Topological aspects in the photonic crystal analog of single-particle transport in quantum Hall systems

TL;DR

This paper develops a perturbative theory for photonic transport in gyrotropic photonic crystals, demonstrating how to simulate quantum Hall effects for photons and proposing an experimental setup to observe topological phenomena.

Contribution

It introduces a novel perturbative approach to model topological quantum Hall physics in photonic crystals, bridging electronic and photonic topological systems.

Findings

Derived semiclassical equations for photon dynamics in gyrotropic crystals.

Showed permittivity grading can simulate electric and magnetic fields for photons.

Proposed an experimental configuration to observe photonic quantum Hall effects.

Abstract

We present a perturbative approach to derive the semiclassical equations of motion for the two-dimensional electron dynamics under the simultaneous presence of static electric and magnetic fields, where the quantized Hall conductance is known to be directly related to the topological properties of translationally invariant magnetic Bloch bands. In close analogy to this approach, we develop a perturbative theory of two-dimensional photonic transport in gyrotropic photonic crystals to mimic the physics of quantum Hall systems. We show that a suitable permittivity grading of a gyrotropic photonic crystal is able to simulate the simultaneous presence of analog electric and magnetic field forces for photons, and we rigorously derive the topology-related term in the equation for the electromagnetic energy velocity that is formally equivalent to the electronic case. A possible experimental configuration is proposed to observe a bulk photonic analog to the quantum Hall physics in graded gyromagnetic photonic crystals.