A Discrete Model for Resonance Near Embedded Bound States

We present a discrete model for resonance in periodic dielectric slabs arising from the interaction of electromagnetic plane waves with guided modes at frequencies embedded in the continuum. Two infinite rows of interacting masses in the model support propagating and evanescent waves simultaneously. This allows for modes to be exponentially trapped near an obstacle at continuum frequencies. The discrete model manifests resonant transmission features of the periodic slab, and it includes parameters of asymmetry that are connected to the detuning of the resonance. Moreover, resonant transmission in both systems is described by a rigorous universal formula that explicitly incorporates a detuning parameter.