OPTIMAL PHASE MODULATION FOR GRADIENT-INDEX OPTICAL FILTERS

Fourier transforms provide a basis for the design of gradient-index op tical filters. A variety of techniques that differ in their treatment of the complex part or phase of the transformed refractive-index profi le are reported. Here we describe a method of using the phase of the i ndex profile as a variable to permit a closed-form, constrained optimi zation of rugate filters. Use of an optimal phase function in Fourier- based filter designs reduces the product of index contrast and thickne ss for desired reflectance spectra. The shape of the reflectance spect rum is recovered with greater fidelity by suppression of Gibbs oscilla tions and shifting of sidelobes into desired wavelength regions.