Quasi-soliton solution to the model of two-color optical waves in PT-symmetry structures

Soliton propagation of laser radiation in various nonlinear media is of great importance because of its numerous applications. Active periodic structures with parity-time symmetry provide the possibility for the solitons generation due to the balance of energy gain and loss. In the present paper, we derive an approximate analytical soliton solution to a model of two-color laser radiation propagation in an active periodic structure. The model describes the interaction of four coupled counterpropagating waves and consists of four nonlinear Schrödinger equations with respect to slowly varying envelopes for waves at the fundamental and doubled frequencies. It takes into account Bragg coupling and asymmetric Bragg coupling at both frequencies. Under the assumption of large detuning from Bragg resonance at the doubled frequency, we used a multiple scales approach to derive an approximate analytical two-color soliton solution. The obtained quasi-soliton solution was verified in a numerical experiment on the basis of a conservative finite-difference scheme. The stability of the obtained quasi-soliton was also investigated numerically.