Polarization-based branch selection of bound states in the continuum in dielectric waveguide modes anti-crossed by a metal grating

We investigate bound states in the continuum (BICs) in a planar dielectric waveguide structure consisting of a gold grating on a dielectric layer with a back layer of metal. In this structure, Friedrich?Wintgen (FW) BICs caused by the destructive interference between the radiations from two waveguide modes appear near the anti-crossing point of the dispersion curves. In this study, it is revealed that the branch at which the BIC appears changes according to the polarization of the modes. Based on a temporal coupled mode theory, it is shown that the BIC branch is determined by the sign of the product of the coupling coefficients between the two waveguide modes and external radiation, which is consistent with FW theory. The signs of the coupling coefficients are estimated by the waveguide-mode decomposition of the numerically obtained electric fields and are confirmed to vary depending on the polarization.