All-Dielectric Tight-Binding Photonics via a Band-Gap Vacuum

Abstract

Tight-binding photonics bridges condensed-matter physics and optics, providing a powerful framework for engineering band structures and topological phases with light. For photons, however, the vacuum is gapless, so resonators in air carry radiative tails that produce spurious long-range couplings. Here we embed resonators in a photonic band-gap vacuum (BgV), a photonic crystal whose band gap plays for photons the role vacuum plays for bound electrons. The BgV localizes each resonance exponentially, so designed short-range couplings define the lattice Hamiltonian. We thereby experimentally realize a faithful Benalcazar-Bernevig-Hughes Hamiltonian in an all-dielectric photonic crystal, resolving corner resonances and their orbitals in microwave measurements. Unlike the vacuum surrounding electrons, the BgV is itself designable, controlling relative couplings and closed-loop interference through its band dispersion and Bloch modes. Full-wave calculations and extracted models show that uniformly modifying the BgV, with all resonators fixed, switches the quantized polarization of a two-dimensional Su-Schrieffer-Heeger lattice and converts a zero-flux lattice into a $π$-flux one. We also numerically realize three-dimensional pyrochlore and hyperhoneycomb lattices with space groups $R\bar{3}m$ and $C2/c$, the latter a nodal-loop semimetal with topological drumhead surface states. These results establish the BgV as a designable vacuum for all-dielectric tight-binding photonics in two and three dimensions.