Discrete and Weyl density of states for photonic dispersion relation

Abstract

The current density of states (DOS) calculations do not take into account the essential discreteness of the state space, since they rely on the unbounded continuum approximation. Recently, discrete DOS based on the quantum-mechanically allowable minimum-energy interval has been introduced for the quadratic dispersion relation. In this work, we consider systems exhibiting a photonic (photon-like) dispersion relation and calculate the related density and number of states (NOS). Also, a Weyl’s conjecture-based DOS function is calculated for photons and acoustic phonons at a low-frequency limit, by considering the bounded continuum approach. We show that the discrete DOS function reduces to expressions of bounded and unbounded continua in the appropriate limits.