Berry Phase, Berry Connection, and Chern Number for a Continuum Bianisotropic Material From a Classical Electromagnetics Perspective

Abstract

Abstract-The properties that quantify photonic topological insulators (PTIs), Berry phase, Berry connection, and Chern number, are typically obtained by making analogies between classical Maxwell's equations and the quantum mechanical Schrödinger equation, writing both in Hamiltonian form. However, the aforementioned quantities are not necessarily quantum in nature, and for photonic systems they can be explained using only classical concepts. Here we provide a derivation and description of PTI quantities using classical Maxwell's equations, we demonstrate how an electromagnetic mode can acquire Berry phase, and we discuss the ramifications of this effect. We consider several examples, including wave propagation in a biased plasma, and radiation by a rotating isotropic emitter. These concepts are discussed without invoking quantum mechanics, and can be easily understood from an engineering electromagnetics perspective.Index Terms-Berry Phase, surface wave, photonic topological insulator.

Optical momentum and angular momentum in complex media: from the Abraham–Minkowski debate to unusual properties of surface plasmon-polaritons

“…As a result, the energy, momentum, spin, and orbital AM densities in the medium can be written in a laconic unified form (2.15) using the corresponding quantum-mechanical operators and proper inner product modified by the ẽ and m indices of the medium. This coincides with the general approach to electromagnetic bi-linear forms developed by Silveirinha [81][82][83].…”

“…In particular, it is not clear if one can separate the spin and orbital degrees of freedom in anisotropic media. Close correspondence of our approach to some of the results of [18,[81][82][83]101] (dealing with quite general bi-anisotropic media), suggests that the analysis presented in this work can be extended to more complex cases.…”

“…Exactly the same formalism for electromagnetic bi-linear forms (including Berry connection and other topological characteristics) in dispersive media was recently suggested in works by Silveirinha [81][82][83]. Thus, the above equations bring together approaches developed by (i) Philbin (kinetic Minkowski-type momentum and AM in dispersive media) [16,17], (ii) Bliokh et al (canonical momentum and AM pictures in free space) [35,41,52,55,56], and (iii) Silveirinha (electromagnetic bi-linear forms in dispersive media) [81][82][83].…”

“…In such 'standard' formalism in free space, the energy density and kinetic Poynting momentum density are still given by the dual-symmetric expressions (1.1) and (2.1), whereas the canonical momentum, spin, and spin AM densities (1.6)-(1.8) become [54,55]: = + Adopting the definitions (5.4) and (5.5) would mean that only the phase gradients of the electric (but not magnetic) field produce momentum and orbital AM, and only rotations of the electric (but not magnetic) field generate the spin AM. On the one hand, this is not satisfactory from a general physical perspective, where electromagnetic waves involve electric and magnetic fields on equal footing [52,[55][56][57][81][82][83]. On the other hand, the electric-biased quantities (5.4) and (5.5) can be useful in some practical problems considering interactions of fields with electric-dipole particles or atoms, which are not sensitive to magnetic fields [47-49, 59, 60].…”

Nonlocal topological electromagnetic phases of matter

“…These are artificial materials composed of two or more different constituents which form a macroscopic crystalline structure. A few important examples are gyrotropic photonic crystals [31][32][33], Floquet topological insulators [39][40][41] and bianisotropic metamaterials [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56]. Instead, we focus on the microscopic domain and utilize the periodicity of the atomic lattice itself.…”