Exactly Solvable Model for Nonlinear Pulse Propagation in Optical Fibers
نویسنده
چکیده
The nonlinear Schrödinger (NLS) equation is a fundamental model for the nonlinear propagation of light pulses in optical fibers. We consider an integrable generalization of the NLS equation which was first derived by means of bi-Hamiltonian methods in [A. S. Fokas, Phys. D 87 (1995), 145–150]. The purpose of the present paper is threefold: (a) We show how this generalized NLS equation arises as a model for nonlinear pulse propagation in monomode optical fibers when certain higher-order nonlinear effects are taken into account; (b) We show that the equation is equivalent, up to a simple change of variables, to the first negative member of the integrable hierarchy associated with the derivative nonlinear Schrödinger equation; (c) We analyze traveling-wave solutions. PACS numbers (2008): 42.81.Dp, 02.30.Ik.
منابع مشابه
Time-Frequency (Wigner) Analysis of Linear and Nonlinear Pulse Propagation in Optical Fibers
Time-frequency analysis, and, in particular, Wigner analysis, is applied to the study of picosecond pulse propagation through optical fibers in both the linear and nonlinear regimes. The effects of firstand second-order group velocity dispersion (GVD) and self-phase modulation (SPM) are first analyzed separately. The phenomena resulting from the interplay between GVD and SPM in fibers (e.g., so...
متن کاملSpectrally Resolved Approach for Modeling Short Pulse Amplification in Er-Doped Fibers
We study pulse propagation in Er-doped fiber amplifiers (EDFA) within the framework of a spectrally resolved pulse rate-propagation equations model. Our model accounts for the effects of gain dispersion, gain saturation, waveguide and chromatic dispersion, and amplified spontaneous emission. This model allows us to approximate the effects of nonlinear resonant dispersion on short pulse amplific...
متن کاملCollective variable theory for optical solitons in fibers.
We present a projection-operator method to express the generalized nonlinear Schrödinger equation for pulse propagation in optical fibers, in terms of the pulse parameters, called collective variables, such as the pulse width, amplitude, chirp, and frequency. The collective variable (CV) equations of motion are derived by imposing a set of constraints on the CVs to minimize the soliton dressing...
متن کاملCoupled-mode theory approach to nonlinear pulse propagation in optical fibers.
The formalism of coupled-mode theory is adopted for describing nonlinear pulse propagation in optical fibers, the coupling being induced by the nonlinear part of the refractive index. This approach describes in a natural way the influence of the waveguide, and in principle allows of the possibility of investigating soliton propagation when more than one mode is excited.
متن کاملPhase analysis of nonlinear femtosecond pulse propagation and self-frequency shift in optical fibers
Phase sensitive analysis of femtosecond pulse propagation in optical fibers employing frequency resolved optical gating (FROG) is presented and compared to numerical simulations employing a modified cubic nonlinear Schr€ odinger equation (NLSE). Phase information obtained from deconvolution of the experimental traces allows the observation and characterization of specific pulse propagation feat...
متن کامل