# Reflection and transmission in nonlocal susceptibility models with multiple resonances

## TL;DR

This paper develops a comprehensive model for electromagnetic reflection and transmission in nonlocal dielectric materials with multiple resonances, incorporating boundary effects and exciton dispersion, and analyzes their spectral energy densities.

## Contribution

It introduces exact formulas for reflection and transmission in multi-resonance nonlocal media with arbitrary boundary conditions, extending existing models to include exciton dispersion and multiple resonances.

## Key findings

- Improved single-band approximation for exciton bands
- Extended model to include linear $k$ terms in dispersion
- Calculated spectral energy density for various multi-resonance models

## Abstract

We consider a semi-infinite dielectric with multiple spatially dispersive resonances in the susceptibility. The effect of the boundary is described by an arbitrary reflection coefficient for polarization waves in the material at the surface, with specific values corresponding to various additional boundary conditions (ABCs) for Maxwell's equations. We derive exact expressions for the electromagnetic reflection and transmission coefficients and present the results for a variety of materials with multiple exciton bands. We find an improved single-band approximation for heavy/light exciton bands and extend our model to exciton dispersion relations with linear $k$ terms which occur in uniaxial crystals. Finally, we calculate the spectral energy density of thermal and zero-point radiation for a variety of multi-resonance models and ABCs.