  We study a photonic analog of a modified Fano-Anderson model -- a waveguide
array with two additional waveguides and by using the coupled mode theory we
calculate its spectral and scattering properties. We classify eigenomodes
according to vertical symmetry of the structure given by self-coupling
coefficients of the additional waveguides and establish the conditions for BIC
existence. We use the Weierstrass factorization theorem and interpret the
scattering spectra of the systems with broken symmetry in terms of the
eigenmodes. The Fano resonance related with excitation of quasi-BIC is
explained as arising from the interference between this mode and another leaky
mode.
