Inverse design of third-order Dirac exceptional points in photonic crystals

TL;DR

This paper introduces an inverse-design approach to create photonic crystals with complex spectral degeneracies, specifically third-order Dirac exceptional points, leading to enhanced spontaneous emission rates.

Contribution

It presents a novel inverse-design method for discovering photonic structures with higher-order spectral degeneracies, including the first demonstration of third-order Dirac exceptional points in photonic crystals.

Findings

Demonstrated photonic crystals with third-order Dirac points formed by accidental mode degeneracy.

Showed that at EP3, the spontaneous emission rate can be enhanced by a factor of 8 in passive structures.

Suggested larger enhancements are possible with gain or higher-order exceptional points.

Abstract

We propose a novel inverse-design method that enables brute-force discovery of photonic crystal (PhC) structures with complex spectral degeneracies. As a proof of principle, we demonstrate PhCs exhibiting third-order Dirac points formed by the \emph{accidental} degeneracy of modes of monopolar, dipolar, and quadrupolar nature. We show that under suitable conditions, these modes can coalesce and form a third-order exceptional point (EP3), leading to diverging Petermann factors. We show that the spontaneous emission (SE) rate of emitters at such EP3s, related to the local density of states, can be enhanced by a factor of 8 in purely lossy (passive) structures, with larger enhancements $\sim \sqrt{n^3}$ possible at exceptional points of higher order $n$ or in materials with gain.