# Surface-plasmon-polariton wave propagation supported by anisotropic materials: multiple modes and mixed exponential and linear localization characteristics

## TL;DR

This paper investigates surface-plasmon-polariton (SPP) wave propagation at interfaces involving anisotropic materials, revealing multiple modes, unique decay characteristics, and conditions for their existence, expanding understanding of plasmonic wave behavior.

## Contribution

It introduces the concept of SPP-V waves with mixed exponential and linear decay in anisotropic materials and provides explicit solutions for their dispersion relations.

## Key findings

- Multiple SPP modes can propagate in anisotropic interfaces.
- SPP-V waves exhibit combined exponential and linear decay.
- Conditions for SPP-V wave existence are analytically established.

## Abstract

The canonical boundary-value problem for surface-plasmon-polariton (SPP) waves guided by the planar interface of a dielectric material and a plasmonic material was solved for cases wherein either partnering material could be a uniaxial material with optic axis lying in the interface plane.Numerical studies revealed that two different SPP waves, with different phase speeds, propagation lengths, and penetration depths, can propagate in a given direction in the interface plane; in contrast, the planar interface of isotropic partnering materials supports only one SPP wave for each propagation direction. Also, for a unique propagation direction in each quadrant of the interface plane, it was demonstrated that a new type of SPP wave--called a surface-plasmon-polariton-Voigt (SPP-V) wave--can exist. The fields of these SPP-V waves decay as the product of a linear and an exponential function of the distance from the interface in the anisotropic partnering material; in contrast, the fields of conventional SPP waves decay only exponentially with distance from the interface. Explicit analytic solutions of the dispersion relation for SPP-V waves exist and help establish constraints on the constitutive-parameter regimes for the partnering materials that support SPP-V-wave propagation.