Revisiting the effective medium approximation in all-dielectric subwavelength multilayers: Breakdown and rebuilding

Abstract

Here, we present a comprehensive analysis of the effective medium approximation (EMA) breakdown in all-dielectric deep-subwavelength multilayers made of alternating layers by means of the transfer matrix method. We demonstrated that the approximation is invalid at the vicinity of the effective medium's critical angle for total internal reflection and obtained an analytical criterion for the breakdown of the EMA, which depends on the layer thickness, the incident angle, and the permittivity difference between the alternate layers. We rebuilt the EMA by adding higher-order correction onto the traditional effective permittivity. Furthermore, we found that the EMA breakdown that arises from the boundary effect cannot be repaired in the traditional homogenization strategy with only one layer of effective medium. By adding an artificial matched layer after the conventional effective layer, the boundary effect breakdown was neatly removed.