# Presentation: 477286

## Shedding and Interaction of solitons in imperfect medium

- Misha Chertkov (Theoretical Division, LANL)

- LANL, 02/05/03

*``Statistical Physics  of  *
*Fiber Optics *
*Communications”*

- Zoltan Toroczkai (LANL)
- Pavel Lushnikov (LANL)
- Jamison Moeser (Brown U)
- Tobias Schaefer (Brown U)
- Avner Peleg (LANL)

- _In collaboration with_
- Ildar Gabitov (LANL)
- Igor Kolokolov (Budker Inst.)
- Vladimir Lebedev (Landau Inst.)
- Yeo-Jin Chung (LANL)
- Sasha Dyachenko (Landau Inst.)

## What was the idea? Fiber Optics. Statistics.

- What was the idea? Fiber Optics. Statistics.
- What we did first (Pinning method of pulse confinement in a fiber with fluctuating dispersion)
- What we did recently (_Shedding and interaction of solitons in imperfect medium_)
- Other activities and plans (Polarization Mode Dispersion, Wave-length Division Mulitplexing, Dispersion Management, etc)
-  Suggestions for Extensive DNS, Experiment, Field Trials

## Fiber Electrodynamics

## Nonlinear Schrodinger Equation

**Model A**

## Dispersion management

**Model B**

- Lin, Kogelnik, Cohen ‘80

- dispersion compensation aims to prevent
- broadening of the pulse (in linear regime)
- four wave mixing (nonlinearity) is suppressed
- effect of additive noise is suppressed

## Noise in dispersion. Statistical Description.

_**Questions:**_** **Does an initially localized pulse
-                   survive propagation?
-                   Are probability distribution functions
-                   of various pulse parameters getting
-                   steady?

**DSF,  Gripp, Mollenauer Opt. Lett. 23, 1603, 1998**
**Optical-time-domain-reflection method.**
**Measurements from only one end of fiber by **
**phase mismatch at the Stokes frequency**
**Mollenauer, Mamyshev, Neubelt ‘96**

## Question:  Is there a constraint that one can impose on the random chromatic

-                               dispersion to reduce pulse broadening?

- Noise is strong
-     D >> 1

## Pinning method

- Constraint prescription:
-                                 the accumulated dispersion  should be pinned to zero
-                                 periodically or quasi-periodically

## Restricted (pinned) noise

**Model A**

## Slide 10

## Restricted (pinned) noise.   DM case.

_**Weak  nonlinearity**_

## Slide 12

## Numerical Simulations

**Fourier split-step scheme**
**          ****Fourier modes**
**  **

_**Model A**_

_**Model B**_

## Slide 14

## Slide 15

## Slide 16

## Moral

_*Practical recommendations for *__*improving*__* fiber system performance*_
_*that is *__*limited by randomness*__* in chromatic dispersion.*_
- The limitation originates from the accumulation of the integral
- dispersion. The distance between naturally occurring nearest zeros
- grows with fiber length. This growth causes pulse degradation.
- We have shown that the signal can be stabilized by periodic or
- quasi-periodic pinning of the accumulated dispersion.

- M.Chertkov,I. Gabitov,J.Moeser
- US patent+PNAS 98, 14211 (2001)
- M.C.,I.G., P. Lushnikov, Z.Toroczkai, JOSAB (2002)

## Shedding and Interaction of solitons

- I.Kolokolov, V.Lebedev,
- JETP Lett. 10/01
- MC, Y. Chung, A. Dyachenko, IG,IK,VL  PRE Feb 2003

_**Shedding and Interaction of solitons**_
_**     **__**in imperfect medium**_

- Model A

## Single Soliton Story

- “Asymptotic freedom”:
- soliton is distinguishable from
- the radiation at any  z

- Self-averaging

## Radiation tail + forerunner

## Interaction of Shedding Solitons

## Soliton position shift is

- Gaussian zero mean
- random variable

## Multi-soliton   case

- _Infinite pattern_ (continuous flow of information)

*The z-dependence is similar *
*to the one described by *
*Elgin-Gordon-Haus jitter*

## Pinning

- _Bare case_

- _Pinned case_

**Single soliton decay**

**Two-soliton interaction**

## Statistical Physics of Fiber Communications

***We planned to addressed:***

_**Single pulse dynamics**_
** ****Fluctuating dispersion **
** *****Dispersion Management and Fluctuations***
**Raman term +noise**
***Polarization Mode Dispersion***
**Additive (Elgin-Gordon-Hauss) noise optimization**
**Joint effect of the additive and multiplicative noises**
**Mutual equilibrium of a pulse and radiation closed in a box**
**   ****(****wave turbulence**** on a top of a pulse) driven by a noise**

_**Many-pulse, -channel interaction**_
**Statistics of the noise driven by the interaction**
**Suppression of the four-wave mixing (ghost pulses) by the pinning?**
**Dynamics in a channel under the WDM**

_**Multi mode fibers**_
** ****noise induced enhancement of the information flow**
** ****... **
**     **