Directional coupling for solitary waves in quadratic nonlinearity

The propagation of temporal solitary waves, formed in the second-order nonlinear medium, is analysed in waveguide directional couplers. The influence of the thirdorder nonlinearity on the switching effect is also presented. Recently, the great effort of nonlinear guided-wave phenomena research is focused on the cascaded second-order process which can produce relatively large intensity-dependent phase changes of the wave propagating in optical waveguides [1-7]. Among a variety of nonlinear effects, the cascaded second order nonlinearity can be a source of forming temporal or spatial solitons [3-7]. The phase mismatched second harmonic generation (ω+ω) and difference frequency generation (2ω−ω) lead to effective intensity-dependent phase changes of the pulse at both frequencies. This allows to form the pair of solitary waves at fundamental frequency and second harmonics with amplitude envelopes not changed along the propagation. In this paper, the propagation of the temporal solitary waves, formed in the second-order nonlinear medium, is investigated in nonlinear directional couplers [8-12] (Fig.1). The slowly varying complex amplitudes of fundamental wave U and second harmonic V in the directional coupler structure fulfil equations [13]: M.A. Karpierz, Directional coupling for solitary waves .... 392