Energy of natural interface modes

TL;DR

This paper investigates the thermodynamics of surface electromagnetic modes at interfaces between vacuum and lossy media, analyzing different density of states definitions and their implications for surface polaritons.

Contribution

It introduces a comprehensive analysis of thermodynamic properties of surface modes using various density of states definitions, including the Barash-Ginzburg approach, in dispersive and absorptive systems.

Findings

Different density of states definitions coincide for dissipationless materials

Thermodynamic functions are expressed in terms of density of states

Temperature dependence of surface mode thermodynamics is demonstrated

Abstract

The paper is devoted to the thermodynamics of normal surface electromagnetic fields within a nonuniform dispersive and absorptive system. This system is formed by vacuum and lossy medium separated by a plane interface. As a medium, we used dielectric and metal samples characterized by local and nonlocal optical properties. Thermodynamic properties of surface eigenmodes of plane interfaces are discussed. Various definitions of density of states and spectral characteristics of surface polaritons in equilibrium at the interface formed by vacuum and lossy medium are described and discussed. All formulas for thermodynamic functions are represented in terms of density of states. The generalized density of states is calculated based on the Barash-Ginzburg theory and dispersion relations for the surface states in different approaches. It is exemplified that different definitions of the density of states are identical in the case of dissipationless materials. The spectral functions and integrated over all frequencies thermodynamic characteristics and their temperature dependences are demonstrated.