Sensitivity of a dielectric layered structure on a scale below the periodicity: A fully local homogenized model

We inspect the unusual scattering properties reported recently for structures alternating dielectric layers of subwavelength thicknesses near the critical angle for total reflection. In TE polarization, the unusual scattering properties are captured by an effective model with an accuracy less than 1% up to kd~0.1. It is shown that the propagation is simply dispersive with local dispersion while the boundary layer effects are captured through a nonintuitive transmission condition. The resulting model involves two parameters depending only on the characteristics of the multilayer and which are given in closed forms. Besides, we show that a discrete description of the spectrum using the layer thickness d as unit of measure misses the complexity of the continuous spectrum exhibiting strong variations within the scale d. This ultrasensitivity to variations below d is attributable to strong boundary layer effects and, for large structures, to a cooperation between the boundaries and the phase accumulation within the structure.