Resonant transmission through a multiple periodic scattering system

Abstract

We investigate the propagation and transmission of electromagnetic (EM) waves in the subwavelength regime when a multiple periodic scattering system (MPSS) is illuminated by a monochromatic plane wave. This system has a cascaded structure with square hole arrays periodically perforated on a metal slab with arbitrary slab thickness and arbitrary air-gap. The framework of this paper is based on a modal expansion theory, in which the EM fields in pure vacuum are expanded in terms of plane waves, while those in the holes of the slab are expressed in terms of waveguide modes. The boundary conditions for the EM waves lead to a system of equations whose solution can be obtained quasianalytically in a monomodal approximation method. We study the transmission spectrum and field distribution in the MPSS, varying geometrical parameters such as the air-gap and/or number N of slabs in the context of symmetrical and asymmetrical geometries. We find that an MPSS with N ≥ 2 provides discrete transmission windows whose resonance order linearly increases against N and the associated resonance wavelengths are confined to a specific finite band for large N. The EM fields at the resonance states are quite uniquely distributed in the MPSS, depending not only on the resonance wavelength, but also either on even N or on odd N. We also demonstrate that the transmission of the EM energy is strongly boosted by the evanescent electric fields mirror-symmetrically distributed in the air-gaps of the MPSS.