Symmetry-protected mode coupling near normal incidence for narrow-band transmission filtering in a dielectric grating

Abstract

A narrow-band transmission filter is demonstrated near normal incidence that operates through relaxation of supported-mode selection rules and is explained in the context of group theory. We calculated the transverse magnetic and transverse electric dispersion relations of a dielectric grating in the subwavelength and near-wavelength region using finite element modal analysis and determine the modes' corresponding irreducible representations. Coupling to select transverse magnetic modes at normal incidence is optimized to yield broadband high reflectance that acts as the background for the transmission filter. While some modes couple at normal incidence, others are shown to remain inaccessible due to symmetry mismatch. Away from normal incidence, the reduced symmetry relaxes the selection rules, enabling weak coupling between the incident field and these symmetry-protected modes. This weak coupling produces narrow transmission bands within the opaque background. Furthermore, by choosing the plane of incidence to include or exclude the grating periodicity, we show that orthogonal mode sets can independently be selected to couple to the incident light, yielding separate transmission bands. This spectral filtering is experimentally demonstrated with a suspended silicon grating in the infrared spectrum ($7--14\ensuremath{\mu}\mathrm{m}$), which agrees well with simulated transmittance spectra and modal analysis.