Highly robust anisotropic zero refraction effects in semi-Dirac photonic crystals

The ultra-low-loss epsilon-and-mu-near-zero (EMNZ) waveguide based on photonic crystals (PCs) supports uniform field distributions at a single frequency, corresponding to a specific configuration of PCs' structural and material parameters. However, its applications are limited by the high sensitivity of anisotropic EMNZ, as accidental semi-Dirac points are prone to degeneration even with minor variations in any of the PCs' parameters. Here, we report highly robust anisotropic zero refraction effects in two types of two-dimensional symmetry-reduced PCs: square-lattice elliptical air holes and rectangular-lattice circular air holes. These C₂-symmetric PCs exhibit behavior resembling EMNZ or impedance-mismatched materials in two perpendicular directions, owing to the presence of semi-Dirac cones at the Brillouin zone center. Moreover, the anisotropic EMNZ and zero-phase optical transmission performances for a fixed PC structure are shown to be consistently valid within a wide variation range of the background refractive index, accompanied by a tunable working frequency of EMNZ at the semi-Dirac point. This finding starkly contrasts with the accidental zero refraction effects observed at a single working frequency for a given structure and material.