Computer Simulation of Transition Regimes of Solitons in Four-Photon Resonant Parametric Processes in Case of Two-Photon Resonance

Vladimir Feshchenko,Galina Feshchenko

doi:10.4236/ajcm.2016.63028

Abstract

The transition regimes of solitons in four-photon resonant processes in the case of two-photon absorption of the fundamental radiation are numerically investigated. The standard system of equations for the amplitudes of probability of finding the system in state with certain energy is used to derive the expression for the induced polarization in the nonlinear medium. As for the equations for the amplitudes of the optical pulses, the general case is considered in which both the amplitudes and phases are space-time dependent. We focus on the finite difference methods and the case of simultaneously propagating solitons at all frequencies of the interacting waves (simultons). The obtained results indicate that upon certain threshold conditions all interacting pulses become the solitons of Lorentzian shape. The numerical analysis has also shown that the soliton amplitudes significantly depend on the ratio between the nonlinear polarizability at the fundamental frequency ω0 and that of combination of ω0 and the trigger-field frequency ω1(2ω0 + ω1). In the second part of the paper, we apply the method of phase planes to show that at typical values of parameters, the solitons are stable.

Highlights

Solitons or self-reinforcing solitary waves can emerge spontaneously in a physical system in which some energyHow to cite this paper: Feshchenko, V. and Feshchenko, G. (2016) Computer Simulation of Transition Regimes of Solitons in Four-Photon Resonant Parametric Processes in Case of Two-Photon Resonance
If a system possesses the necessary properties to allow the existence of solitons, it is highly likely that any large excitation will lead to their formation [1]-[3]
The present paper is devoted to the computer simulation of transition regimes of resonant four-photon interaction (RFPI) solitons in the case of two-photon resonance

Summary

Introduction

How to cite this paper: Feshchenko, V. and Feshchenko, G. (2016) Computer Simulation of Transition Regimes of Solitons in Four-Photon Resonant Parametric Processes in Case of Two-Photon Resonance. In our previous research [8], we established the possibility of the existence of simultons (simultaneously propagating solitons at different frequencies) in the case of nonstationary Raman scattering with excitation of polar optical phonons under the conditions of the interaction of ultrashort pulses of exciting and Stokes radiation in nonlinear crystals. The second topical problem in modern nonlinear optics is the production of coherent and frequency-tunable radiation in the far ultraviolet (UV) and infrared (IR) In these spectral areas, solid materials have broad absorption bands and this narrows down the application of nonlinear crystals for the generation of electromagnetic radiation. The present paper is devoted to the computer simulation of transition regimes of RFPI solitons in the case of two-photon resonance.

Fundamental Principle

Transition Regime

Stability

Conclusion