Space-time optical vortices in planar coupled waveguides with quadratic nonlinearity

We study a possibility spatiotemporal optical vortices propagating in a structure consisting of two connected waveguides with quadratic nonlinearity. The system under study is a planar nonlinear crystal whose refractive index in cross-section has two maxima corresponding to two waveguides. In this case, the electromagnetic field can penetrate between the waveguides, and due to that a communication between waveguides is realized. We focus on the study of the propagation dynamics of spatiotemporal optical vortices in such a system varying the distance between waveguides, the initial time shift between beams, and the initial phase shift between them.