Parametric waves trapping in active periodic structures with quadratic nonlinearity under strong group velocity mismatch

Studies focusing on formation and stable propagation of two-color solitons in active periodic structures are essential and in great demand. Previously, the formation of four-wave soliton in active periodic structure under SHG was investigated analytically and numerically for group synchronism of interacting waves in the framework of the coupled waves approach. In the present work, we focus on the peculiarities of the four-wave soliton formation under strong group mismatch of the interaction waves. Our investigation is based on the four coupled Schrödinger-type equations for forward and backward waves on the fundamental and doubled frequencies. The influence of the difference in the waves velocities on the transmitting and reflective properties of the active periodic structure was also studied.