Physicists Find Fiber's Limit

Scientists from Bell Labs have calculated the theoretical limits on the carrying capacity of glass optical fiber and concluded that there's still a long way to go before optical systems reach those limits (see Bell Labs Calculates Limits). The results were published yesterday in the journal Nature.

Partha Mitra, lead author of the paper, says his work will point the way for future research by showing which approaches are likely to come up against fundamental physical limits and which aren't. It could also aid engineers whose task it is to model the enormously complicated properties of DWDM (dense wavelength-division multiplexing) systems.

Unlike system vendors, physicists measure the information-carrying capacity of a fiber in bit/s per Hertz of spectral bandwidth (bit/s/Hz). To find the capacity in Gbit/s or Tbit/s, this number has to be multiplied by the available bandwidth of a system (that's bandwidth in the physics sense, in Hz, rather than its common telecom usage, which essentially means capacity).

Mitra and his co-author Jason Stark calculated that the theoretical limit imposed by the physical properties of optical fiber on a communication system is about 3 bit/s/Hz. This corresponds to a maximum payload of 150 Tbit/s on a single fiber, assuming that the fiber can carry signals across the wavelength range 1260 to 1620 nanometers.

Mitra points out that all existing optical systems have a lower limit of 1 bit/s/Hz. That's because they encode data using a simple on-off keying technique, which represents bits by the presence or absence of light. "We've shown that the theoretical limits are substantially greater than this," he says. "What this means is that by changing the modulation scheme, it's possible to get more data into a fiber than was thought possible."

The downside? While the work at Bell Labs suggests that fiber has plenty of room to grow, new technologies -- more complicated modulation schemes and coherent detectors, which measure both power and phase of the incoming signal -- will be needed to make the most of it.

Few would argue with Bell Labs' rather basic conclusion -- that fiber has more capacity than is currently being used. It's a no-brainer. What's new is that the researchers have been able to quantify how much surplus capacity there is, something that can't be deduced from existing communications theory.

The classical formula for calculating capacity, known as Shannon theory, predicts that capacity will increase indefinitely as the power of the optical signal goes up. That's because the signal keeps getter stronger relative to the noise, which is fixed.

In real life, however, strange "non-linear" phenomena come into play, and start creating more noise at high optical power. Mitra calls it the cocktail-party effect. "If everyone's talking at once, then you have to raise your voice in order to be heard, and if everyone raises their voice, then you can't hear anything." Much the same thing can occur among channels in the same fiber generated by DWDM systems.

The origin of non-linear effects is the fact that, rather unexpectedly, the speed of light inside a silica fiber does depend on its intensity, or instantaneous power. (Remember, the speed of light is only constant in a vacuum.) This is most likely to be observed in DWDM systems where lots channels of data are packed into the same fiber, creating very high total optical powers.

"People knew that non-linearities were doing something, but they couldn't quantify it precisely," says Mitra.

Mitra and Stark were able to include non-linearities in the calculations for the first time. Why hadn't this been done before? Simply because it required some creative mathematical thinking to reduce the equations to ones that could be solved analytically.

— Pauline Rigby, Senior Editor, Light Reading
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ownstock 12/4/2012 | 8:06:07 PM
re: Physicists Find Fiber's Limit Clearly 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?
ppm 12/4/2012 | 8:06:34 PM
re: Physicists Find Fiber's Limit hahaha

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 (!)
ownstock 12/4/2012 | 8:06:36 PM
re: Physicists Find Fiber's Limit Exactly! 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.
ubwdm 12/4/2012 | 8:06:43 PM
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))

ownstock 12/4/2012 | 8:06:58 PM
re: Physicists Find Fiber's Limit Gentlemen, 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...
ubwdm 12/4/2012 | 8:06:59 PM
re: Physicists Find Fiber's Limit Check out Hajimiri model. I was surpised that
you mentioned L.G. Kazovsky's paper and not

The reference: The Design of CMOS radio-frequency
integrated circuits, by Thomas H. Lee of Stanford.

ppm 12/4/2012 | 8:07:02 PM
re: Physicists Find Fiber's Limit I 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 ...
ppm 12/4/2012 | 8:07:03 PM
re: Physicists Find Fiber's Limit Thanks for reiterating the point about adding
phase only signals producing amplitude noise.
I would have thought that was elementary. Oh

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.
ppm 12/4/2012 | 8:07:03 PM
re: Physicists Find Fiber's Limit Here'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.

calpole 12/4/2012 | 8:07:04 PM
re: Physicists Find Fiber's Limit Phase 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..

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