# Presentation: 303614

## Statistical physics approach 

- _to evaluation of __outage probability__ _
- _in __optical communications_

- Misha Chertkov (Theoretical Division, LANL)

- _In collaboration with_
- Vladimir Chernyak (Corning)
- Ildar Gabitov (LANL + Tucson)
- Igor Kolokolov (Landau Inst.)
- Vladimir Lebedev (Landau Inst.)
- Avner Peleg  (LANL)

## What is the idea:  Fiber Optics + Statistics.

- What is the idea:  Fiber Optics + Statistics.
- Introduction: Material. Fiber Electro-dynamics. Noise. Disorder.
-  _***Impairment***_** **                                                          **  **_***Consequence***_** **** **
- Amplifier Noise                                      jitter, degradation
- Birefringent disorder                            Polarization Mode Dispersion
-                                                             broadening, pulse splitting, jitter

_**Joint effect**__** of **__**noise**__** and  **__**birefringent **__**disorder**_

-    Bit-error-rate. Does it fluctuate?
- How to evaluate/calculate BER (<<1) ?

-     Practical consequences
-  for optical communications

-      Theoretical interest
- e.g. analogy with spin-glasses

## Fiber Electrodynamics

## Linear    vs    Nonlinear

## Polarization

## Additive (amplifier) noise

_*Linear:*_
- jitter and amplitude degradation
- are equally important

_*Soliton:*_
- jitter essentially more important
- than amplitude degradation
-                             Elgin (1985)
-                                   Gordon-Haus

- short correlated !
-    i.e. different for
-    different pulses

##         Disorder in Birefringence

## Polarization Mode Dispersion (PMD)

- pulse splitting
- broadening
-      jitter

##  1               1              1               0              0

-  1               1              1               0              0

- input

- output

## Bit-Error-Rate

## Filters and ``tricks”

## Noise and disorder.   Order of averaging.

_*Linear model*_

## C. Xie, H. Sunnerud,

- M. Karlsson, P.Andrekson,
- ``Polarization-Mode
- Dispersion-Induced in soliton
- Transmission systems”,
- IEEE Photonics Techn. Lett.
- Vol.13,Oct. 2001.

- Monte-Carlo numerics
- with 10 000 fiber realizations
- (artificial rescaling of decision
- level)

## Noise average

_**Noise average**_

- in the interesting range one
-  has to keep in
- only the leading in            term!!

## Optical filter always applies

## Bare case

- _PDF of Bit-Error-Rate_

- Saddle-point
- (optimal fluctuation)
-  calculations

- Setting the clock

- First order compensation (nonzero chirp)

- First order compensation (zero chirp)

## Slide 17

## C. Xie, H. Sunnerud,

- M. Karlsson, P.Andrekson,
- ``Polarization-Mode
- Dispersion-Induced in soliton
- Transmission systems”,
- IEEE Photonics Techn. Lett.
- Vol.13,Oct. 2001.

## Example:

## Higher-order compensation

## Slide 21

## Linear

- V.Chernyak,MC,I.Kolokolov,V.Lebedev
- Phys.RevE to appear; Optics. Lett. 28, (2003);  Optics. Express. 11, 1607 (2003);
- JETP Lett. 78, 198-201 (2003)
- VC,MC,I. Gabitov,IK,VL,
- to appear in special issue of Journal of Lightware Technology (invited)
_***Nonlinear( soliton transmission)***_
- VC,MC,IK, Avner Peleg
- submitted to Euro.Phys.Lett

_*Bare case*_

- Soliton jitter (due to noise) is the dominant destructive factor

## Extended (algebraic like) tail of the double statistics !!

_***Functional Order Parameter ***__***approach***__*** ***_
_***for ***__***glassy***__*** states in infinite-range exchange ***__***spin systems***_
_***Double ***__***(super)***__*** statistics***_

- Amplifier                      Noise                      Thermal
- Birefringent                 Disorder                  Exchange,    J
- Pulse intensity                                     Glassy states overlap,   q
-                                        PDF
- BER                                        Overlap Probability,

- Extended (algebraic like) tail of the double statistics !!

- No replicas!!!

- Replicas+Numerics

## Conclusions

-           Noise  and  disorder
-               CAN   NOT
-        be considered separately !

- Probability Distribution Function of BER
-                                is
- the proper method/tool of extreme outages (for PMD)
-                   and their compensation analysis

-          No other alternative to the theory
-    in evaluation of the extremely low valued BER