Periods of Energy Exchange Under the Mutual Effects of Four-Wave Mixing, Self-Phase Modulation and Cross-Phase Modulation

In the present work a new regime of periodical energy exchange between pump, signal and idler waves, under the influence of the process of four-wave mixing (FWM), with additional consideration of the effects of self-phase modulation (SPM) and cross-phase modulation (XPM), is presented. In our previous papers a theoretical model which successfully describes the amplification and periodic energy exchange between the three optical waves in CW regime of laser source propagation (short-cut equations) was developed. Exact analytical solutions, describing the periodic changes in the intensities of pump, signal and idler waves, were found and expressed by the Jacobi elliptic functions. The period of the energy exchange between the waves can be presented by elliptic integral of the first kind. In the current research, the periods of energy exchange between the pump, signal and idler waves in the process of FWM, additionally taking into account the effects of SPM and XPM, are investigated. A comparison between the obtained results has been made. It is shown that the effects of self-phase modulation and cross-phase modulation increase the period of energy exchange.