FILTER-RESPONSE LINE-SHAPES OF RESONANT WAVE-GUIDE GRATINGS

The line shape symmetry properties of planar dielectric resonant waveg uide-grating filters are theoretically characterized for both TE and T M polarization. Classical antireflection theory is applied to the desi gn of guided-mode resonance filters and it is shown that the symmetry of the line-shape response is determined by the location of the resona nce relative to the minimum of the antireflection band. The conditions that allow a single dielectric layer to simultaneously function as bo th a waveguide grating and as an antireflection thin film are presente d. Single-layer antireflection waveguide gratings are shown to yield h ighly symmetrical filter-response line shapes with suppressed sideband reflectivity and 100% reflectivity at the resonance wavelength. The p arametric locations of the symmetrical line-shape responses are predic ted approximately by solving the resonance-location equation with the grating thickness set equal to a multiple of a half-resonance-waveleng th. Graphical representations of these solutions are provided. Symmetr ic waveguide-grating filters are shown to yield symmetrical line shape s with near-zero sideband reflectivity, whereas asymmetric filters pro duce symmetrical line shapes but suffer from increased sideband reflec tance that increases as the asymmetry of the filter grows. Numerous ca lculated examples are presented to demonstrate that ideal reflection f ilters can be designed by combining thin-film antireflection effects a nd resonance effects in a single dielectric layer.