Topological surface states at the free space termination of uncorrugated finite square photonic crystals

We present a square-lattice photonic crystal that supports chiral topological photonic surface states at the interface to free space. Such unidirectional, back-scattering-immune surface states, as opposed to topological states at the interface between band-gap materials, allow to simplify the design of out-coupling from surface modes to functionalized radiated fields, removing the usual impedance matching conditions. The photonic crystal consists of gyromagnetic rods, which under the time-reversal-symmetry breaking induced by an external magnetic field together with a carefully tuned bulk band structure allow for the emergence of chiral topologically protected surface states. We demonstrate the topological nature of the surface states through unit cell and supercell band structure calculations showing the existence of a topological mode below the light-line where the sum of the Chern numbers in the bands below is non-zero. Additionally we perform direct scattering and a subsequent spatial, frequency dependent, Fourier Transform analysis that independently demonstrates the topological surface mode’s chiral dispersion relation, unidirectional propagation, and immunity to back-scattering.