Optimal phase modulation for gradient-index optical filters

Abstract

Fourier transforms provide a basis for the design of gradient-index optical filters. A variety of techniques that differ in their treatment of the complex part or phase of the transformed refractive-index profile are reported. Here we describe a method of using the phase of the index profile as a variable to permit a closed-form, constrained optimization of rugate filters. Use of an optimal phase function in Fourier-based filter designs reduces the product of index contrast and thickness for desired reflectance spectra. The shape of the reflectance spectrum is recovered with greater fidelity by suppression of Gibbs oscillations and shifting of sidelobes into desired wavelength regions.