs long time ago and have been with a few successful startups. I probably know more about Lucent's failure. I have to say it is absurd and childish to correlate this paper with the fact that Lucent is falling.

re: Physicists Find Fiber's LimitI agree that I have pointed out only the effect of SPM and XPM. With proper dispersion compensation, we can reduce the first order RIN due to non-linear phase , however second-order RIN can not be compensated due to simple nature of sinusoidal addition( a mathematical artifact of RIN expression due to PM-AM).

re: Physicists Find Fiber's LimitDirect quote from Natures reviewers, which you can access online at www.nature.com and registering for free...

"When calculating the effects of CPM, Mitra and Stark have implicitly assumed a modulation technique involving time-varying intensity. It is already known that using a constant-intensity modulation technique, such as phase or frequency modulation, can eliminate CPM. The fibre's refractive index varies slightly with the wavelength of light, which tends to convert phase or frequency modulation to intensity modulation. This wavelength dispersion must be carefully compensated for to maintain constant intensity. If we follow the same calculations as Mitra and Stark, and constant intensity is maintained, then the spectral-efficiency limit should increase with transmitted power, in contrast with their results. In reality, as the power increases, spectral efficiency would eventually be limited by other nonlinear effects, such as four-wave mixing.

As Mitra and Stark point out, nonlinearities such as CPM can be cancelled out, in principle, by using a number of clever tricks. Better optical fibres can also help GÇö for example, hollow fibres with air cores have a reduced nonlinear response. In ordinary optical fibres, light can propagate in two orthogonal polarizations GÇö that is, with electric field lines along two perpendicular directions. A simple way to double spectral efficiency is to send two independent signals with these different polarizations and use polarization-resolved detection. Even without polarization-resolved detection, sending neighbouring signals with perpendicular polarizations is a well-known method to reduce nonlinearities."

One of those "clever tricks" is to use balanced coherent detection...which also allows you to use full IQ modulation...and it cancels first order RIN down to shot noise. OK, so it will not cancel noise cross signal terms...

People have locked external cavity semiconductor lasers for many years...I believe you can buy half way decent equipment off the shelf....data I have seen approaches the best analog RF PLO results...

Anyway, last word is: Mitra and Stark are wrong, CPM is not a fundamental limit to the bandwidth of fiber, and people have done much, much better than 3 bits/hz over fiber...and routinely achieve much better than 20 dB SNR (on analog subchannels), and do so over long distances, and through EDFAs...in the field, today.

With the misguided technical analysis they are getting from the likes of Mitra and Stark, who probably represent the best they have, no wonder LU is headed for the dumpster...

re: Physicists Find Fiber's Limit"They even don't know, without dispersion, non-linearity can do no harm to either IMDD or Angle modulated system!!!!!"

I think your statement is only true for SPM/XPM but FWM and the scattering effects can deplete the signal. Moreover with no dispersion the signals do not "walk away" from each other and FWM effects (for example) are amplified.

re: Physicists Find Fiber's LimitNow, I have read the Nature' arcticle.

Ya, now I am even more convinced that it's a school physics calculation with a bunch of school physics approximations.

They talk about RIN (relative intensity noise) with a vaguely defined term \eta_c. Putting that value in Shanon's capacity theorem without reading any paper on RIN due to fiber non-linearity is quite stupid thing, and they did it. They even don't know, without dispersion, non-linearity can do no harm to either IMDD or Angle modulated system!!!!! It all happens because of PM-IM or IM-PM conversion!!! Where is this in their calculation!!! Then they would have arrived at the right equation.

I don't want to point out other mistakes, which are useless. If Nature continues to publish such articles, soon or later it will be another light-reading magazine.

re: Physicists Find Fiber's LimitFirst of all, we are talking about theoretical limit. So, at the begining I have told that I assume receiver is ready for 100Tb/s . 200 photon per bit is nearly equal to 15dBm @100 Tb/s for a receiver sensitivity of 10^-9 PE.

Quantum limit of receiver may not be the problem for 100 Tb/s transmission question is whether we can have that broad-band receiver and sunch a modulator or any OTDM technique that can give 100Tb/s transmission.

I cited the example of 1 micro-meter to illustrate the theoretical fact that at that small distance dispersion and non-linear effect will be negligible. Please, go by its intension.

re: Physicists Find Fiber's LimitThe word 'peak capacity' can arise if there is some optimization curve in multidimensional plot where fiber length and physical parameters are treated as independent parameters and we agree that accepted received signal performance follows certain requirements like 1 dB eye-closure or below 1dB receiver sensitivity penalty @10^-12 BER or any other SONET SR or IR requirement. Thanks to the strong interplay between signal format, dispersion and non-linearity, we can always get a value of peak bitrate but only for a certain distance. If distance is also plotted as an independent parameter and someone says that he has achieved a peak value for bit-rate from the plot, the very concept of it is quite unacceptable because of the nature of Non-linear Schodinger Euqation where the space variable 'z' (the length) appear as a first-order derivative as a consequence of paraxial approximation. Variance SPM, XPM and FWM power are all propotional to the distance and when any non-liear phase affects on IM systems through PM-IM conversion, varinace of Relative Intensity Noise becomes propotional to distance for a smaller value of total-dispersion and varies as a sine of distance for more accurate approximation. In contrast to that , Fiber filter function has an exponent that is always propotional to 'z'. Since, 'Q' value is inversely dependent on the variance , Log(BER) plot for a given receiver power is inversely propotional to the distance if the RIN due to fiber impairment is more dominant than the receiver noise.

Now, if we search for a bit-rate optimization keeping the constraint of 1 dB eye-closure or 14dB 'Q' as accepted signal quality, optimization of bit-rate with respect to distance is meaningless because of very mathematical nature of NLS. That's why it is more important to talk about Bit-rate distance product than bit-rate only for capacity. This has been well known fact since the days of electrical transmission theory.

re: Physicists Find Fiber's LimitI see - you think that the nonlinear crosstalk is the limiting factor for holographic storage as well (as opposed to simple linear crosstalk which comes from say finite thickness of the medium and therefore finite width of the diffraction peak). That's quite interesting.

In terms of index saturation, you are right that the output SNR can be improved by increasing the playback power - what I was assuming is that due to the noisiness of the * writing * process, a minimum index change is required to write an image, so if the total index change was finite that would limit the number of images. However, I can imagine that the inter image nonlinear crosstalk is a dominant effect ...

re: Physicists Find Fiber's LimitOK, we've all had a good go at this so let's wrap it up.

Firstly let's look at photons. Optical receivers need to detect the incoming photons and turn them into electrons to allow us to use the data. One extreme is that you could use a single photon to represent a bit - this could work, but in the presence of noise the number of photons that you need for each bit rises.

I've seen receivers designed that operate at 20 photons per bit, but more realistic designs operate at 200 photons per bit.

That relates to the optical power, and so drives the minimum power that you need in a fibre. The example given earlier of sending 100 Tbit/s over 1 um is a little spurious, given the enourmous optical power you would need to detect the bits at the receiver.

This is only lightly related to the information density that you can achieve. For a long haul fibre optic system, that has some optical amplifiers and some spans of fibre, then I believe the crew from Bell Labs. Some of the limits are really fundamental - like photons, and some are engineering limits to a particular system design.

I think the real fundamental limit is how many publications like lightreading will publish press releases, without reading or understanding the material. Until lightreading changes its business plan and stops needing to get as many eyeballs, and therefore stops publishing the most controversial stories that it can get away with, then we will continue to have debates on these boards.

C'mon lightreading, time to scape up a story about something really heretical, and get more people reading your site...

re: Physicists Find Fiber's LimitRead the article in Nature first. A formula is given for the peak capacity value, depending on the system parameters. The dependence on system length is logarithmic (a reasonably weak dependence). It also tells you that bit rate times distance is not a good metric.

BTW, the article is entitled "nonlinear limits" not "fundamental limits".

re: Physicists Find Fiber's Limit I have read all the messages, but not the original article on Nature. Really impressed about the knowledge of everyone.

IMHO, whatever claimed as the fundamental limit of the fiber is a mistake. Certainly ways can be invented to mitigate the nonlinear effect on the fiber, using different modulation scheme at the source and a more sensitive receiver coupled with processing gain can reduce the SNR required for the channel.

The article in Nature might just be addressing the current fiber with its optical properties and probably assumed some kind of modulation scheme will be used, and the sensitivity of the receiver diode. Some clever math tricks then derived the 3b/Hz number. Definitely a valid exercise.

To claim that as the fundamental limit of fiber capacity is just wrong.

re: Physicists Find Fiber's LimitWell, talking about the capacity without distance has no meaning. We can always transmit 100Tb/s over a micro-meter if transmitter and receiver is available for 100Tb/s.

All capacity limiting factors like optical noise, dispersion and non-linearity are propotional [ or exponentially varies] with the transmission distance if dispersion and non-linearity has weak coupling. Hence, such school physics calculation is useless without a bit-rate-distance product.

re: Physicists Find Fiber's Limit"One very effective way to combat fiber nonlinearities is to break the channel into n-subchannels".

Huh, a real copper comm guy. Why don't you just spell out DMT? That way you can maybe tell us a thing or two about ADSL?

Let me just say that if you get a textbook, you will find out NLS is well, nonlinear. The Maxwell's equation for a conductor or the ABCD parameters for a twisted pair is however linear. Surprised?

DMT won't help fiber much. SPM does decrease as "sub-channel" gets smaller. But XPM is increased. In case of DWDM, it is hard to conclude as a general rule (Depending on optical power density, etc), but DMT won't increase capacity. Believe it or not, the Bell Labs authors do know a few things about fiber communications... enough to publish it on "Nature".

re: Physicists Find Fiber's LimitWell, it is sweltering hot here in SilliValley, and it must be affecting my mind...so rather than just sweat and waste time, I am going to type and waste time.

I will give some hints:

1) One very effective way to combat fiber nonlinearities is to break the channel into n-subchannels...now in general, for each subchannel in the channel, there is an optimal bandwidth...which among other things is a direct function of the modulation and the detection method. Each of these subchannels is then made piecewise (much more) linear...not perfectly linear mind you, but significantly better...

2) Generalized optical IQ modulation has been done quite nicely for many years...in fact so has general IQ modulation and balanced coherent detection. At least three companies I am aware of field such equipment today and have for many years (only one has not passed field trials yet): Harmonic, which uses complex modulation, Synchronous which uses complex modulation and balanced detection, and the third of which uses all of the above and coherent detection.

The article may be correct based on the assumptions it makes, and how they choose to attack the problem, but as my mentor told me, always remember how you spell assume...

re: Physicists Find Fiber's LimitIn the recent announcements at OFC 2001 (see http://www.lightreading.com/do... ), Alcatel and NEC reached 0.8b/s/Hz. (40 Gb/s signals, 50 GHz spacing)

re: Physicists Find Fiber's LimitA hologram - spatial fringes with certain frequency. You can think it as ITU channel in DWDM. A nonlinear media acts like RF mixer. As the number of holograms/ITU channels in a fiber increases, signals mixe with themselves (SPM) and with each other (XPM). The result is that noise will increase squarely with frequency range, or number of channels (and distance). So noise density (/per Hz) will increase with formation (bit per Hz). Initially, system with finite power budget will be limited by linear noise (transmitter/receiver noise). When more information or optical power is pumped into system, this cocktail party noise is the limit. Amplifier noise is also partly nonlinear.

And the most significant of all, it is this cocktail party noise that violates Shannan theory, other noise don't. The (Bits/per Hz) is not really a complete measure for a nonlinear media.

Likewise, in case of holographic memory, index saturation is not the killer since you could always increase playback power, at least theoretically. "Cocktail party Noise" is.

BTW, ture, there are ways to combat nonlinear effect. But how many bit you can get per soliton?

As to 3bps/Hz, I think it comes from OTDM - record is about 15 fs pulse in 200 nm. about 2.5 bps/Hz.

But, if you add bi-di and polarization, you can get 10 bps/Hz per link for a short fiber.

re: Physicists Find Fiber's LimitThe examples you cite are not so much evidence that "we knew it all along," rather, they offer evidence to indicate that false conclusions can be reached by misapplying laws of physics. After it can be shown that the conclusions are false, it is actually a frequent occurrence that rethinking and reapplying physical laws and theories proves consistency after all, which is a far cry from claiming that "we knew it all the time." People who make such claims are typically suffering from bruised egos, and are looking for a fig leaf of credibility to hide behind.

re: Physicists Find Fiber's LimitAfter carefully reading all the postings, I have to say ownstock has a valid point. Some years ago a very respected physicist got a Nobel Prize for the theory of superconductivity. The theory predicted that it is impossible to have superconductivity at room temperature. Then again a few years ago, it was discovered otherwise. The same Nobel laureate now claims it is indeed very natural to have superconduction at room temperature. In fact he insists his original theory predicted it if one would have just digged little deeper. Optical gyroscope was initially were believed to be impossible because it violated the theory of general relativity. After it worked, they claim it works actually in support of general relativity.

The assumption of the paper published was nonlinearity is a fact of life in optical fiber. Wrong! What if through some clever scheme (digital or analog) nonlinratities could be suppressed. Then again if that happens, the physicists would say, we knew it all along.

re: Physicists Find Fiber's LimitAfter reading all the posts, (but have not read the Nature article), it seems that todays advanced DWDM based systems are operating at best 0.4b/s/Hz...(calculated from a 10Gb/s OOK modulated signal operating in a 25GHz channel spacing using optimal matched filtering for baseband filtering). This is still a far cry from the 3b/s/Hz mentioned in the Nature article. But to go to higher throughputs will require somehting extraordinary...

Lets say we start with a 16-ary multi level PAM instead OOK (this would be difficult with current DWDM lasers). This would assign a 4 bits/symbol, this would increase the throughput to 1.6b/s/Hz, but this type of signalling is poor because all the quantization levels are in the 'real' amplitude plane; you could not transmit this signal too far before AWGN and any optical ASE would start intefering with decision thresholds. We need to use the phase plane to spread out the quantizing radii so that better Eb/No at the receiver, this is how the V.22 on up to V.90 modems were able to transmit greater BW's over 4 kHz of copper BW. The same holds true for HFC cable systems sending 256-QAM in each 6 MHz channel space.

The problem is that no-one (that I know of) manufactures or has an equivalent light based IQ modulator (that would operate at 193.1THz for example).

Even if you could build something like this, then the non-linear effects (PMD, chromatic and time disersion) will start to interfere with demodulation, so then you would need to adaptively equalize these non-linearities with technology that so far does not exist...not to mention we'll probably need FEC over all of this!! This is very hard to do at 100Mb/sec let alone over 10Gb/s...only time and technology will tell.

re: Physicists Find Fiber's Limit20 years ago John Pierce published some papers on the photon counting channel and derived the quantum limit. I think, if my memory serves me, it's about 0.8 photons per bit. The 3 bits/Hz seems odd, unless it is based on a certain modulation scheme. We'll know the real answer if someone builds a good optical phase locked loop...

talking of peer-reviewed papers, you might want to look one up. About a year ago, Desurvire published a nice paper in an IEEE journal. It talked about the ultimate limit of an optically amplified system - it compared and contrasted lumped and distributed amplified systems.

So just looking at the noise from amplifiers in long haul systems, the limits he calculated were 3 bit/s/Hz for distributed amplifier systems and 6 bit/s/Hz for lumped systems. Which comes very close to the Bell Labs results, without including non-linearities.

All of which is a very long way from the 0.1 bit/s/Hz we are using today.

re: Physicists Find Fiber's LimitThat's interesting - I've thought a little bit about that problem ... I presume you are referring to the nonlinearity having to do with the refractive index change saturating after writing a certain number of holograms. I have a vague recollection that the maximum delta(n)'s are of the order of a fraction of a percent.

re: Physicists Find Fiber's LimitWell, ownstock is completely wrong. His reaction is typical of many DWDM beginers in some startups I met last years though.

To achieve 3 bps/Hz for a sigle 50Ghz channel is not difficult. Even 10 bps/Hz is possible in the lab for a few spool of fibers. But try it for 100+ channels for a few thousand KM transmissions, then you will start to appeciate the laws of physics.

This reminds me that when I did my disertation many years ago, I analysed the capacity of holographical memory with similiar mathematical method. The established theory at time predicted that a 1cmX1cmX1cm LiNbO3 could hold the library of Congress, but reality was millions times under. The cause: nonlinearity.

re: Physicists Find Fiber's LimitThere are plenty of IEEE papers with 30 pages of unnecessary theorems and lemmas followed by a non-result. While Nature is not a traditional communication theory journal, it is as valid a forum as any to report a new way of computing information capacities in the presence of nonlinearities. Information theory was to some extent born whole, there are few fundamentally new results in any case after Shannon's original publications.

I have failed to see a single valid technical point that you have raised. I sympathise with your suspicion of the ivory tower, but I am afraid that the IEEE and other journals are as full of unnecessarily narrow publications, whether from academics or not. Apart from Turbo and LDPC codes (the latter being already a rediscovery), there has been little over the last couple decades that constitutes basic advances in understanding.

Let me point out something simple. You brought up a 10bit/s/Hz as a number. At 20dB SNR, which you also mention, the Shannon formula for a linear channel only gives you 7bits or so (log2(100)=7 approx). There are inconsistencies in your thinking even for a linear channel.

The limits in question are quite real. As for specifying parameter values, that is clearly inescapeable; this is not the speed of light in vacuum or the gravitational constant that is being determined. However, an estimate for realistic parameter values is adequately valuable. The same issues arise in predicting limits for semiconductor memory chips, for example. The world is imperfect: one has to start somewhere.

First, there is a BIG difference between writing for a peer reviewed journal, and a trade publication...they are two very different things.

Something like an IEEE or OSA technical journal is the first, and LR or Time is the latter (for example).

JMHO, but Nature is NOT the first place anyone of caliber in communications would think to publish. OTOH it would be an ideal place to publish a supposedly "fundamental limit" in fiber optics.

Precisely because they knew by going there it would not go through a tough and thorough peer review, and/or the editors would tolerate their combination of hype-title and "let's pretend it is this way" problem constraints. Sophistry.

My effort is not intended to confuse, but rather to expose the effort on the part of others to confuse / spin / hype / etc.

I have given (more than) enough information for those with technical expertise in the field of communication theory and/or fiber optics to understand...

From my limited knowledge of comm sys what you say is true for a "memoryless, gaussian channel" for a copper local loop. This efficiency of modulation is fundamentally correlated with the channel noise characteristics, which in case of fiber are very different from the copper.

re: Physicists Find Fiber's Limitownstock, why don't you write a paper in a peer reviewed trade publication negating their findings. Hiding behind LR's message board to confuse the readers doesnot demonstrate your true knowledge. It only justifies your vision to confuse everyone.

re: Physicists Find Fiber's LimitReiterate: If you set up the wrong constraints, you will get a wrong answer...because of that, the claim of deriving fundamental limit is just plain WRONG!

The real issue is there are efficient brute force (aka easy and well known) ways to minimize the nonlinearities in fiber that they did not even consider...and to achieve well over 3 bps/Hz...so their paper is not worth the pulp it was printed on!

Sorry to say this is a typical ivory tower, tunnel vision paper...hyped to the max...designed to derive a clever (but very wrong) answer...

re: Physicists Find Fiber's LimitAll the effects you mention (Echoes, crosstalk, need to equalize) are present in linear systems. The fact that it is difficult to achieve the capacity of a linear channel does not speak to the capacity itself.

FEC does not distinguish linear from nonlinear channels. To get close to capacity you certainly need error correction in any system.

All communication systems have nonlinearities. Even vacuum has some, theoretically. The real question is, to take the nonlinear effects into account in a given system with given parameters. *Long haul* optical communications unfortunately suffer from severe nonlinear effects. These are well known; what has not been understood before is how to estimate the capacity limitations from the nonlinear effects.

Of course, if you take a short piece of optical fibre, you don't see the nonlinear effects at issue here: so you have to be specific about system length, etc. If you take a few meters of fibre, nonlinear effects are pretty much completely negligible. If you were to intersperse repeaters with very short spans of fibre, the capacity limits would approach that of a linear system. Of course, this is not economically feasible.

If you read the original article carefully, which is in the context of long haul optical communications, the relevant questions are discussed.

Let me teach you something...a Copper wire system is far, far from linear...to get that kind of density (10bps/Hz) requires some real hard work in equalization and FEC...and it is all done with less than 20 dB SNR and in the presence of echo and crosstalk...makes the non-linearities in fiber look like child play...

Just shows that you should not go to wideband digital OOK signals...

There are a couple of companies out there that are utilizing just this kind of technology (analog optical carrier and exotic modulation), so that if scaled, it would far surpass the figures sited in the article...and doing it in fiber...with greatly REDUCED nonlinear effects...

At least one is in field trial with a major carrier.

re: Physicists Find Fiber's LimitI think anyone with FDM analog technology could do it, Kestrel comes to mind...there are a couple of others...don't know if Harmonic is doing it today, but they do have the technology...

Basically anyone putting RF carriers down fiber...that is the whole HFC market...

re: Physicists Find Fiber's LimitCapacity of a channel is not set by the modem: the modulater/demodulator is useful *upto* the basic channel capacity. A 10bits/s/Hz (or for that matter 10bits/s/Hz) modem is fine over a a linear channel like copper wire, say - since those channels can support high bit rates. The point is that nonlinearities limit the capacity of optical fiber to significantly smaller values than the linear channels traditionally used in telecommunications. The capacity of a 10 bit modem attached to a 3 bit channel is still 3 bits ...

I don't post here, just thought I should point out the conceptual error in the last message.

re: Physicists Find Fiber's LimitLR: Far from calculating a fundamantal limit, as you imply in your banner, these guys calculate a limiting case...and not well at that. Consider their assumption of an information density of only 3 bits/Hz...a common analog modem can achieve 10 bits/Hz...

Bottom line: There are much more efficient ways of transmitting information over fiber than commonly employed today. DWDM/OOK is just plain wasteful of bandwidth...

I would however be concerned about the need for more (unlit) fiber in the future...demand will stabilize in the face of high bandwidth growth, as people figure out how to stuff more into a single fiber...

re: Physicists Find Fiber's LimitWhat is a "molecular photon?" Is it something similar to excimer (perhaps keeping the molecule intact yet giving out photon)? What wavelength range are you talking here?

Even math and physics no longer works. Great.

The proof I supplied for applying the central

limit theorem is perfectly valid at any given

time. Having different carriers makes no

difference. Adding a separate phase to each

of N random phases still leaves those phases

random. Proof: If phi_n are uniformly

i.i.d. distributed, so are phi_n+n*omega*t.

As for the NLS, it does not require

quasimonochromatic fields. The E^2 term in

the dielectric constant is the total field

intensity, not any spectral density.

Gosh, too many textbooks will now have to be

rewritten ... or maybe not (!)

Where did you get that idea? Have you ever seen

n(w) = n0(w) + n1 * (E*conj(E))

?

WDM implies frequency differences in the base carriers. So you cannot make the assertion that WDM with phase modulation tends to Gaussian anything. FDM is ultra-WDM. You cannot ignore the frequency differences of the subchannels, even for a single wavelength.

Even if you did, most fiber NL effects scale non-linearly with power spectral density of the source (not total optical power)...so when the effective spectral density is greatly reduced, as is the case here, the NL effects are also significantly reduced...

you mentioned L.G. Kazovsky's paper and not

Hajimiri's.

The reference: The Design of CMOS radio-frequency

integrated circuits, by Thomas H. Lee of Stanford.

if I were you. Following Mark Kac in his famous

adage, "be wise and discretize", and you don't

have to worry too much about those mathematical

subtleties, it is taken care of automatically

for you ...

phase only signals producing amplitude noise.

I would have thought that was elementary. Oh

well.

About solitons, I agree with you that spectral

efficiencies of soliton systems are actually

pretty low, significantly less than 1bit/s/Hz,

because you have to keep the solitons apart

by a sufficiently long time slot. I presume

that at least theoretically one could use so

called multi-solitons to get the spectral

efficiencies up and get closer to a bit - but

then with the complexities of a WDM system to

deal with, I have my suspicions that even

multi-solitons won't go very high with

spectral efficiencies either. I think solitons

may have other merits, but they are not the

road to very high spectral efficiencies.

a sufficiently * narrow * total bandwidth, you

can get spectral efficiencies close to

a linear channel, because it is the interplay

between nonlinearities and dispersion that

causes problems. One way of looking at

the problem is, compute the nonlinear

length and the dispersion length. If one

of these is much longer than the other

one, then you are either in the pure

SPM or pure dispersion limit: in either

of those cases, you'll be back to the linear

channel formula for spectral efficiencies.

To take an extreme example just for pedagogical

purposes, if you stuck a bunch of audio

bandwidth channels side by side, in fiber,

covering a * small * total bandwidth, say

1GHz, I have no doubt that you can get

spectral efficiencies predicted by the linear

SNR, as long as you are not killed by the

phase noise generated by nonlinear mixing

of amplifier ASE and signal (which will

happen for long enough systems and will take

away a factor of two).

* However * the spectral efficiency when a very

broad bandwidth is being used, in a WDM system,

it is a very different story. That is where the

paper applies: to consider theoretical limits

to the fiber, you really have to excite the

whole allowable bandwidth.

Of the systems you refer to, please quote:

(1) total data rate

(2) total bandwidth (*including channel spacing*)

If (1)/(2) is significantly large, my prediction

is that (2) is comparatively small to the

total optical bandwidth.

Finally, here is a simple proof for you that

what the Kahn and Ho say about getting rid of

CPM using phase modulation is not really

correct for WDM systems: ubwdm has by now

pointed this out multiple times: suppose

you * did * produce a number of phase only

signals exp[i phi_n(t)] which carry

information. Now consider any instant of time,

and consider the total complex amplitude

at a given time:

A(t) = Sum_n exp[i phi_n(t)]

Since the signals are information bearing, at

any instant of time phi_n(t) are random.

Therefore, by applying the law of large numbers,

A(t) tends to a complex Gaussian distribution

with amplitude and phase fluctuations as

the number of WDM channels grow large.

This leads to CPM, and for large enough total

bandwidths, long enough fibers, etc, will

destroy the spectral efficiency compared to

the linear channel. As far as I am concerned,

that is the message of this paper ...

Note that you do not escape the problems by

dividing a very wide band into very narrow

channels, because the CPM seen by a given

channel will not depend on its own bandwidth.

Therefore, it is sort of irrelevant whether

you have sharp filters at your output or not.

you may need that to * get * to the allowed

(nonlinear) limit because that will require

coherent detection (otherwise you lose phase).

Unless, as ubwdm points out, you use tdm.

GVD and fiber-nonlinearity can not be simply

determined by the use of common theoretical techniques in wireless..like

assumimg Tikanov distrivution of phase error etc..

..Interestingly, no good dynamic theory exists for

OPLL in presence of ISI due to

GVD and non-linearity..(

I mean starting from the fundamental

assumptions of Eto calculus etc ..)except a few standard

old papers by L.G.Kazovsky..

I guess, PPM and UBWDM will do us a favor,

by providing a very good dynmic theory of

OPLL locking, in presence of phase noise

due to GVD and non-linearity..Let do

complete cooking than a half-baked potatos..

..Since, I am not that good theory,

I couldn't solve the problem, I hope

PPM will take the challenge..I swear

it's an amazingly good problem on eto calculus..

-Calpole

The channels (as seen pre-PLL) do overlap due to some spectral spreading, even after filtering, but this is perfectly allowable, so long as the data that emerges out of the subchannel in-lock has an acceptable error rate, and the time to achieve lock is also acceptable. Note the filtering is electrical, not optical, so can be very sharp and narrow.

Since each of the channels can be treated almost independently (save for some channel spacing), they can easily be tailored for the local dispersion slope. This can be done using adaptive algorithms commonly found in low cost MODEM (signal processing) chips.

Although the overall spectral density of the commercial equipment from each of these companies is not 10 bps/Hz, it can be significantly above 3 bps/Hz.

The fact that this type of system was not even discussed is the reason they had to go to Nature to get press...the general approach (to high spectral density data) is fairly common knowledge, and has been done (some might say over done!) in the relevant journals...

His ignorance was as remarkable as his knowledge. Of contemporary literature, philosophy and politics he appeared to know next to nothing. Upon my quoting Thomas Carlyle, he inquired in the naivest way who he might be and what he had done. My surprise reached a climax, however, when I found incidentally that he was ignorant of the Copernican Theory and of the composition of the Solar System. That any civilized human being in this nineteenth century should not be aware that the earth travelled round the sun appeared to me to be such an extraordinary fact that I could hardly realize it.

"You appear to be astonished," he said, smiling at my expression of surprise. "Now that I do know it I shall do my best to forget it."

"To forget it!"

"You see," he explained, I consider that a man's brain originally is like a little empty attic, and you have to stock it with such furniture as you choose. A fool takes in all the lumber of every sort that he comes across, so that the knowledge which might be useful to him gets crowded out, or at best is jumbled up with a lot of other things, so that he has a difficulty in laying his hands upon it. Now the skillful workman is very careful indeed as to what he takes into his brain-attic. He will have nothing but the tools which may help him in doing his work, but of these he has a large assortment, and all in the most perfect order. It is a mistake to think that that little room has elastic walls and can distend to any extent. Depend upon it there comes a time when for every addition of knowledge you forget something that you knew before. It is of the highest importance, therefore, not to have useless facts elbowing out the useful ones."

"But the Solar System!" I protested.

"What the deuce is it to me?" he interrupted impatiently: "you say that we go round the sun. If we went round the moon it would not make a pennyworth of difference to me or to my work."

km

what do you think of CORV products in the area??

thanks in advance.

km

1). FM has nothing to do with phase modulation

in question.

The phase modulation in question as raised by

reviewers is a modulation on E field, or a

phasor as called in Goodman's. The intensity of

a phasor (E*conj(E)) is then always constant.

Take a phasor into NLS, you will see SPM and

XPM does not set a limit for its propagation,

as the reviewers pointed out.

Now let's talk about more realistic multi

channel systems since capacity is the question.

This is what the reviewers should go further.

We can have two type of systems: Multiplicative or additive. DWDM is additive. So everything about "a phasor" is now totaly off, now we have a lot of cross terms, each representing the inter

channel crosstalk and the results are much worse

than OOK systems since phase is more sensitive

to everything.

For a multiplicative (modulated) system, you can have bandwidth limited multichannels. You can do

that by cascading multiple MZ modulators

(as Centerpoint, Kestrel are doing). So now

we are essentially similiar to OTDM business when capacity is the question: Will nonlinear SPM and XPM set a limit for capacity. The answer is now not so obvious but still yes! Because now the nonlinearity and dispersion will broaden or compress each channel differently also it varies along the fiber for each channel, which limit how

close the channel can be placed. But,you may ask, what about soliton? The answer is: Well, the soliton efficiency has not changed compared to DWDM case. We still cannot do better than the NON-Shannon conforming limit.

Now, back to the FM confusion. FM modulates carrier frequency on the RF power. The instanous intensity is not constant. In optics, the equivalent carrier frequency is the wavelength.

The confusion is actually quite consistent with other stuff being said, again due to lack of basic training.

as well as theoretical knowledge of FM,

having worked on wireless communication systems.

In any case, FM signals do not violate my

statement about band limitation: a pure

phase signal is guaranteed to have out of band

power. FM is no exception. One can try to suppress

out of band power but cannot get rid of it.

For a refresher, see Proakis P.215-217.

Adding together independent FM signals which

are spaced close enough together to have high

spectral efficiency (ie no interchannel

spacings) is also guaranteed to generate large

amplitude modulations.

I think I don't need to respond to the bizzare

statement about needing square law detectors to

obtain amplitude fluctuations from a beating

signal. Adding nontrivial phase only signals

together produce non-phase-only signals, namely

signals with amplitude fluctuations. As these

propagate down the fiber, these will generate

CPM in the usual way.

The coherent subband systems that I have seen

touted don't have anywhere near the spectral

efficiencies corresponding to the constellations

used.

Spectral efficiency = bit rate /total bandwidth

(*including* interchannel spacings). The large

constellations are meaningless - you simply

have to look at the delivered total data rates

and the total bandwidths counting channel

spacing. One can put arbitrary complicated

signals on channels spaced far apart - that

will do nothing to improve the true spectral efficiency.

into gobbleydegook, so I find it hard to respond.

The capacity estimate in the paper is obtained as

usual by bounding mutual entropies, following

general statement of Shannon capacity for the

channel. Strictly speaking, a bound is computed

based on a WGN process at the input, which

inherently contains amplitude and phase

fluctuations.

Phase buildout,

SPI,

Utopia,

Rammon,

Please get lost until you figure out them.

Thanks.

sources you mentioned are updated and are

for a single channel only. Without considering chirp it is meaningless.

of amplitude fluctuations (and hence CPM)

are not quite accurate. The reason is somewhat

subtle: to do that with a WDM system, you

would have to do two things: (1) build

a *bandlimited* phase only signal. This cannot

be done (except for the trivial case

of a constant tone).

Answer: Wrong, it is done every day, all day long: it is called the FM band on your radio...each of the signals on the radio is band limited...wonder how they overcame your math problem? Think a bit...

You also said: Further, one * cannot * enforce the phase only behaviour by designing individual

channels to be phase only - ever hear of beating?

adding two phase only signals in general will

produce amplitude fluctuations.

Answer: Wrong again. Well, first, to be accurate, two phase only signals would generate a sum and difference signal (beating) on a square law detector, but there is no square law detector (at least in the fiber) here.

Next, even if there was, you assume a coherent relation between the modulation signal sources. Don't.

You are correct in that nonlinearity can cause PM to AM conversion...but less PM means less AM, so that is the approach: multiple subchannels: just like on the FM radio.

So in summary, multiple FDM complex modulated signals, each with independent coding, independent sources of modulation, on each of multiple wavelengths, none of which are coherent to each other, but each of which is detected coherently, through an optical filter, on a balanced detector. Subchannels filtered and processed digitally on low cost ICs.

It's in field trials with a major telecom customer today...I guess they forgot to see if it was working...

-Own

standard results publsihed by

Elraife et al in JLT '91 Jan {?]

I guess on limitation of transmission distance

by GVD etc....I verified it. Also

you can verify the same from

'Optical Networking" by Bonnoni, where

there is a contribution from Enrico

Forestari, on it with a different method.

No chirp is assumed.

Also you can see "Coherent Communication"

by Betti etal, that book conatins a lot of

results proving the superiority of

IMDD system in transmission related impairment.

But if you were true [ which is not true either],

then you have used Shanon's theorem

wrongly. Your SNR has to be with respect to based-band

signal in this case. Which means,

your SNR calculation assumes amplitude

modulation if I go by your formula!!!

And you are finding amplitude fluctuation

from beating!!!! You have to calculate

its magnitude after filtering the respective

channel..

Secondly, \eta calculation assumes the separation of

dispersion and non-linearity operator.

No matter whatever be the approach,

either by analytical IST method or numerical SSF

, that is always the inherent assumption and

so is your calculation. I hope this point

is pretty clear. Non-commutation of both the

operator is the starting point..

..

..

Further, as far the paper go, I have

strong feeling that Authors may be

good theoretician but surely venturing

this field for a recent time. Otherwise,

they would have thought of more meaningful

way of getting amplitude fluctuation

to fit into the Shanon's formula.

-Calpole

not what calpole is complaining.

Back to the phase modulation simulation results,

do you include negative chirp in you simulation,

calpole? The numbers do not look realistic to me.

Could you be more specific about the conditions

you used? Any consideration as to channel bandwidth etc?

if you had chosen to read my post carefully.

The NLS has both dispersion and nonlinearity

in it simultaneously. I have no idea what you

mean by decoupling dispersion and nonlinearity.

If there were only nonlinearity, or only

dispersion, the evolution equations are trivial.

I would have thought that this was adequately

elementary.

I think that the basic misunderstanding that you

have stems from a fictional notion of a phase

only (you call it angle only) signal in a WDM

context. I will include below the passage from

my last post that explains why this is in error.

I suggest you perform the following exercise

for yourself. Construct your favourite signal

source (has to be WDM, and has to be

information-bearing). If one allows for

real time cooperation between channels, it

should be mathematically possible (though of

no practical interest) to construct an

*approximately* phase only (or angle only)

electric field even with many channels.

Propagate your equation beyond a dispersion

length. Lo and behold! You will find that amplitude fluctuations have appeared. For

system lengths significantly longer than the

dispersion length, which is what is treated in

the paper, one can pretty much neglect these

initial transients.

-------------------

From before:

The comments in the Kahn and Ho article

about phase modulation schemes getting rid

of amplitude fluctuations (and hence CPM)

are not quite accurate. The reason is somewhat

subtle: to do that with a WDM system, you

would have to do two things: (1) build

a *bandlimited* phase only signal. This cannot

be done (except for the trivial case

of a constant tone). I won't burden you with

the necessary math - try it our for yourself;

you'll find that trying to twist the phase

of a sine wave to make it carry information

will inevitably put power out of band.

(2) Further, one * cannot * enforce the

phase only behaviour by designing individual

channels to be phase only - ever hear of beating?

adding two phase only signals in general will

produce amplitude fluctuations.

In principle, one could make all the WDM

channels cooperate so that the * joint * signal

had a constant phase (up to a small out of band

leakage) initially. However, that would require

electronic bandwidths of THz (if we had that

we wouldn't be discussing WDM in the first case.

Finally, even if you started with a phase

only signal, dispersion would eventually

convert phase fluctuations to amplitude

fluctuations. For these reasons, you cannot

escape amplitude fluctuations and hence

CPM. Therefore the comment about eliminating

CPM is rather glib. However, assuming that

they were the paper reviewers, they voted with

their feet by recommending publication of

the paper.

Let me try to help you out a little:

You worked with four Nobel Laureates.

You have won it five times. You have started

six startups, and built seven DWDM systems

covered everything from components to costomer care. You have used eight optical PLLs with

nine commercial LOs for every ten Terabits.

It shows.

Now please get lost in your communication classes,

at least until you figure out vacuum polarization in copper.

OT: First, in reality, the Nobel prize is only as good as the person that receives it...the prize by itself does not bestow nobility nor super-intelligence nor ethics. Like most awards, it is half technical and half political.

I have worked for/with several Nobel laureats (four to be exact) in my career, and they ranged from very smart and honorable (earned it and deserved it, poor politicians) to average smart and sneaky (stole their colleagues or students work and called it their own, great politicians).

Sorry, but getting the Nobel prize is not the be-all, and end-all proof of intelligence. LU is a loser company, period. If they are still at LU, they are losers...all the more because they are there with all their great credentials, etc. Probably what we call "walking dead", or "retired-in-place (RIP)". I know one Nobel prize winner (one of the ones I worked for many years ago) pimping a start-up for options and cash...letting his name (and the prize) be associated with a flakey VC-run spin-flip operation.

Now, as to nobody having done a good optical LO, you only confirm my assertion that you do not read.

Suggest you check out the following:

http://www.tuc.nrao.edu/~demer...

I can give you commercial references if you like for complete LO/detector systems you can buy off the shelf, but I will leve that to you as homework.

-Own

continue to debate without attacking

personally..But, there are many things with

which, I can not agree on the article...

"""

First, you have this discussion about bit

rates at fixed eye opening penalties.

You probably won't take this well, but the

quantity discussed in the article is the

channel capacity. This is the maximal possible

rate of error free transmission. Using some

particular modulation and ECC scheme, one can talk

about bit rates and the corresponding BER or other

penalty measure. That is more ad hoc than the

capacity. Admittedly, the capacity is a

theoretical limit than a practical quantity;

however, that is the quantity in the paper,

not the quantities you want to discuss. It

provides a wall that the bit rates for fixed

penalties cannot cross (and if you have a good

enough coding scheme, like a turbo code, you can

make the (bit rate) vs (SNR per bit (EbNo))

curves approximate the capacity limit. Almost

by definition, the quantities you are interested

in are more derivative (and therefore need

transformation) before being compared to

channel capacity. """"

>>>>>>Your above assessment is correct. No problem

in converging in opinian.

It is true that CPM, FWM build up with system

length. This is in fact the effect that leads

to the capacity limits discussed in the paper

(specifically from CPM). It is just that the

buildup is different from that of amplifier

noise or other additive forms of noise. In

fact, the length dependence is specifically

present in the formula for the peak capacity

if you care to look (through I0).

The peak capacity goes to zero at infinite length.

However, the dependence is not a simple inverse

relation to distance, and therefore peak rate

times length is not a good metric. In fact, the

results show that the bit-rate times length

metric needs revision for the nonlinear

effects to be treated properly.

>>>>>>> Well, here is the problem. The formula

of \eta that you have used to assess the

SNR due to CPM either in IMDD or coherent

system defies the reality. If you talk about

angle-modulated systems, CPM affects via

following way

[1] PM-AM conversion of Modulated Phase generates RIN

[2] This RIN is transferred as CPM to other channel and cause SNR degradation of

base-band signal in phase.

Problem with the treatment is that if

I consider IMDD system then also your

\eta is wrong and if I consider

angle-modulated system then also the assessment of

\eta is wrong even analytically.

>>>>>>>>>>>>>>>>>>>>>..

>>>>>>>>>>>>>>>>>>.....

I don't know where you got the idea that

dispersion is being neglected -

the NLS has both dispersion and nonlinearity

in it. The dispersion coefficient appears

explicitly in the different formulae. The

*relevant* bandwidth is in the GHz rather than

the THz range, since the discussion is about

WDM systems. For the same reason, higher

order dispersion can be neglected. Dispersion

between channels leads to suppression of distant

channels, as also discussed.

>>>>>>>>>>.Here is the problem. You have decoupled

Dispersion and Non-linearity .

\Detlta \E_{field} term in your

expression should be term that depends on

dispersion. I don't see it.

Also, even if individual channels are in GHz, since

you are considering so many of them,

third order dispersion is definietly the most important parameters as \beta_2 will

vary accross the channel depending on

\beta_3. You have assumed all the channels

have equal \beta_2

parameters.

*********************

Also, I don't see where you get the bit about

intensity noise: the paper deals explicitly

with the E field, which means it deals with

coherent communication (amplitude and phase).

>>>>>>>If there is no-Intensity noise

how could get an effect of SNR degradation in

baseband due to CPM in Angle-modulated systems???

A discussion of Q values in this context is

misleading because the noise in question is not

Gaussian. If it were, there would not be any

discussion. We'd be back to the linear channel

case.

>>>> OK, though there are some points,

I am not diverting the attension ..>>>

The comments in the Kahn and Ho article

about phase modulation schemes getting rid

of amplitude fluctuations (and hence CPM)

are not quite accurate. The reason is somewhat

subtle: to do that with a WDM system, you

would have to do two things: (1) build

a *bandlimited* phase only signal. This cannot

be done (except for the trivial case

of a constant tone). I won't burden you with

the necessary math - try it our for yourself;

you'll find that trying to twist the phase

of a sine wave to make it carry information

will inevitably put power out of band.

(2) Further, one * cannot * enforce the

phase only behaviour by designing individual

channels to be phase only - ever hear of beating?

adding two phase only signals in general will

produce amplitude fluctuations.

In principle, one could make all the WDM

channels cooperate so that the * joint * signal

had a constant phase (up to a small out of band

leakage) initially. However, that would require

electronic bandwidths of THz (if we had that

we wouldn't be discussing WDM in the first case.

Finally, even if you started with a phase

only signal, dispersion would eventually

convert phase fluctuations to amplitude

fluctuations. For these reasons, you cannot

escape amplitude fluctuations and hence

CPM. Therefore the comment about eliminating

CPM is rather glib. However, assuming that

they were the paper reviewers, they voted with

their feet by recommending publication of

the paper.

As for estimating the quantity \eta - (I presume

that is that you mean by \eta_c) -

analytical estimates are always different

from numerical ones. They are approximate,

but they are in closed form and give insight

that is difficult and inefficient to derive

from numerics.

ppm.

"He who knows that he knows ... " etc.

continue to debate without attacking

personally..But, there are many things with

which, I can not agree on the article...

"""

First, you have this discussion about bit

rates at fixed eye opening penalties.

You probably won't take this well, but the

quantity discussed in the article is the

channel capacity. This is the maximal possible

rate of error free transmission. Using some

particular modulation and ECC scheme, one can talk

about bit rates and the corresponding BER or other

penalty measure. That is more ad hoc than the

capacity. Admittedly, the capacity is a

theoretical limit than a practical quantity;

however, that is the quantity in the paper,

not the quantities you want to discuss. It

provides a wall that the bit rates for fixed

penalties cannot cross (and if you have a good

enough coding scheme, like a turbo code, you can

make the (bit rate) vs (SNR per bit (EbNo))

curves approximate the capacity limit. Almost

by definition, the quantities you are interested

in are more derivative (and therefore need

transformation) before being compared to

channel capacity. """"

>>>>>>Your above assessment is correct. No problem

in converging in opinian.

It is true that CPM, FWM build up with system

length. This is in fact the effect that leads

to the capacity limits discussed in the paper

(specifically from CPM). It is just that the

buildup is different from that of amplifier

noise or other additive forms of noise. In

fact, the length dependence is specifically

present in the formula for the peak capacity

if you care to look (through I0).

The peak capacity goes to zero at infinite length.

However, the dependence is not a simple inverse

relation to distance, and therefore peak rate

times length is not a good metric. In fact, the

results show that the bit-rate times length

metric needs revision for the nonlinear

effects to be treated properly.

>>>>>>> Well, here is the problem. The formula

of \eta that you have used to assess the

SNR due to CPM either in IMDD or coherent

system defies the reality. If you talk about

angle-modulated systems, CPM affects via

following way

[1] PM-AM conversion of Modulated Phase generates RIN

[2] This RIN is transferred as CPM to other channel and cause SNR degradation of

base-band signal in phase.

Problem with the treatment is that if

I consider IMDD system then also your

\eta is wrong and if I consider

angle-modulated system then also the assessment of

\eta is wrong even analytically.

>>>>>>>>>>>>>>>>>>>>>..

>>>>>>>>>>>>>>>>>>.....

I don't know where you got the idea that

dispersion is being neglected -

the NLS has both dispersion and nonlinearity

in it. The dispersion coefficient appears

explicitly in the different formulae. The

*relevant* bandwidth is in the GHz rather than

the THz range, since the discussion is about

WDM systems. For the same reason, higher

order dispersion can be neglected. Dispersion

between channels leads to suppression of distant

channels, as also discussed.

>>>>>>>>>>.Here is the problem. You have decoupled

Dispersion and Non-linearity .

\Detlta \E_{field} term in your

expression should be term that depends on

dispersion. I don't see it.

Also, even if individual channels are in GHz, since

you are considering so many of them,

third order dispersion is definietly the most important parameters as \beta_2 will

vary accross the channel depending on

\beta_3. You have assumed all the channels

have equal \beta_2

parameters.

*********************

Also, I don't see where you get the bit about

intensity noise: the paper deals explicitly

with the E field, which means it deals with

coherent communication (amplitude and phase).

>>>>>>>If there is no-Intensity noise

how could get an effect of SNR degradation in

baseband due to CPM in Angle-modulated systems???

A discussion of Q values in this context is

misleading because the noise in question is not

Gaussian. If it were, there would not be any

discussion. We'd be back to the linear channel

case.

>>>> OK, though there are some points,

I am not diverting the attension ..>>>

The comments in the Kahn and Ho article

about phase modulation schemes getting rid

of amplitude fluctuations (and hence CPM)

are not quite accurate. The reason is somewhat

subtle: to do that with a WDM system, you

would have to do two things: (1) build

a *bandlimited* phase only signal. This cannot

be done (except for the trivial case

of a constant tone). I won't burden you with

the necessary math - try it our for yourself;

you'll find that trying to twist the phase

of a sine wave to make it carry information

will inevitably put power out of band.

(2) Further, one * cannot * enforce the

phase only behaviour by designing individual

channels to be phase only - ever hear of beating?

adding two phase only signals in general will

produce amplitude fluctuations.

In principle, one could make all the WDM

channels cooperate so that the * joint * signal

had a constant phase (up to a small out of band

leakage) initially. However, that would require

electronic bandwidths of THz (if we had that

we wouldn't be discussing WDM in the first case.

Finally, even if you started with a phase

only signal, dispersion would eventually

convert phase fluctuations to amplitude

fluctuations. For these reasons, you cannot

escape amplitude fluctuations and hence

CPM. Therefore the comment about eliminating

CPM is rather glib. However, assuming that

they were the paper reviewers, they voted with

their feet by recommending publication of

the paper.

As for estimating the quantity \eta - (I presume

that is that you mean by \eta_c) -

analytical estimates are always different

from numerical ones. They are approximate,

but they are in closed form and give insight

that is difficult and inefficient to derive

from numerics.

ppm.

"He who knows that he knows ... " etc.

I have not read your thesis, however, I have this

strange feeling that it wouldn't help me

advance my knowledge about the issues at hand.

About your post: let me point out a few things.

First, you have this discussion about bit

rates at fixed eye opening penalties.

You probably won't take this well, but the

quantity discussed in the article is the

channel capacity. This is the maximal possible

rate of error free transmission. Using some

particular modulation and ECC scheme, one can talk

about bit rates and the corresponding BER or other

penalty measure. That is more ad hoc than the

capacity. Admittedly, the capacity is a

theoretical limit than a practical quantity;

however, that is the quantity in the paper,

not the quantities you want to discuss. It

provides a wall that the bit rates for fixed

penalties cannot cross (and if you have a good

enough coding scheme, like a turbo code, you can

make the (bit rate) vs (SNR per bit (EbNo))

curves approximate the capacity limit. Almost

by definition, the quantities you are interested

in are more derivative (and therefore need

transformation) before being compared to

channel capacity.

It is true that CPM, FWM build up with system

length. This is in fact the effect that leads

to the capacity limits discussed in the paper

(specifically from CPM). It is just that the

buildup is different from that of amplifier

noise or other additive forms of noise. In

fact, the length dependence is specifically

present in the formula for the peak capacity

if you care to look (through I0).

The peak capacity goes to zero at infinite length.

However, the dependence is not a simple inverse

relation to distance, and therefore peak rate

times length is not a good metric. In fact, the

results show that the bit-rate times length

metric needs revision for the nonlinear

effects to be treated properly.

I don't know where you got the idea that

dispersion is being neglected -

the NLS has both dispersion and nonlinearity

in it. The dispersion coefficient appears

explicitly in the different formulae. The

*relevant* bandwidth is in the GHz rather than

the THz range, since the discussion is about

WDM systems. For the same reason, higher

order dispersion can be neglected. Dispersion

between channels leads to suppression of distant

channels, as also discussed.

Also, I don't see where you get the bit about

intensity noise: the paper deals explicitly

with the E field, which means it deals with

coherent communication (amplitude and phase).

A discussion of Q values in this context is

misleading because the noise in question is not

Gaussian. If it were, there would not be any

discussion. We'd be back to the linear channel

case.

The comments in the Kahn and Ho article

about phase modulation schemes getting rid

of amplitude fluctuations (and hence CPM)

are not quite accurate. The reason is somewhat

subtle: to do that with a WDM system, you

would have to do two things: (1) build

a *bandlimited* phase only signal. This cannot

be done (except for the trivial case

of a constant tone). I won't burden you with

the necessary math - try it our for yourself;

you'll find that trying to twist the phase

of a sine wave to make it carry information

will inevitably put power out of band.

(2) Further, one * cannot * enforce the

phase only behaviour by designing individual

channels to be phase only - ever hear of beating?

adding two phase only signals in general will

produce amplitude fluctuations.

In principle, one could make all the WDM

channels cooperate so that the * joint * signal

had a constant phase (up to a small out of band

leakage) initially. However, that would require

electronic bandwidths of THz (if we had that

we wouldn't be discussing WDM in the first case.

Finally, even if you started with a phase

only signal, dispersion would eventually

convert phase fluctuations to amplitude

fluctuations. For these reasons, you cannot

escape amplitude fluctuations and hence

CPM. Therefore the comment about eliminating

CPM is rather glib. However, assuming that

they were the paper reviewers, they voted with

their feet by recommending publication of

the paper.

As for estimating the quantity \eta - (I presume

that is that you mean by \eta_c) -

analytical estimates are always different

from numerical ones. They are approximate,

but they are in closed form and give insight

that is difficult and inefficient to derive

from numerics.

ppm.

"He who knows that he knows ... " etc.

the article. Let switch over to the

new topic as pointed out by ubwdm: Wheather

coherent systems hold the key to enhance the capacity in future..

Actually, I started my research on coherent systems as it was very hot till the middle of

the last decade. As far as my simulation results

reveal, angle-modulated systems suffer much

more severely from dispersion and

non-linearity. So, bitrate-distance product is

always much less for angle-modulated systems.

Here is a table of maximum transmission distance

at 10Gb/s over SMF-28 with only dispersion.

by taking 1dB eye-penalty as the requirement.

NRZ-IMDD----67 Km

PSK--------53 Km

MSK------47 Km

CPFSK---- 40 Km

So, definitely for long-haul and even for medium

haul, angle-modulated systems don't seem to have

a future simply because of its poorer performance

against dispersion and non-linearity.

Howerever, in Fiber-wireless systems,

in future, Coherent systems have a bright

future for a seamless communication.

Many losers are left in Lucent,true,but it takes

a true loser to make a statement such as

"only people left there are losers".

Please read it again.

2). Look, I am not here to defend the paper.

There are actually a few loose connections

and I agree with you that some aspects are treated not well in the paper, but the merit of the paper is clear to me. It shows from NLS that nonlinearity sets a capacity limit for a typical fiber(as we knew it for a while) and it actually shows relationship between many variables, some are system metric and some are not. It does not mean you cannot work around the limitations. For example, what if one builds

new fibers with alternating linearity coefficient

(similiar to alternating dispersion in truewave fiber) or new hollow fibers with exotic cladding? No, the paper does not build real systems for you, nor does it claim to.

[1] How valid is the estimation of

\eta_c?

It is not as accurate as some of simulations I've

seen (maybe you did some of them?) for a given

problem, but what's important here are the concepts and qualitative behaviors.

[2]How wise it is to calculate the RIN

due to non-linearity

without considering dispersion [ Mind it

they have used it only for

useless pupose ] when

author is talking about Tb/s???

The authors assume that dispersion won't help

the fiber capacity, which sounds reasonable

to me. I will address the phase modulation separately bellow. In case of soliton, it is possible to balance them out, but as I said before, the result is lower than their cases. No, they have not mathematically proven it is true.

[3] @50 Tb/s, third and fourth order dispersion

will be very crucial. How can they neglect

it in their calculation???

Again, they are under same assumption.

Now, points raised by reviewers:

1) Will coherent phase modulation (I could tell everything about the original concept and the patent, but it is a different story) improve the

capacity? Maybe, I am not sure. Would it change

discussions in the paper? It centainly

would. Why it is ignored? Because coherent modulation is not practical in at least

forseable future, not until optical PLL is

practical. Lasers work because of coherency, holographic-anything does not work because of

the required coherence.

So, the conclusion: the paper presented one of

better analysis that relates to today's understanding. It proves one thing for sure:

The capacity of a fiber as we know it today

has a capacity limit that's much lower than that

of Shannon's theory and increasing power would

not help.

You may not appreciate it because you are just out of school or whatever, but don't attack Nature because it published it.

And I don't think you have any evidence that it is pure political.

and even if it is written by a Nobel Lauriet

does not gurantee the fact that he will talk

sense all time.

Now, look at this: I have pointed out only

a few crucial mistakes in the paper.

So, far none of you has been able to defend

that article, because it has been a sloppy

article and now you are defending saying that

it has been written by a Nobel Lauriet????

One of the authors of the article should be more ashamed because Nobel Commitee trusted

him and now he is out to encash it

by throwing any trash that he likes?

Defend the arcticle technically ubwdm.

I have just finished my PhD in this field

and I know no matter whether that crab

is written by a Nobel Lauriet or

a big 'Ass', can not be defended

technically. If you have courage, answer following

questions:

[1] How valid is the estimation of

\eta_c?

[2]How wise it is to calculate the RIN

due to non-linearity

without considering dispersion [ Mind it

they have used it only for

useless pupose ] when

author is talking about Tb/s???

[3] @50 Tb/s, third and fourth order dispersion

will be very crucial. How can they neglect

it in their calculation???

Please, don't defend it by saying it is from

a Nobel Lauriet. Defend it technically so

that I can learn something from the erudite

person like you. Again, I will be happy

to find that I am mistaken if you can prove

it.

Quite a few Nobel prize winners would be losers

because they would all lose to nameless on the net... Just like the authors of this paper.

"If that article was in your honest technical opinion "one of the best" on WDM you have ever read, I can only conclude that you must not read very much!"

That's hardly surprising to anyone here. My statement is "The paper is one of best among tens of thousands published every year".

" Apparently you have not published much either. Kahn and Ho's review called it: "a contribution", after they completely trashed their assumptions and therefore the conclusions based on them. "

And the paper gets published on Nature.

" Oh, by the way...the nonlinearity in Copper comes from several sources..."

As ppm pointed out, you forgot about vacuum polarization, if you ever learned it in your

communication classes.

"Guess none of those successful start-ups paid for you...I can guess why..."

You must be really interested in that... Sorry,

I won't tell you anything. It is not part of

this discussion...

If that article was in your honest technical opinion "one of the best" on WDM you have ever read, I can only conclude that you must not read very much!

Apparently you have not published much either. Kahn and Ho's review called it: "a contribution", after they completely trashed their assumptions and therefore the conclusions based on them.

Hint: That's what we call damnation by feigned praise!

Oh, by the way...the nonlinearity in Copper comes from several sources...point diodes due from poor contacts and twisted wires...line amplifiers...inadequate power supplies...but we managed to find ways around the problems...one at a time...

Finally, most of what we are discussing is not taught in EM class, it is taught in Communication Theory, or Communications Systems Analysis, which you would realize if you had taken any of the courses.

Hint: That's what we call: inadequate education!

Guess none of those successful start-ups paid for you...I can guess why...

2. " They even don't know, without dispersion,

non-linearity can do no harm to either

IMDD or Angle modulated system!!!!!"

Comment: Huh, graduated from a graduate

course, but need to improve problem solving skills. Why?

a). Fiber or waveguide without dispersion for

whole spectrum, when the capacity is

the question?

b). The phase shift of the second order

SPM/XPM indeed "does no harm" to an angle

or pure phase modulated SIGNAL. But it

will HARM an angle modulated SYSTEM

because the SYSTEM in question has

>>>>>>>>>>>>>

Well, I have commented purely on fiber

transmission assuming it to be infinite

bandwidth system to treat and simplify the

problem of non-linearity.

Most of the finite-bandwidth system can be

modelded as a filter and

filters can also cause PM-IM

or IM-PM conversion and that way non-linearity

can affect the signal quality even

if dispersion is absent. But I have made

comment pertaining to the assumptions

used in the 'Nature's paper. There is

no point bringing an well known obvious issue.

3. "With proper dispersion compensation,

we can reduce the first order RIN due to

non-linear phase , ..."

Comment: Get a clue.

>>>>>Well, this has been estblished in

a paper in IEEE-JLT, April-2000 issue..

..

I guess that was a paper on CPFSK system and

the impact of fiber non-linearity on it.

>>>>>>>>

Sad part of the story about the article in Nature

is that its treatment of RIN through

\eta parameter is extremely vague. It's

too crude to be even 1% truth, and I know

it from my past long experince of simulation of

NLS and other RIN related stuff.

So, I can never digest that story.

It was published because it was from Bel-lab,

and I can ensure you without the kind

politics from the reviewer, such kind of

crab can never be published. Since,

I had a good respect for Nature, I was

disheartened to see a paper which even does

not fit into the standard of

3rd graded journal like 'Journal of

Optical Communication" from Germany.

It is impossible to argue on this board.

I am not going to correct every statements,

but a couple are enough to show their

true colors...

1) "Let me teach you something...a Copper wire system is far, far from linear...to get that kind of density (10bps/Hz) requires some real hard work in equalization and FEC...and it is all done with less than 20 dB SNR and in the presence of echo and crosstalk...makes the non-linearities in fiber look like child play..."

Comment: Need better basic training in graduate level EM theory.

2. " They even don't know, without dispersion,

non-linearity can do no harm to either

IMDD or Angle modulated system!!!!!"

Comment: Huh, graduated from a graduate

course, but need to improve problem solving skills. Why?

a). Fiber or waveguide without dispersion for

whole spectrum, when the capacity is

the question?

b). The phase shift of the second order

SPM/XPM indeed "does no harm" to an angle

or pure phase modulated SIGNAL. But it

will HARM an angle modulated SYSTEM

because the SYSTEM in question has

finite bandwidth and has multiple channels.

3. "With proper dispersion compensation,

we can reduce the first order RIN due to

non-linear phase , ..."

Comment: Get a clue.

It is apparent that many are confused by the

paper. The paper is one of best among tens of

thousands published every year, most of which

indeed are useless. To attack the quality of

"Nature" sounds more like sour grape than

anything else. The paper gives a good analysis

about nonlinear nature of fiber, but not for transmission with electrical or optical regeneration. It is very valuable esp. to those of us who are building long haul, ultra long haul/submarine systems who learned many issues with expensive and time consuming experiments. Those who have done it understand that they

are not "fundamental limits" for the SYSTEM,

as only a few clueless here claim so.

It's obvious that the paper does not cover the

case when DCM used along the fiber reconditions the signal just like it does not cover systems with 2R/3R every 100KM. In real systems signals could be demuxed and optically reshaped to overcome some nonlinear effects. But again, the paper helps us to analyse these issues.

BTW, I left Bell Labs long time ago and have been with a few successful startups. I probably know

more about Lucent's failure. I have to say it is

absurd and childish to correlate this paper

with the fact that Lucent is falling.

SPM and XPM. With proper dispersion compensation,

we can reduce the first order RIN due to

non-linear phase , however second-order RIN

can not be compensated due to simple nature

of sinusoidal addition( a mathematical

artifact of RIN expression due to PM-AM).

Finally, any merit can be attached to that paper?

"When calculating the effects of CPM, Mitra and Stark have implicitly assumed a modulation technique involving time-varying intensity. It is already known that using a constant-intensity modulation technique, such as phase or frequency modulation, can eliminate CPM. The fibre's refractive index varies slightly with the wavelength of light, which tends to convert phase or frequency modulation to intensity modulation. This wavelength dispersion must be carefully compensated for to maintain constant intensity. If we follow the same calculations as Mitra and Stark, and constant intensity is maintained, then the spectral-efficiency limit should increase with transmitted power, in contrast with their results. In reality, as the power increases, spectral efficiency would eventually be limited by other nonlinear effects, such as four-wave mixing.

As Mitra and Stark point out, nonlinearities such as CPM can be cancelled out, in principle, by using a number of clever tricks. Better optical fibres can also help GÇö for example, hollow fibres with air cores have a reduced nonlinear response. In ordinary optical fibres, light can propagate in two orthogonal polarizations GÇö that is, with electric field lines along two perpendicular directions. A simple way to double spectral efficiency is to send two independent signals with these different polarizations and use polarization-resolved detection. Even without polarization-resolved detection, sending neighbouring signals with perpendicular polarizations is a well-known method to reduce nonlinearities."

One of those "clever tricks" is to use balanced coherent detection...which also allows you to use full IQ modulation...and it cancels first order RIN down to shot noise. OK, so it will not cancel noise cross signal terms...

People have locked external cavity semiconductor lasers for many years...I believe you can buy half way decent equipment off the shelf....data I have seen approaches the best analog RF PLO results...

Anyway, last word is: Mitra and Stark are wrong, CPM is not a fundamental limit to the bandwidth of fiber, and people have done much, much better than 3 bits/hz over fiber...and routinely achieve much better than 20 dB SNR (on analog subchannels), and do so over long distances, and through EDFAs...in the field, today.

With the misguided technical analysis they are getting from the likes of Mitra and Stark, who probably represent the best they have, no wonder LU is headed for the dumpster...

-Own

non-linearity can do no harm to either

IMDD or Angle modulated system!!!!!"

I think your statement is only true for SPM/XPM

but FWM and the scattering effects can deplete the

signal.

Moreover with no dispersion the signals do not "walk away" from each other and FWM effects (for example) are amplified.

DSF fiber are not good for WDM...

Ya, now I am even more convinced that it's

a school physics calculation with a bunch of

school

physics approximations.

They talk about RIN (relative intensity noise)

with a vaguely defined term \eta_c.

Putting that value in Shanon's capacity theorem without reading any paper on RIN due to fiber non-linearity is quite stupid thing, and they did it.

They even don't know, without dispersion,

non-linearity can do no harm to either

IMDD or Angle modulated system!!!!!

It all happens because of PM-IM or IM-PM

conversion!!! Where is this in their calculation!!! Then they would have arrived

at the right equation.

I don't want to point out other mistakes, which are useless. If Nature continues to publish

such articles, soon or later it will be another

light-reading magazine.

limit. So, at the begining I have told that

I assume receiver is ready for 100Tb/s .

200 photon per bit is nearly equal to

15dBm @100 Tb/s for a receiver sensitivity of

10^-9 PE.

Quantum limit of receiver may not be the problem

for 100 Tb/s transmission question is

whether we can have that broad-band receiver and

sunch a modulator or any OTDM technique that can

give 100Tb/s transmission.

I cited the example of 1 micro-meter to illustrate the theoretical fact that

at that small distance dispersion and

non-linear effect will be negligible.

Please, go by its intension.

is some optimization curve in multidimensional

plot where fiber length and physical parameters

are treated as independent parameters and we

agree that accepted received signal performance

follows certain requirements like

1 dB eye-closure or below 1dB receiver sensitivity penalty @10^-12 BER or any other

SONET SR or IR requirement. Thanks to the

strong interplay between signal format, dispersion and non-linearity, we can always

get a value of peak bitrate but only for

a certain distance. If distance is also plotted

as an independent parameter and someone says

that he has achieved a peak value for

bit-rate from the plot, the very concept of

it is quite unacceptable because of the nature

of Non-linear Schodinger Euqation where

the space variable 'z' (the length)

appear as a first-order derivative

as a consequence of paraxial approximation.

Variance SPM, XPM and FWM power are all propotional to the distance and when any non-liear

phase affects on IM systems through

PM-IM conversion, varinace of Relative Intensity Noise

becomes propotional to distance for a smaller value of total-dispersion and varies as a sine of distance for more accurate approximation.

In contrast to that , Fiber filter function

has an exponent that is always propotional to

'z'. Since, 'Q' value is inversely dependent on

the variance , Log(BER) plot for a given

receiver power is inversely propotional to the

distance if the RIN due to fiber impairment

is more dominant than the receiver noise.

Now, if we search for a bit-rate optimization

keeping the constraint of 1 dB eye-closure

or 14dB 'Q' as accepted signal quality,

optimization of bit-rate with respect to

distance is meaningless because of very mathematical nature of

NLS. That's why it is

more important to talk about Bit-rate distance

product than bit-rate only for capacity.

This has been well known fact since the days of

electrical transmission theory.

is the limiting factor for holographic storage

as well (as opposed to simple linear crosstalk

which comes from say finite thickness of the

medium and therefore finite width of the

diffraction peak). That's quite interesting.

In terms of index saturation, you are right that

the output SNR can be improved by increasing the

playback power - what I was assuming is that

due to the noisiness of the * writing * process,

a minimum index change is required to write

an image, so if the total index change was

finite that would limit the number of images.

However, I can imagine that the inter image

nonlinear crosstalk is a dominant effect ...

ppm

Firstly let's look at photons. Optical receivers need to detect the incoming photons and turn them into electrons to allow us to use the data. One extreme is that you could use a single photon to represent a bit - this could work, but in the presence of noise the number of photons that you need for each bit rises.

I've seen receivers designed that operate at 20 photons per bit, but more realistic designs operate at 200 photons per bit.

That relates to the optical power, and so drives the minimum power that you need in a fibre. The example given earlier of sending 100 Tbit/s over 1 um is a little spurious, given the enourmous optical power you would need to detect the bits at the receiver.

This is only lightly related to the information density that you can achieve. For a long haul fibre optic system, that has some optical amplifiers and some spans of fibre, then I believe the crew from Bell Labs. Some of the limits are really fundamental - like photons, and some are engineering limits to a particular system design.

I think the real fundamental limit is how many publications like lightreading will publish press releases, without reading or understanding the material. Until lightreading changes its business plan and stops needing to get as many eyeballs, and therefore stops publishing the most controversial stories that it can get away with, then we will continue to have debates on these boards.

C'mon lightreading, time to scape up a story about something really heretical, and get more people reading your site...

P.

is given for the peak capacity value, depending

on the system parameters. The dependence on

system length is logarithmic (a reasonably

weak dependence). It also tells you that bit rate

times distance is not a good metric.

BTW, the article is entitled "nonlinear limits"

not "fundamental limits".

ppm

I have read all the messages, but not the original article on Nature. Really impressed

about the knowledge of everyone.

IMHO, whatever claimed as the fundamental limit

of the fiber is a mistake. Certainly ways can be

invented to mitigate the nonlinear effect on the

fiber, using different modulation scheme at the

source and a more sensitive receiver coupled with

processing gain can reduce the SNR required for

the channel.

The article in Nature might just be addressing

the current fiber with its optical properties and

probably assumed some kind of modulation scheme

will be used, and the sensitivity of the receiver

diode. Some clever math tricks then derived the

3b/Hz number. Definitely a valid exercise.

To claim that as the fundamental limit of fiber

capacity is just wrong.

random thought

A man with a good mind, who is not afraid to use it, is a rare thing...

Apparently you are rare...

Thank you for showing up here...

-Own

has no meaning. We can always transmit

100Tb/s over a micro-meter if transmitter and

receiver is available for 100Tb/s.

All capacity limiting factors like optical

noise, dispersion and non-linearity are propotional [ or exponentially varies] with the

transmission distance if dispersion and

non-linearity has weak coupling. Hence,

such school physics calculation is useless

without a bit-rate-distance product.

Huh, a real copper comm guy. Why don't you

just spell out DMT? That way you can maybe

tell us a thing or two about ADSL?

Let me just say that if you get a textbook,

you will find out NLS is well, nonlinear.

The Maxwell's equation for a conductor or

the ABCD parameters for a twisted pair is

however linear. Surprised?

DMT won't help fiber much. SPM does decrease

as "sub-channel" gets smaller. But XPM is

increased. In case of DWDM, it is hard to

conclude as a general rule (Depending on optical power density, etc), but DMT won't increase capacity. Believe it or not, the Bell Labs

authors do know a few things about fiber communications... enough to publish it

on "Nature".

I will give some hints:

1) One very effective way to combat fiber nonlinearities is to break the channel into n-subchannels...now in general, for each subchannel in the channel, there is an optimal bandwidth...which among other things is a direct function of the modulation and the detection method. Each of these subchannels is then made piecewise (much more) linear...not perfectly linear mind you, but significantly better...

2) Generalized optical IQ modulation has been done quite nicely for many years...in fact so has general IQ modulation and balanced coherent detection. At least three companies I am aware of field such equipment today and have for many years (only one has not passed field trials yet): Harmonic, which uses complex modulation, Synchronous which uses complex modulation and balanced detection, and the third of which uses all of the above and coherent detection.

The article may be correct based on the assumptions it makes, and how they choose to attack the problem, but as my mentor told me, always remember how you spell assume...

-Own

frequency. You can think it as ITU channel in DWDM. A nonlinear media acts like RF mixer.

As the number of holograms/ITU channels

in a fiber increases, signals mixe

with themselves (SPM) and with each other (XPM).

The result is that noise will increase squarely with frequency range, or number of channels (and distance). So noise density (/per Hz) will increase with formation (bit per Hz). Initially, system with finite power budget will be limited by linear noise (transmitter/receiver noise). When more information or optical power is pumped into system, this cocktail party noise is the limit. Amplifier noise is also partly nonlinear.

And the most significant of all, it is this cocktail party noise that violates Shannan theory, other noise don't. The (Bits/per Hz)

is not really a complete measure for a nonlinear

media.

Likewise, in case of holographic memory, index saturation is not the killer since you could always increase playback power, at least theoretically. "Cocktail party Noise" is.

BTW, ture, there are ways to combat nonlinear effect. But how many bit you can get per soliton?

As to 3bps/Hz, I think it comes from

OTDM - record is about 15 fs pulse in 200 nm. about 2.5 bps/Hz.

But, if you add bi-di and polarization, you can get 10 bps/Hz per link for a short fiber.

The assumption of the paper published was nonlinearity is a fact of life in optical fiber. Wrong! What if through some clever scheme (digital or analog) nonlinratities could be suppressed. Then again if that happens, the physicists would say, we knew it all along.

Lets say we start with a 16-ary multi level PAM instead OOK (this would be difficult with current DWDM lasers). This would assign a 4 bits/symbol, this would increase the throughput to 1.6b/s/Hz, but this type of signalling is poor because all the quantization levels are in the 'real' amplitude plane; you could not transmit this signal too far before AWGN and any optical ASE would start intefering with decision thresholds. We need to use the phase plane to spread out the quantizing radii so that better Eb/No at the receiver, this is how the V.22 on up to V.90 modems were able to transmit greater BW's over 4 kHz of copper BW. The same holds true for HFC cable systems sending 256-QAM in each 6 MHz channel space.

The problem is that no-one (that I know of) manufactures or has an equivalent light based IQ modulator (that would operate at 193.1THz for example).

Even if you could build something like this, then the non-linear effects (PMD, chromatic and time disersion) will start to interfere with demodulation, so then you would need to adaptively equalize these non-linearities with technology that so far does not exist...not to mention we'll probably need FEC over all of this!!

This is very hard to do at 100Mb/sec let alone over 10Gb/s...only time and technology will tell.

At this point I'll settle for 0.4b/s/Hz...

Cheers

talking of peer-reviewed papers, you might want to look one up. About a year ago, Desurvire published a nice paper in an IEEE journal. It talked about the ultimate limit of an optically amplified system - it compared and contrasted lumped and distributed amplified systems.

So just looking at the noise from amplifiers in long haul systems, the limits he calculated were 3 bit/s/Hz for distributed amplifier systems and 6 bit/s/Hz for lumped systems. Which comes very close to the Bell Labs results, without including non-linearities.

All of which is a very long way from the 0.1 bit/s/Hz we are using today.

P.

bit about that problem ... I presume you are

referring to the nonlinearity having to do

with the refractive index change saturating

after writing a certain number of holograms.

I have a vague recollection that the maximum

delta(n)'s are of the order of a fraction of

a percent.

Best

ppm.

reaction is typical of many DWDM beginers

in some startups I met last years though.

To achieve 3 bps/Hz for a sigle 50Ghz channel

is not difficult. Even 10 bps/Hz is possible

in the lab for a few spool of fibers. But try it for 100+ channels for a few thousand KM transmissions, then you will start to appeciate the laws of physics.

This reminds me that when I did my disertation

many years ago, I analysed the capacity of holographical memory with similiar mathematical method. The established theory at time predicted that a 1cmX1cmX1cm LiNbO3 could hold the library of Congress, but reality was millions times under.

The cause: nonlinearity.

of unnecessary theorems and lemmas followed by

a non-result. While Nature is not a traditional

communication theory journal, it is as valid

a forum as any to report a new way of

computing information capacities in the

presence of nonlinearities. Information theory

was to some extent born whole, there are few fundamentally new results in any case after Shannon's original publications.

I have failed to see a single valid technical point that you have raised. I sympathise with

your suspicion of the ivory tower, but I am

afraid that the IEEE and other journals are

as full of unnecessarily narrow publications,

whether from academics or not. Apart from

Turbo and LDPC codes (the latter being already

a rediscovery), there has been little over

the last couple decades that constitutes

basic advances in understanding.

Let me point out something simple. You brought

up a 10bit/s/Hz as a number. At 20dB SNR, which

you also mention, the Shannon formula for a

linear channel only gives you 7bits or so

(log2(100)=7 approx). There are inconsistencies

in your thinking even for a linear channel.

The limits in question are quite real. As for

specifying parameter values, that is clearly

inescapeable; this is not the speed of light

in vacuum or the gravitational constant that

is being determined. However, an estimate

for realistic parameter values is adequately

valuable. The same issues arise in predicting

limits for semiconductor memory chips, for

example. The world is imperfect: one has to

start somewhere.

Best,

ppm.

First, there is a BIG difference between writing for a peer reviewed journal, and a trade publication...they are two very different things.

Something like an IEEE or OSA technical journal is the first, and LR or Time is the latter (for example).

JMHO, but Nature is NOT the first place anyone of caliber in communications would think to publish. OTOH it would be an ideal place to publish a supposedly "fundamental limit" in fiber optics.

Precisely because they knew by going there it would not go through a tough and thorough peer review, and/or the editors would tolerate their combination of hype-title and "let's pretend it is this way" problem constraints. Sophistry.

My effort is not intended to confuse, but rather to expose the effort on the part of others to confuse / spin / hype / etc.

I have given (more than) enough information for those with technical expertise in the field of communication theory and/or fiber optics to understand...

-Own

From my limited knowledge of comm sys

what you say is true for a "memoryless,

gaussian channel" for a copper local loop.

This efficiency of modulation is

fundamentally correlated with the channel

noise characteristics, which in case of

fiber are very different from the copper.

why don't you write a paper in a peer reviewed

trade publication negating their findings.

Hiding behind LR's message board to confuse

the readers doesnot demonstrate your true

knowledge. It only justifies your vision to

confuse everyone.

The real issue is there are efficient brute force (aka easy and well known) ways to minimize the nonlinearities in fiber that they did not even consider...and to achieve well over 3 bps/Hz...so their paper is not worth the pulp it was printed on!

Sorry to say this is a typical ivory tower, tunnel vision paper...hyped to the max...designed to derive a clever (but very wrong) answer...

Enough time wasted on this....

-Own

need to equalize) are present in linear systems.

The fact that it is difficult to achieve the

capacity of a linear channel does not speak to

the capacity itself.

FEC does not distinguish linear from nonlinear

channels. To get close to capacity you certainly

need error correction in any system.

All communication systems have

nonlinearities. Even vacuum has some,

theoretically. The real question is, to take

the nonlinear effects into account in a given

system with given parameters. *Long haul*

optical communications unfortunately suffer

from severe nonlinear effects. These are well

known; what has not been understood before is

how to estimate the capacity limitations from

the nonlinear effects.

Of course, if you take a short piece of

optical fibre, you don't see the nonlinear

effects at issue here: so you have to be

specific about system length, etc. If you take

a few meters of fibre, nonlinear effects are

pretty much completely negligible. If you were

to intersperse repeaters with very short

spans of fibre, the capacity limits would

approach that of a linear system. Of course,

this is not economically feasible.

If you read the original article carefully,

which is in the context of long haul optical

communications, the relevant questions are discussed.

Best,

ppm.

Would it be ok for you to name them?

Thanks

nano

Let me teach you something...a Copper wire system is far, far from linear...to get that kind of density (10bps/Hz) requires some real hard work in equalization and FEC...and it is all done with less than 20 dB SNR and in the presence of echo and crosstalk...makes the non-linearities in fiber look like child play...

Just shows that you should not go to wideband digital OOK signals...

There are a couple of companies out there that are utilizing just this kind of technology (analog optical carrier and exotic modulation), so that if scaled, it would far surpass the figures sited in the article...and doing it in fiber...with greatly REDUCED nonlinear effects...

At least one is in field trial with a major carrier.

-Own

Basically anyone putting RF carriers down fiber...that is the whole HFC market...

-Own

should have read 16bits/s/Hz.

the modulater/demodulator is useful *upto* the

basic channel capacity. A 10bits/s/Hz (or for

that matter 10bits/s/Hz) modem is fine over a

a linear channel like copper wire, say - since

those channels can support high bit rates. The

point is that nonlinearities limit the capacity

of optical fiber to significantly smaller values

than the linear channels traditionally used in

telecommunications. The capacity of a 10 bit

modem attached to a 3 bit channel is still

3 bits ...

I don't post here, just thought I should point

out the conceptual error in the last message.

Best,

ppm.

Bottom line: There are much more efficient ways of transmitting information over fiber than commonly employed today. DWDM/OOK is just plain wasteful of bandwidth...

I would however be concerned about the need for more (unlit) fiber in the future...demand will stabilize in the face of high bandwidth growth, as people figure out how to stuff more into a single fiber...

-Own

Curious

electric field poling for rewrtiable

interferance patterns for data storage.

http://colossalstorage.net/col...