Quasi-stable rotating solitons supported by a single spiraling waveguide

We investigate numerically light propagation in a single spiraling waveguide formed in a nonlinear photorefractive medium for high spatial frequency of the waveguide rotation. High here means above the frequencies that correspond to the stable rotary motion. The general procedure for finding exact fundamental solitonic solutions in the spiraling guiding structures is based on the modified Petviashvili’s iteration method. In the high frequency regime, the method gives only the solitons of low accuracy, that is, the quasi-stable solitonic solutions that radiate while propagating. Such solitons, still supported by the spiraling waveguide, perform quasi-stable rotational oscillatory motion, with inevitable soliton decay. We find that, for each set of physical parameters, there exists a beam power with minimal (in some cases practically negligible) wave radiation.