Nonparaxial solitons and their interaction dynamics in coupled nonlinear Helmholtz systems

Abstract

It is well-known that the nonparaxiality plays an important role in the fabrication of nanoscale devices. In this paper, we study the existence of nonparaxial solitons in a dimensionless coupled nonlinear Schrödinger system with cross-phase modulation (XPM), which enables the propagation of ultra-broad nonparaxial pulses in a birefringent optical waveguide. Despite the fact that the system is a nonintegrable one (Tamilselvan et al., 2020), we obtain a bright soliton solution analytically by employing the standard Hirota’s bilinearization method. Subsequently we numerically investigate the scattering dynamics of two and three bright solitary waves using the general solution as the seed one by adopting the split-step Fourier method based on the Feit-Flock algorithm. We explain how the soliton parameters such as separation distance and relative phase influence the interaction between the nonparaxial bright solitons. In particular, we report a bunch of interesting phenomena of soliton interactions, which include oscillating bound solitons when the phase of the two solitary waves are equal and parallel propagation as the phase is changed to out-of phase with a zig-zag pattern. Similarly the in-phase three solitary waves also exhibit a novel interaction which mimics a triple knot structure which has never been observed before in the framework of coupled nonlinear Helmholtz systems. We believe that our results would pave a way for future research generating optical memories based on the nonparaxial solitons.