Directional Polarization‐Independent Double‐Zero‐Index Material in a Three‐Dimensional Photonic Crystal With a Fourfold Semi‐Dirac Point

ABSTRACT We propose a strategy to realize directional polarization‐independent double‐zero‐index materials within a three‐dimensional photonic crystal. In the transition between two nodal rings with opposite Zak phases, a fourfold semi‐Dirac point emerges at the Brillouin zone center. This point exhibits linear dispersions along one direction and quadratic dispersions along perpendicular directions in the momentum space. At the frequency of the semi‐Dirac point, both the effective permittivity and permeability of the photonic crystal simultaneously reach zero along the direction of linear dispersions, whereas only one of them becomes zero along the directions of quadratic dispersions. We investigate typical wave manipulation characteristics of this directional double‐zero‐index material, such as total transmission of circularly polarized electromagnetic waves and highly collimated directional emission. Our study clarifies the connection between topological phase transitions, band dispersions, and double‐zero‐index properties in artificial materials, offering a general method for achieving directional double‐zero‐index materials with potential applications in wave manipulation.