Fabry-Perot bound states in the continuum supported by a coupled waveguide array

We explore the modal and scattering properties of the combined Fano-Anderson coupled waveguide structure. The system consists of a periodic chain of waveguides and two side-coupled pairs of waveguides, which form the Fabry-Perot resonator. We formulate a theoretical model based on the coupled-mode theory for obtaining the modal spectra and scattering coefficients. We demonstrate that the system support the Fabry-Perot bound states in the continuum, show how leaky resonances evolve into these bound states and describe corresponding spectral features.