Indifferent electromagnetic modes: bound states and topology

Abstract

At zero energy the Dirac equation has interesting behaviour. The asymmetry in the number of spin up and spin down modes is determined by the topology of both space and the gauge field in which the system sits. An analogous phenomenon also occurs in electromagnetism. Writing Maxwell's equations in a Dirac-like form, we identify cases where a material parameter plays the role of energy. At zero energy we thus find electromagnetic modes that are indifferent to local changes in the material parameters, depending only on their asymptotic values at infinity. We give several examples, and show that this theory has implications for non-Hermitian media, where it can be used to construct permittivity profiles that are either reflectionless, or act as coherent perfect absorbers, or lasers.

10 pages, 6 figures

References in corpus (10)

• Topological Photonics
• Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials
• Coherent Perfect Absorbers: Time-reversed Lasers
• Do Linear Dispersions of Classical Waves Mean Dirac Cones?
• Bulk-edge correspondence for topological photonic continua
• Quantum Gravity in 2+1 Dimensions
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Cited by in corpus (10)

• Shape-preserving beam transmission through non-Hermitian disordered lattices
• Optical $N$-invariant of graphene's viscous Hall fluid
• Transforming space with non-Hermitian dielectrics
• A universal form of complex potentials with spectral singularities
• Anisotropy-induced Extrinsic Chirality and Chiral Discrimination of Surface Plasmon Polaritons
• A universal form of arrays with spectral singularities
• Testing the Wave-Particle Duality of Gravitational Wave Using the Spin-Orbital-Hall Effect of Structured Light
• Tutorial: Topology, waves, and the refractive index
• Removing grazing incidence reflection with half-bound states and non-Hermitian systems
• Zero index electromagnetic materials