Abstract
Topological photonic systems have recently emerged as an exciting new paradigm to guide light without back-reflections. The Chern topological numbers of a photonic platform are usually written in terms of the Berry curvature, which depends on the normal modes of the system. Here, we use a gauge invariant Green’s function method to determine from first principles the topological invariants of photonic crystals. The proposed formalism does not require the calculation of the photonic band-structure, and can be easily implemented using the operators obtained with a standard plane-wave expansion. Furthermore, it is shown that the theory can be readily applied to the classification of topological phases of non-Hermitian photonic crystals with lossy or gainy materials, e.g., parity-time symmetric photonic crystals.
Highlights
Topological photonic systems have recently emerged as an exciting new paradigm to guide light without back-reflections
It was recently discovered that the topological classification remains feasible even when the operator H^k is non-Hermitian[18,19,20,21,22,23,24,25,26]; thereby lossy or gainy photonic systems are characterized by different topological phases
B:Z: TPhe integral is over the first Brillouin zone (BZ) and F k 1⁄4 n2F F nk is the Berry curvature; the summation in n is over all the “filled” photonic bands (F) below the gap, i.e., modes with ωnk < ωgap, with ωgap some frequency in the band gap
Summary
Topological photonic systems have recently emerged as an exciting new paradigm to guide light without back-reflections. It is shown that the theory can be readily applied to the classification of topological phases of non-Hermitian photonic crystals with lossy or gainy materials, e.g., parity-time symmetric photonic crystals. It was shown that the photonic Chern number can be understood as the quantum of the fluctuation-induced light angular-momentum in a topological material cavity[15,16,17]. It was recently discovered that the topological classification remains feasible even when the operator H^k is non-Hermitian[18,19,20,21,22,23,24,25,26]; thereby lossy or gainy photonic systems are characterized by different topological phases. Each topological phase is characterized by an integer number (the Chern number), which is a topological invariant insensitive to weak perturbations of the Hamiltonian
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