Computer Simulation of Transition Regimes of Solitons in Stimulated Raman Scattering with Excitation of Polar Optical Phonons

Galyna Feshchenko,Vladimir Feshchenko

doi:10.4236/ajcm.2015.53031

Abstract

The system of nonlinear equations modeling the process of nonstationary stimulated Raman scattering (SRS) in noncentrosymmetric crystals for the waves on laser, Stokes, polariton, and phonon frequencies is investigated by using the numerical methods. The general case for amplitudes of waves that resulted in doubling of the number of equations is considered. It is shown that the application of the methods of finite differences to the computer simulation of transition regimes is completely consistent with the analytical results found for the asymptotical solutions in form of solitons. The obtained results also indicate that the laser pulses of Gaussian shape appearing at the boundary of nonlinear medium tend to become solitons of Lorentzian shape. It was also found that the formation of solitons occurs when the vibrations of optical phonons and that of electromagnetic wave were either in or out of phase. It is shown that all electromagnetic waves entering the medium with different speeds become solitons having the same speed. In the second part of the paper we considered the computer simulation of soliton stability with respect to small (weak) perturbations of all interacting waves. In the present paper we considered the case of evolution of those disturbances in the vicinity of peaks of solitons. The numerical analysis showed that in wide range of parameters the solitons were stable.

Highlights

IntroductionA fast progress in producing ultrashort pulses stimulates the constantly growing interest in obtaining the additional information on both the optical characteristics of matter (the longitudinal and transverse relaxation times, the constants of the transition, etc.) and the possibility of creation of super short pulses propagating in a medium without energy losses [1] [2]
A fast progress in producing ultrashort pulses stimulates the constantly growing interest in obtaining the additional information on both the optical characteristics of matter and the possibility of creation of super short pulses propagating in a medium without energy losses [1] [2]
Using different numerical methods in computer simulation of space-time evolution of the interacting waves is the effective approach in analysis of the equations analytical solutions of which could not be found [9]-[11]

Summary

Introduction

A fast progress in producing ultrashort pulses stimulates the constantly growing interest in obtaining the additional information on both the optical characteristics of matter (the longitudinal and transverse relaxation times, the constants of the transition, etc.) and the possibility of creation of super short pulses propagating in a medium without energy losses [1] [2]. One of the effects that results in solitons is SRS under the conditions of the interaction of ultrashort pulses of exciting and Stokes radiation in a medium [3]-[5]. To make clear, whether the SRS pulses go over to the soliton regime, it is necessary to solve the complete set of nonstationary equations which describes the temporal evolution of all interacting waves from the boundary of the medium. In this paper we use the assumption that solitons can exist if, at least, three conditions are satisfied: 1) the asymptotical solution in form of solitons is found; 2) the results of transition regime are consistent with the ones found in the previous part; 3) the obtained results are stable with respect to small (weak) perturbations.

Basic Equations

Finite-Difference Equivalent of Basic System of Equations

Transition Regime of the Stimulated Raman Scattering Solitons

Stability of the Stimulated Raman Scattering Solitons

Conclusion