Topological photonics: From crystals to particles

Photonic crystal topological insulators host protected states at their edges. In the band structure these edge states appear as continuous bands crossing the photonic band gap. They allow light to propagate unidirectionally and without scattering. In practice it is essential tomake devices relying on these effects asminiature as possible. Here we study photonic topological insulator particles (finite crystals). In such particles the edge state frequencies are discrete. Nevertheless, the discrete states support pseudospin-dependent unidirectional propagation. They allow light to bend around sharp corners similarly to the continuous edge states and act as topologically protected whispering gallery modes, which can store and filter light as well as manipulate its angular momentum. Though we consider a particular all-dielectric realization that does not require a magnetic field, the results in the findings are general, explaining multiple experimental observations of discrete transmission peaks in photonic topological insulators.