Analytical solution for wave propagation through a graded index interface between a right-handed and a left-handed material

TL;DR

This paper provides an exact analytical solution for wave transmission and reflection in structures with graded index profiles involving left-handed materials, validated by numerical simulations, advancing understanding of wave behavior in complex media.

Contribution

It introduces a novel exact analytical solution to Helmholtz' equation for hyperbolic tangent graded index profiles involving left-handed materials.

Findings

Analytical expressions match numerical results accurately.

Model accommodates arbitrary spectral dispersion.

Enhanced understanding of wave behavior in graded index structures.

Abstract

We have investigated the transmission and reflection properties of structures incorporating left-handed materials with graded index of refraction. We present an exact analytical solution to Helmholtz' equation for a graded index profile changing according to a hyperbolic tangent function along the propagation direction. We derive expressions for the field intensity along the graded index structure, and we show excellent agreement between the analytical solution and the corresponding results obtained by accurate numerical simulations. Our model straightforwardly allows for arbitrary spectral dispersion.