Characterization of line shape symmetry properties of guided-mode resonance filters

The response line shape symmetry properties of planar dielectric resonant waveguide-grating filters in asymmetric and in symmetric geometries are theoretically characterized for TE and TM polarizations. Classical antireflection theory is applied to the design of these guided-mode resonance filters and it is shown that the line shape symmetry is determined by the location of the resonance relative to the antireflection band minimum. Single-layer antireflection waveguide gratings are shown to yield highly symmetrical line shapes with suppressed sideband reflectance and 100% reflectance at the resonance wavelength. The parametric locations of the symmetrical line shapes are predicted 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. An analytical coupled three-wave solution for TM polarization and normal incidence on a dielectric, sinusoidally modulated waveguide grating is derived and found to expedite calculations of the line shape characteristics.