Photon gas with hyperbolic dispersion relations

TL;DR

This paper explores how hyperbolic dispersion relations in metamaterials alter the photon gas density of states, affecting black body radiation and thermodynamics, revealing behaviors akin to lower-dimensional systems.

Contribution

It provides a detailed analysis of the density of states and thermodynamics for photon gases in hyperbolic metamaterials, highlighting their unique spectral properties.

Findings

Spectral density vanishes at certain frequencies

Thermodynamic quantities resemble lower-dimensional photon gases

Hyperbolic dispersion leads to enhanced density of states

Abstract

We investigate the density of states for a photon gas confined in a nonmagnetic metamaterial medium in which some components of the permittivity tensor are negative. We study the effect of the resulting hyperbolic dispersion relations on the black body spectral density. We show that for both of the possible wavevector space topologies, the spectral density vanishes at a certain frequency. We obtain the partition function and derive some thermodynamical quantities of the system. To leading order, the results resemble those of a one- or two-dimensional photon gas with an enhanced density of states.