Propagating Bloch modes above the lightline on a periodic array of cylinders

Optical bound states in the radiation continuum (BICs) have interesting properties and potentially important applications. On periodic structures, the BICs are guided modes above the lightline, and they can be either standing waves or propagating Bloch modes. A one-dimensional (1D) array of circular dielectric cylinders is probably the simplest structure on which different types of BICs exist. Using a highly efficient numerical method, we perform an extensive numerical study for propagating BICs on 1D arrays of circular dielectric cylinders. In addition to the known Bloch BIC which is symmetric with respect to the axis of the array, we obtain a new BIC which is antisymmetric. The existence domains (in the plane of radius and dielectric constant of the cylinders) of both BICs are determined. The boundaries of these domains correspond to either standing waves which are not protected by symmetry or the opening of the second diffraction channel. Numerical results are also presented to illustrate the discontinuities of transmission and reflection coefficients at the BICs, and the resonant behavior near the BICs.