Vortex solitons in quasi-phase-matched photonic crystals with the third harmonic generation

TL;DR

This paper demonstrates the existence and stability of composite vortex solitons in a three-dimensional photonic crystal with third-harmonic generation, using a quasi-phase-matched quadratic nonlinearity with a specific checkerboard structure.

Contribution

It introduces a novel design of photonic crystals enabling stable composite vortex solitons with specific topological charges and phase-matching conditions, advancing nonlinear optics control.

Findings

Stable vortex solitons with different topological charges were found.

The solitons can propagate up to approximately 1 meter.

The structure can be fabricated with existing technologies.

Abstract

We report stable composite vortex solitons in the model of a three-dimensional photonic crystal with the third-harmonic (TH) generation provided by the quasi-phase-matched quadratic nonlinearity. The photonic crystal is designed with a checkerboard structure in the $\left( x\text{,}% y\right) $ plane, while the second-order nonlinear susceptibility, $d(z)$, is modulated along the propagation direction as a chains of rectangles with two different periods. This structure can be fabricated by means of available technologies. The composite vortex solitons are built of fundamental-frequency (FF), second-harmonic (SH), and TH components, exhibiting spatial patterns which correspond to vortex with topological charges $s=1$, a quadrupole with $s=2$, and an anti-vortex structure with $s = -1$, respectively. The soliton profiles feature rhombic or square patterns, corresponding to phase-matching conditions $\varphi =0$ or $\pi $, respectively, the rhombic solitons possessing a broader stability region. From the perspective of the experimental feasibility, we show that both the rhombic and square-shaped composite vortex solitons may readily propagate in the photonic crystals over distances up to $\sim 1$ m. The TH component of the soliton with $s=\mp 1$ is produced by the cascaded nonlinear interactions, starting from the FF vortex component with $s=\pm 1$ and proceeding through the quadrupole SH one with $s=2$. These findings offer a novel approach for the creation and control of stable vortex solitons in nonlinear optics.