# Surface waves with negative phase velocity supported by temperature-dependent hyperbolic materials

## TL;DR

This study explores how temperature-dependent hyperbolic materials can support surface waves, including those with negative phase velocity, with propagation characteristics changing with temperature and material composition.

## Contribution

It demonstrates the existence of negative phase velocity surface waves in temperature-sensitive hyperbolic materials and analyzes their propagation behavior.

## Key findings

- Negative phase velocity surface waves can occur at high temperatures.
- The angular range for NPV propagation varies with temperature and material composition.
- Multiple surface wave modes can propagate at high temperatures.

## Abstract

A numerical investigation was undertaken to elucidate the propagation of electromagnetic surface waves guided by the planar interface of two temperature-sensitive materials. One partnering material was chosen to be isotropic and the other to be anisotropic. Both partnering materials were engineered composite materials, based on the temperature-sensitive semiconductor InSb. At low temperatures the anisotropic partnering material is a non-hyperbolic uniaxial material; as the temperature is raised this material becomes a hyperbolic uniaxial material. At low temperatures, a solitary Dyakonov wave propagates along any specific direction in a range of directions parallel to the planar interface. At high temperatures, up to three different surface waves can propagate in certain directions parallel to the planar interface; one of these surface waves propagates with negative phase velocity (NPV). At a fixed temperature, the range of directions for NPV propagation decreases uniformly in extent as the volume fraction of InSb in the isotropic partnering material decreases. At a fixed volume fraction of InSb in the isotropic partnering material, the angular range for NPV propagation varies substantially as the temperature varies.