Calculation of the Berry curvature and Chern number of topological photonic crystals

In this paper, numerical calculations of the Berry curvature and Chern number of two types of two-dimensional photonic crystals consisting isotropic dielectric and anisotropic magneto-optical, gyromagnetic, rods in air in a square lattice are studied. The Chern number, an integer number, is a key parameter to distinguish between trivial and non-trivial photonic crystals. Trivial and non-trivial photonic crystals reveal zero and non-zero Chern numbers. A non-zero Chern number is achieved through the breaking of time-reversal and inversion symmetries. The results for two-dimensional photonic crystals containing isotropic dielectric and gyromagnetic materials under TM mode illustrate zero and 0, 1, -2, and -1 Chern numbers for the first four bands, respectively. The creation of non-zero Chern numbers brings a new way of designing one-way, robust to arbitrary disorder, and zero back-reflection photonic components