Coupled three-color soliton-like pulses with equidistant frequencies at three-wave mixing in a medium with quadratic and cubic susceptibility

Abstract

As well-known, a laser pulses’ propagation in the mode of the multi-wave (or multi-color) solitons attracts considerable attention of researchers in connection with various problems of optical frequencies comb interaction with matter and optical communication, for example. Evidently, the developing of new methods for construction of multi-color solitons or soliton-like structures (or self-trapping structures) and finding their possible shapes is actual problem. Below a new approach for construction of such structures at three optical pulses’ interaction in a medium with combined quadratic and cubic nonlinear response with accounting for various processes of the frequency conversion, and degenerate four-wave mixing, self- and cross-modulation is presented. To construct a mode of three coupled laser pulses propagation without (or with little) changing of their shapes it is necessary to set the shape of the summed all pulses’ intensities with single maximum, which may corresponds to “flat” distribution. The shapes of three pulses are defined if the maximal intensities of all pulses are chosen. The phase differences between waves at doubled or tripled and fundamental frequencies should not change during their propagation but each pulse may be chirped. The necessary condition for such stable mode realization is written. Similar the classical soliton of nonlinear Schrödinger equation, the maximal intensity should correspond to pulses’ durations. Their optimal values can be found only by using computer simulation. The pulses with durations close to the optimal values undergo re-shaping. As a result, the required shapes of pulses for achieving a soliton-like mode of their propagation are obtained.