Temporal coupled mode theory: From bound states in the continuum to uniguided resonances

We revise the temporal coupled mode theory to describe the resonant response of quasiguided modes under oblique incidence in periodic dielectric metasurfaces accounting for the constraints imposed by the symmetry of the unit cell. We derive a universal expression for the Fano resonance line shape in reflection and transmission for subwavelength period metasurfaces and reveal a fundamental link between the Fano parameters and unit cell symmetries, including robust reflection and transmission zeros, as well as spectral signatures of bound states in the continuum. To demonstrate the power of the developed theory, we provide a generalized framework for analyzing asymmetry in the coupling and decoupling coefficients. This allows us to reveal the dual nature of unidirectional guided resonances and counter-propagating modes characterized by single-sided coupling to incident waves, which have been actively discussed in recent years. These insights provide a powerful analytical tool for designing high-Q resonances in metasurfaces through symmetry exploitation.