Angular selection of incident waves by photonic crystals with position-varying Dirac points at the Brillouin zone boundary

We demonstrate the angular selection of incident electromagnetic waves using photonic crystals (PCs) composed of a square lattice of dielectric rods which exhibit position-varying Dirac conical dispersion at the Brillouin zone boundary. At the frequency of the Dirac point, the transmittance can reach unity at a particular incident angle associated with the Dirac dispersion, while for all other incident angles the waves are reflected due to the existence of a directional photonic band gap. By changing the size of the dielectric rods, the position of the Dirac point at the Brillouin zone boundary is variable, which makes the unity transmission angle customizable. Interestingly, we show that such a scheme of angular selection is almost independent of the refractive index of the background medium, as long as it is not too large so that a diffraction effect emerges. By investigating the PC being sandwiched by two different types of media, we find it actually acts as an optical 0 or $\ensuremath{\pi}$ phase modulator at that particular incident angle. By attaching a metasurface to the PC, angular selection in the reflection geometry can also be achieved. Our work establishes a systematic and efficient method to achieve angular selection of arbitrary incident waves based on Dirac dispersions.