Modal analysis on resonant excitation of two-dimensional waveguide grating filters

Modal analysis on resonant excitation of two-dimensional (2-D) waveguide grating filters (WGFs) is proposed. It is shown that the 2-D WGFs can support the excitation of a resonant pair, and the locations of the resonant pair arising from the TE and TM guided-mode resonances (GMRs) can be estimated accurately based on the modal analysis. Multichannel filtering using the resonant pair is investigated, and the antireflection (AR) design of the 2-D WGFs is also studied. It is shown that the reflection sideband can be reduced by placing an AR layer on the bottom of the homogeneous layer, and the well-shaped reflection spectrum with near-zero sideband reflection can be achieved by using the double-faced AR design. By merely increasing the thickness of the homogeneous layer with other parameters maintained, the spectrally dense comb-like filters with good unpolarized filtering features can be achieved. The proposed modal analysis can be extended to study the resonant excitation of 2-D periodic nanoarrays with diverse surface profiles.