A direct perturbation approach to optical soliton propagation with Raman scattering and cross phase modulation

Abstract

The propagation of self-frequency shift of femtosecond soliton pulses is inevitably faced by self-frequency shift, which arises from the Raman effect. The non-linear phenomenon of cross phase modulation (XPM), arising from the collisions between pulses of different frequency, has been proposed as a way to counterbalance the shift in frequency and the subsequent time displacement. However, the co-existence of different frequency channels gives rise to new phenomena, like cross frequency shift and energy exchange between the channels, again due to the Raman effect. The current work is an analytical approach to the phenomena that arise during the co-propagation of sub-picosecond soliton pulses of different frequency. The analysis is based on the direct perturbation method, used on two couple NLS equations and provides insight to the spectral and temporal evolution of the pulses, and to their amplitudes' evolution as well. We look into the effects of incomplete and complete pulse collisions, while the pulses used in the examination are not only of equal widths.