Topological transitions in continuously-deformed photonic crystals

We demonstrate that multiple topological transitions that occur, with high-sensitivity, by continuous change in geometry of a simple 2D dielectric-frame photonic crystal consisting of circular air-holes. These transitions are characterized by the switch between the frequencies of the pand d-orbital Bloch modes encompassing the photonic band gap (PBG). By tuning the radii of the holes and/or the distance between them, multiple transitions between normal and topological PBGs appear. These topological PBGs resemble the quantum spin-Hall insulator of electrons and have two counter-propagating edge states with opposite orbital angular momenta. At each transition geometry, there is a Dirac cone with four-fold degenerate Dirac point at the Brillouin zone center. The topological PBGs, as large as 20% relative to center frequency, lead to in-gap edge states with robust unidirectional transport. In the corresponding 3D slab-membrane photonic crystal with subwavelength thickness, a finite band gap is still attainable.