“…However, due to the instability of one-dimensional NSWs [14,15], this interest shifted towards a search for two-dimensional structures localized near various guiding systems [16]. We studied the formation of two-dimensionally localized NSWs, i.e., nonlinear surface beams (NSBs), in numerical experiments in which the interface of the media was "irradiated" by grazing beams of certain shape [17,18]. In this paper, the main attention is paid to seeking of the optimal (with respect to their efficiency for NSB excitation [19]) region of parameters for Gaussian beams of TE waves incident onto the interface from the linear medium at an angle exceeding that of total internal reflection.…”