Gradient-index optical filter synthesis with controllable and predictable refractive index profiles

Abstract

The Fourier transform thin film synthesis method often results in solutions that call for indices that lie outside the range of values of the available materials. To make the resulting refractive index profiles always realizable in our meta-mode sputtering machine, a modified Fourier transform synthesis method is proposed with which the reflectance spectra can be accurately synthesized with controllable and predictable refractive index profiles. In our procedure, an optimal phase function is explored to yield acceptable refractive index profiles. Then the overall thickness is estimated using the Parseval theorem. Finally, several errors inherent to the Fourier transform method, including the imprecision of the spectral function, the truncation of the film and the apodization of the refractive index profiles, are compensated by successive corrections to the magnitude of the spectral function. An explicit iterative formula based on the derivative of the magnitude function is proposed for the compensation of the spectral mismatches. We show with a number of examples that, with the proposed method, it is possible to synthesize gradient-index optical filters with almost any desired spectral performance using experimentally realizable refractive indices.