Topology and the optical Dirac equation

Abstract

Through understanding Maxwell's equations as an effective Dirac equation (the `optical Dirac equation'), we re--examine the relationship between electromagnetic interface states and topology. We illustrate a simple case where electromagnetic material parameters play the roles of `mass' and `energy' in an equivalent Dirac equation. The modes trapped between a gyrotropic medium and a mirror are then the counterpart of those at a `domain wall', where the mass of the Dirac particle changes sign. Considering the general case of arbitrary electromagnetic media, we provide an analytical proof relating the integral of the Berry curvature (the Chern number) to the number of interface states. We show that this reduces to the usual result for periodic media, and also that the Chern number can be computed without knowledge of how the material parameters depend on frequency.

14 pages, 4 figures

References in corpus (6)

• Topological Photonics
• Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal
• Quantum spin Hall effect of light
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Bulk-edge correspondence for topological photonic continua
• Index theorem for topological heterostructure systems

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• Topological theory of non-Hermitian photonic systems
• Photonic Dirac monopoles and skyrmions: spin-1 quantization
• Physical Violations of the Bulk-Edge Correspondence in Topological Electromagnetics
• Proof of the bulk-edge correspondence through a link between topological photonics and fluctuation-electrodynamics
• Non-local topological electromagnetic phases of matter
• Unidirectional Maxwellian Spin Waves
• Indifferent electromagnetic modes: bound states and topology
• Viscous Maxwell-Chern-Simons theory for topological electromagnetic phases of matter
• Edge modes in 2D electromagnetic slab waveguides: analogues of acoustic plasmons
• Electromagnetic Analogs of Quantum Mechanical Tunnelling
• On the Majorana representation of the optical Dirac equation
• Electron g-factor engineering for non-reciprocal spin photonics
• Dirac Wire
• Dirac particle under dynamical confinement: Fermi acceleration, trembling motion and quantum force
• Tutorial: Topology, waves, and the refractive index
• Paraxial Dirac equation
• Zero index electromagnetic materials
• Electromagnetism at finite temperature: a density operator approach