Dual semi-Dirac cones in three-dimensional photonic crystals
Mingyan Li, Ran Mei, Dongyang Yan, Zhikai Ma, Fang Cao, Yadong Xu, Chang‐Qing Xu, Jie Luo
Abstract
Semi-Dirac cones, characterized by linear-parabolic dispersions, endow photonic crystals with many fascinating properties, such as topological transitions and anisotropic electromagnetic responses. While most preceding investigations concentrated on two-dimensional systems, our exploration of three-dimensional photonic crystals comprising a cubic lattice of core-shell spheroids unveils unusual dispersions in three-dimensional systems---dual semi-Dirac cones. The dual semi-Dirac cones arising from a pair of coexisting triply degenerate modes can be analyzed by effective-Hamiltonian and effective-medium theory, accompanied by topological transitions in equal-frequency surfaces and significant changes in electromagnetic responses. We find that the photonic crystal exhibits highly anisotropic wave transport properties, i.e., drastically different transport properties for waves of different wave-vector directions, within the frequency region between the two semi-Dirac frequencies. However, at the frequencies of semi-Dirac points, the photonic crystal behaves as an effective double-zero medium for two propagation directions, but as a single-zero medium for the remaining direction, specifically for orthogonal polarizations. Our findings contribute valuable insights into three-dimensional artificial materials, presenting features absent in two-dimensional systems.