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Pulse confinement in optical fibers with random dispersion

Puebla, 12/06. Pulse confinement in optical fibers with random dispersion. Misha Chertkov (LANL) Ildar Gabitov (LANL) Jamey Moser (Brown U.). http:/cnls.lanl.gov/~chertkov/Fiber/. Fiber Electrodynamics, Mono-mode, NLS, Dispersion vs Kerr nonlinearity, Dispersion management.

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Pulse confinement in optical fibers with random dispersion

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  1. Puebla, 12/06 Pulse confinement in optical fibers with random dispersion Misha Chertkov (LANL) Ildar Gabitov (LANL) Jamey Moser (Brown U.) http:/cnls.lanl.gov/~chertkov/Fiber/

  2. 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, Multimode random coupling,etc

  3. Fiber Electrodynamics • Monomode • Weak nonlinearity, • slow in z rescaling averaging over amplifiers NLS in the envelope approximation

  4. - peak pulse - Kerr nonlinearity - nonl. retractive index - wavelength - core area - group velocity - char. pulse width - second order dispersion Fiber parameters and jargon Typical values for Dispersion Shifted Fiber (DSF)

  5. - dispersion length - pulse width - nonlinearity length - pulse amplitude Soliton solution Dispersion balances nonlinearity Integrability (Zakharov & Shabat ‘72) Model A Nonlinear Schrodinger Equation

  6. Breathing solution - DM soliton • no exact solution • nearly (but not exactly) Gaussian shape • mechanism: balance of disp. and nonl. Gabitov, Turitsyn ‘96 Smith,Knox,Doran,Blow,Binnion ‘96 Turitsyn et al/Optics Comm 163 (1999) 122 Model B Dispersion management 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

  7. Stochastic model (unrestricted noise) Noise is conservative No jitter Abdullaev and co-authors ‘96-’00 Answers (analytical & numerical) Noise in dispersion 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 Questions:Does an initially localized pulse survive propagation? Are probability distribution functions of various pulse parameters getting steady?

  8. Describes slow evolution of the original field Nonlinearity is weak (first diagram) Unrestricted noise Nonlinearity dies (as z increases) == Pulse degradation Question:Is there a constraint that one can impose on the random chromatic dispersion to reduce pulse broadening?

  9. The restricted model Periodic quasi-periodic Random uniformly distributed ]-.5,.5[ Pinning method Constraint prescription: the accumulated dispersion should be pinned to zero periodically or quasi-periodically

  10. The nonlinear kernel does not decay (with z) in the restricted case !!! unrestricted restricted DM case The averaged equation does have a steady (soliton like) solution in the restricted case Restricted (pinned) noise

  11. Numerical Computations Fourier split-step scheme Fourier modes Model A Model B

  12. Mollenauer, et al. Opt. Lett. 25, 704 (2000) Long haul transmission experiments on fibers constrained from the spans of different types. The periodic compensation of the overall dispersion to the fixed residual value (achieved via insertion of an extra span) optimizes propagation of pulses. 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.

  13. Fibrulence == FiberTurbulence 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 • ...

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