# Nonlinear TM Modes of the Symmetric Hyperbolic Slab Waveguide

## TL;DR

This paper theoretically investigates nonlinear TM modes in a symmetric hyperbolic slab waveguide, revealing how mode properties depend on field intensity and nonlinear effects, including the possibility of zero propagation constants.

## Contribution

It introduces a detailed analysis of nonlinear TM modes in hyperbolic slab waveguides, including dispersion relations and the impact of nonlinearities on mode behavior.

## Key findings

- Modes have two cut-off frequencies when core permittivity exceeds hyperbolic medium's extraordinary permittivity.
- Zero propagation constants are possible, especially in self-defocusing media with increased field intensity.
- Mode width and propagation constant depend on radiation intensity, showing nonlinear modulation effects.

## Abstract

Guided wave modes in a symmetric slab waveguide formed by an isotropic dielectric layer with cubic nonlinear response placed in the hyperbolic surrounding medium are investigated theoretically. Optical axis of the hyperbolic medium is normal to the slab plane. If dielectric permittivity of the waveguide core is more than extraordinary permittivity of the hyperbolic medium each TM mode has two cut-off frequencies. The dispersion relations for these modes are found and numerically solved for cases of focusing and defocussing medium of the core. Number of possible modes at given frequency depends on the applied field intensity. It is shown that zero values of the TM modes propagation constants are possible in the waveguide. Moreover in the self-defocussing case they can be obtained by increasing field intensity. The dependence of a propagation constant and width of the mode on radiation intensity is obtained and analyzed.