# Presentation: 266947

## Pulse confinement 

_**in optical fibers**_
_**with random dispersion**_

_**Misha Chertkov**_** (LANL)  **
** ****Ildar  Gabitov ****(LANL)**
** ****Jamey Moser ****(Brown U.)**

- http:/cnls.lanl.gov/~chertkov/Fiber/

**Los Alamos,  03/13/01**

**Thanks to**
**I. Kolokolov**
**V. Lebedev**
**P. Lushnikov**
**Z. Torozkai**

## Fiber Electrodynamics, 

**Mono-mode, NLS,**
**Dispersion vs Kerr nonlinearity,**
**Dispersion management**

**Variations of fiber parameters, **
**Noise in NLS, **
**Statistics of pulse propagation:**
**objects, questions**

**Random dispersion, pinning,**
**pulse confinement.**
**Theory and numerics.**

**Polarization Mode Dispersion,etc**

## 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

_**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?

## Pinning method

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

## Restricted (pinned) noise

**Model A**

## Slide 9

## Restricted (pinned) noise.   DM case.

_**Strong  nonlinearity**_

## Slide 11

## Numerical Computations

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

_**Model A**_

_**Model B**_

## Slide 13

## Slide 14

## Slide 15

## 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.

## Polarization Mode Dispersion  (PMD)

- random birefringence

- MC,IG, I. Kolokolov,
-       T. Schaefer

-       Nonlinear PMD cannot be suppressed completely  but
-     an essential reduction of pulse broadening can be achieved

## Statistical Physics of Fiber Communications

***Problems to be addressed:***

_**Single pulse dynamics**_
**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?**

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