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 powerful 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 transform. 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 reproduction 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.