Scattering by a periodic array of subwavelength slits II: surface bound state, total transmission and field enhancement in homogenization regimes

Abstract: This is the second part in a series of two papers that concern with the quantitative analysis of the electromagnetic field enhancement and anomalous diffraction by a periodic array of subwavelength slits. In this part, we explore the scattering problem in the homogenization regimes, where the size of the period is much smaller than the incident wavelength. In particular, two homogenization regimes are investigated, where the size of the pattered slits has the same order as the size of the period in the first configuration, and the size of the slit is much smaller than the size of the period in the second configuration. By presenting rigorous asymptotic analysis, we demonstrate that surface plasmonic effect mimicking that of plasmonic metals occurs in the first homogenization regime. The corresponding dispersion curve lies below the light line and the associated eigenmodes are surface bound sates. In addition, for the incident plane wave, we discover and justify a novel phenomenon of total transmission which occurs either at certain frequencies for all incident angles, or at a special incident angle but for all frequencies. For the second homogenization regime, the non-resonant field enhancement is investigated, and it is shown that the fast transition of the magnetic field in the slit induces strong electric field enhancement. Moreover, the enhancement becomes stronger when the coupling of the slits is weaker.