Azimuthons in weakly nonlinear waveguides of different symmetries

TL;DR

This paper demonstrates that weakly guiding nonlinear waveguides with different symmetries support stable rotating solitons called azimuthons, with their dynamics strongly influenced by waveguide shape and modulation depth.

Contribution

It reveals how waveguide symmetry affects azimuthon rotation and deformation, providing analytical and numerical insights into their stability and dynamics.

Findings

Circular waveguides support rigidly rotating azimuthons with predictable frequency.

Square waveguides cause azimuthons to deform and wobble, depending on modulation depth.

A critical modulation depth determines whether azimuthons rotate continuously or wobble.

Abstract

We show that weakly guiding nonlinear waveguides support stable propagation of rotating spatial solitons (azimuthons). We investigate the role of waveguide symmetry on the soliton rotation. We find that azimuthons in circular waveguides always rotate rigidly during propagation and the analytically predicted rotation frequency is in excellent agreement with numerical simulations. On the other hand, azimuthons in square waveguides may experience spatial deformation during propagation. Moreover, we show that there is a critical value for the modulation depth of azimuthons above which solitons just wobble back and forth, and below which they rotate continuously. We explain these dynamics using the concept of energy difference between different orientations of the azimuthon.