Hidden symmetry-induced effective moving double-zero-index metamaterials.

Materials possessing an effective zero refractive index are often associated with Dirac-like cone dispersion at the center of the Brillouin zone (BZ). It has been reported the presence of hidden symmetry-enforced triply degenerate points [nexus points (NP)] away from the Brillouin zone center with the stacked dielectric photonic crystals. The spin-1 Dirac-like dispersion in the xy plane near the nexus point suggests a method for achieving zero refractive index materials. The stacked photonic crystals at the nexus points can be deemed as an effective moving double-zero-index medium (MDZIM) traveling with a speed relative to the laboratory reference. The ability of this moving double-zero-index medium to enable perfect wave tunneling across barriers without reflection has been demonstrated, dependent on the incident waves' specific angular orientations.

Simple yet effective analysis of waveguide mode symmetry: generalized eigenvalue approach based on Maxwell's equations.

Particular waveguide structures and refractive index distribution can lead to specified degeneracy of eigenmodes. To obtain an accurate understanding of this phenomenon, we propose a simple yet effective approach, i.e., generalized eigenvalue approach based on Maxwell's equations, for the analysis of waveguide mode symmetry. In this method, Maxwell's equations are reformulated into generalized eigenvalue problems. The waveguide eigenmodes are completely determined by the generalized eigenvalue problem given by two matrices (M, N), where M is 6 × 6 waveguide Hamiltonian and N is a constant singular matrix. Close examination shows that N usually commute with the corresponding matrix of a certain symmetry operation, thus the waveguide eigenmode symmetry is essentially determined by M, in contrast to the tedious and complex procedure given in the previous work [Opt. Express25, 29822 (2017)10.1364/OE.25.029822]. Based on this new approach, we discuss several symmetry operations and the corresponding symmetries including chiral, parity-time reversal, rotation symmetry, wherein the constraints of symmetry requirements on material parameters are derived in a much simpler way. In several waveguides with balanced gain and loss, anisotropy, and geometrical symmetry, the analysis of waveguide mode symmetry based on our simple yet effective approach is consistent with previous results, and shows perfect agreement with full-wave simulations.