Propagating bound states in the continuum at the surface of a photonic crystal

Bound states in the continuum (BICs) are trapped or guided modes with their frequencies within the radiation continuum. On periodic structures, BICs have interesting properties and potentially important applications. It is known that BICs can exist at the surface of a photonic crystal (PhC), and they are distinctively different from the well-known surface Bloch modes below the lightline. However, for a given structure with specific geometric and material parameters, it is difficult to predict whether BICs exist or not. In this paper, using an efficient computational method, we calculate BICs at the surface of a two-dimensional PhC consisting of dielectric rods, and determine the existence domain in the plane of the refractive index and the radius of the surface rods. The boundary of the existence domain reveals that the BICs cease to exist when the bulk PhC can no longer confine light. In addition, the frequency and wavenumber of the BIC can approach the lightline, leading to bound states on the lightline and special highly confined surface Bloch modes below the lightline.