Semidiscrete optical vortex droplets in quasi-phase-matched photonic crystals

TL;DR

This paper proposes a novel scheme for creating semidiscrete self-trapped optical vortex droplets in a continuous photonic crystal with quadratic and cubic nonlinearities, revealing stable multistable states and potential for transmitting structured light.

Contribution

It introduces a fully continuous medium approach to semidiscrete vortex droplets in photonic crystals with quasi-phase-matching, expanding beyond previous discrete or hybrid systems.

Findings

Identification of two types of vortex droplets: onsite- and intersite-centered.

Mapping of stability regions for different stripe numbers .

Demonstration of multistability with degenerate states.

Abstract

A new scheme for producing semidiscrete self-trapped vortices (\textquotedblleft swirling photon droplets\textquotedblright ) in photonic crystals with competing quadratic ($\chi ^{(2)}$) and self-defocusing cubic ($\chi ^{(3)}$) nonlinearities is proposed. The photonic crystal is designed with a striped structure, in the form of spatially periodic modulation of the $\chi ^{(2)}$ susceptibility, which is imposed by the quasi-phase-matching technique. Unlike previous realizations of semidiscrete optical modes in composite media, built as combinations of continuous and arrayed discrete waveguides, the semidiscrete vortex droplets are produced here in the fully continuous medium. This work reveals that the system supports two types of semidiscrete vortex droplets, \textit{viz}., onsite- and intersite-centered ones, which feature, respectively, odd and even numbers of stripes, $\mathcal{N}$. Stability areas for the states with different values of $\mathcal{N}$ are identified in the system's parameter space. Some stability areas overlap with each others, giving rise to multistability of states with different $\mathcal{N}$. The coexisting states are mutually degenerate, featuring equal values of the Hamiltonian and propagation constant. An experimental scheme to realize the droplets is outlined, suggesting new possibilities for the long-distance transmission of structured light carrying orbital angular momentum in nonlinear media.