Saddle point singularity and optical phase transition in bilayer hyperbolic metamaterials

TL;DR

This paper investigates the photonic density of states in bilayer hyperbolic metamaterials, revealing saddle point singularities and phase transitions analogous to electronic Fermi surfaces, with implications for optical properties.

Contribution

It introduces a theoretical and numerical analysis of van Hove singularities and Lifshitz phase transitions in hyperbolic metamaterials, highlighting their topological and spectral features.

Findings

Identification of van Hove singularity in photonic spectra

Observation of Lifshitz-type phase transition between hyperbolic states

Analogy between photonic and electronic Fermi surface behaviors

Abstract

We study theoretically and numerically high density of states for hyperbolic bilayered metamaterials (HMM). It reveals that density response of HMM is reminiscent of Fermi electronic band structure of metal or semiconductors. By the method of Green function a van Hove type singularity is found in photonic density spectra of HMM with saddle point localization on photonic Fermi surface (FS) of metamaterial. Similar to the electronic systems, the photonic FS experiences instabilities induced by the changes in volume fractions of its constituents that leads to the Lifshitz type zero-temperature phase transition between FS of types I and II hyperbolic states at the topology protected critical point.