Analysis of the influence of the spectral response for a rugate filter by modifying the frequency domain

Since the application of Fourier transform theory for synthetizing rugate filters, it was demonstrated to be a power-ful mathematical method for achieving general spectral responses. This synthesis method establishes a relationship of a function of transmittance, denoted as "Q," with its corresponding refractive index profile via Fourier trans-form. The real space (transmittance versus wavelength) relates to the frequency space (refractive index versus film thickness). This work analyzes how spatial frequencies (rugate index profile optical thickness) contribute to achieve a better spectral response and considers enlargement of the rugate profile's optical thickness in extending repro-duction of the expected spectral response. In combination, the stored wave inverse Fourier transform refinement method was used to obtain a reduction in the lower and upper refractive indices. We illustrate with three examples and results. (c) 2022 Optica Publishing Group