Vortex solitons in large-scale waveguide arrays with adjustable discrete rotational symmetry

TL;DR

This paper investigates how adjustable discrete rotational symmetry in large-scale elliptical waveguide arrays influences vortex soliton properties, stability, and phase singularity splitting, providing insights into their behavior in nonlinear optical systems.

Contribution

It introduces a method to control vortex soliton characteristics by varying the array's discrete rotational symmetry without changing the number of waveguides.

Findings

Higher-order vortex singularities split into charge-1 singularities when symmetry is restricted.

Stable vortex solitons are predominantly higher-charge in arrays with adjustable symmetry.

Variation in symmetry significantly affects the stability and linear modes of vortex states.

Abstract

We consider vortex solitons in large-scale arrays composed of N elliptical waveguides placed on a ring, which can be fabricated using fs-laser writing technique in transparent nonlinear dielectrics. By introducing variable twist angles between longer axes of neighboring elliptical waveguides on a ring, we create circular arrays with adjustable discrete rotational symmetry ranging from C_N to C_1, when the number of waveguides N on the ring remains fixed. This allows to consider the impact of discrete rotational symmetry on the properties of available vortex solitons without changing the number of guiding channels in the structure, and to predict how exactly splitting of higher-order phase singularities into sets of charge-1 singularities occurs in vortex states, when they are forbidden by the discrete rotational symmetry of the structure that imposes the restrictions on the maximal possible vortex charge. It is found that separation between split charge-1 phase singularities in such higher-order vortex states increases with increase of the order of solution. We also study linear spectra of such arrays and show how variation of their discrete rotational symmetry affects linear eigenmodes, whose combinations can give rise to vortex modes. We also show that variation of discrete rotational symmetry in arrays with fixed number of guiding channels N has strong impact on stability of vortex solitons. Thus, only higher-charge vortex solitons are stable in such large-scale arrays and the number of stable states typically decreases with decrease of the order of discrete rotational symmetry of the structure at fixed N.