Filter-response line shapes of resonant waveguide gratings

The line shape symmetry properties of planar dielectric resonant waveguide-grating filters are theoretically characterized for both TE and TM polarization. Classical antireflection theory is applied to the design of guided-mode resonance filters and it is shown that the symmetry of the line-shape response is determined by the location of the resonance relative to the minimum of the antireflection band. The conditions that allow a single dielectric layer to simultaneously function as both a waveguide grating and as an antireflection thin film are presented. Single-layer antireflection waveguide gratings are shown to yield highly symmetrical filter-response line shapes with suppressed sideband reflectivity and 100% reflectivity at the resonance wavelength. The parametric locations of the symmetrical line-shape responses are predicted approximately by solving the resonance-location equation with the grating thickness set equal to a multiple of a half-resonance-wavelength. Graphical representations of these solutions are provided. Symmetric waveguide-grating filters are shown to yield symmetrical line shapes with near-zero sideband reflectivity, whereas asymmetric filters produce symmetrical line shapes but suffer from increased sideband reflectance that increases as the asymmetry of the filter grows. Numerous calculated examples are presented to demonstrate that ideal reflection filters can be designed by combining thin-film antireflection effects and resonance effects in a single dielectric layer.