The properties of guided-mode resonance reflection filters constructed with multiple thin-film layers are addressed. Greatly improved filter characteristics are shown to follow by the incorporation of multiple homogeneous layers with the spatially modulated layer. Calculated results for single-layer, double-layer, and triple-layer filter structures are presented. Whereas good filter characteristics are obtainable with single layers that are half-resonance-wavelength thick, there remains a residual reflection in the sidebands unless the cover and the substrate permittivities are equal. With double-layer and triple-layer designs, extensive wavelength ranges with low sideband-reflectance values are shown to be possible without requiring equal cover and substrate permittivities. The antireflection properties of the layer stack can be understood if the modulated layer is modeled as a homogeneous layer characterized by its average relative permittivity. However, as the grating-modulation index increases, this approximation deteriorates. In particular it is found that, for a given high modulation index, the double-layer antireflection thin-film approximation fails, whereas for the same modulation in a triple-layer system it holds firmly. Multilayer designs can thus have significantly large filter passbands, as they may contain heavily modulated resonant gratings without corruption of the ideal filter characteristics.
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