LANL, 02/05/03. Shedding and Interaction of solitons in imperfect medium. Misha Chertkov (Theoretical Division, LANL). In collaboration with Ildar Gabitov (LANL) Igor Kolokolov (Budker Inst.) Vladimir Lebedev (Landau Inst.) Yeo-Jin Chung (LANL) Sasha Dyachenko (Landau Inst.).
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Shedding and Interaction of solitons in imperfect medium
Misha Chertkov(Theoretical Division, LANL)
In collaboration with
Ildar Gabitov (LANL)
Igor Kolokolov (Budker Inst.)
Vladimir Lebedev (Landau Inst.)
Yeo-Jin Chung (LANL)
Sasha Dyachenko (Landau Inst.)
``Statistical Physics of
Zoltan Toroczkai (LANL)
Pavel Lushnikov (LANL)
Jamison Moeser (Brown U)
Tobias Schaefer (Brown U)
Avner Peleg (LANL)
averaging over amplifiers
NLS in the envelope approximation
- pulse width
- nonlinearity length
- pulse amplitude
Dispersion balances nonlinearity
Integrability (Zakharov & Shabat ‘72)
Nonlinear Schrodinger Equation
Gabitov, Turitsyn ‘96
Turitsyn et al/Optics Comm
163 (1999) 122
Lin, Kogelnik, Cohen ‘80
Noise is conservative
Abdullaev and co-authors ‘96-’00
Noise in dispersion. Statistical Description.
DSF, Gripp, Mollenauer Opt. Lett. 23, 1603, 1998
Measurements from only one end of fiber by
phase mismatch at the Stokes frequency
Mollenauer, Mamyshev, Neubelt ‘96
Questions:Does an initially localized pulse
Are probability distribution functions
of various pulse parameters getting
Describes slow evolution of the original field
if nonlinearity is weak
Nonlinearity dies (as z increases)
== Pulse degradation
Noise is strong
D >> 1
Question:Is there a constraint that one can impose on the random chromatic
dispersion to reduce pulse broadening?
the accumulated dispersion should be pinned to zero
periodically or quasi-periodically
The nonlinear kernel
does not decay (with z) !!!
noise and pinning period
The averaged equation
does have a steady (soliton like)
solution in the restricted case
Restricted (pinned) noise
does have a steady solution
Restricted (pinned) noise. DM case.
Fourier split-step scheme
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.
US patent+PNAS 98, 14211 (2001)
M.C.,I.G., P. Lushnikov, Z.Toroczkai, JOSAB (2002)
in imperfect medium
JETP Lett. 10/01
MC, Y. Chung, A. Dyachenko, IG,IK,VL PRE Feb 2003
Second order adiabatic pert. theory
(Kaup ’90) +
*What statistics does describe the radiation emitted due to disorder
by a single soliton, pattern of solitons?
How far do the radiation wings extend from the peak of the soliton(s)?
What is the structure of the wings?
*How strong is the radiation mediating interaction between the solitons?
How is the interaction modified if we vary the soliton positions
and phases within a pattern of solitons?
soliton is distinguishable from
the radiation at any z
Radiation tail + forerunner
Soliton position shift is
Gaussian zero mean
The z-dependence is similar
to the one described by
Infinite pattern(continuous flow of information)
Single soliton decay
We planned to addressed: