A comparison of design techniques for gradient-index thin film optical filters

M.Ing.This work comprises the implementation and comparison of five design techniques for the design of gradient-index thin film optical filters: classical rugate, inverse Fourier transform, a wavelet-based design procedure, as well as the flip-flop and the genetic optimization techniques. Designs for a high-reflectance filter, a beamsplitter, a discrete level filter, a distributed filter, and an anti-reflection coating were used to compare the various filter synthesis techniques. The optical thickness of the various examples was maintained below 30 and the refractive index excursion limits were between 1.5 and 3.2. The overall performance of a specific design was evaluated by a weighted merit function. The classical rugate filter uses a sinusoidal refractive index modulation that produces a single reflection band. More complex filters are realized by linear superposition of these elementary profiles. Sidelobe and ripple suppression are obtained by applying quintic windowing functions to the refractive index profile and adding matching layers at the edges of the filter. This filter design procedure has the best figure of merit of 3.73 for the discrete level filter, and the second best of 3.09 for the high-reflectance filter. The inverse Fourier transform links the refractive index profile and reflection spectrum of an optical filter by an approximate relation. It is self-correcting and iterative in nature. It produces filters with the highest optical density. The procedure excels in the design of the distributed filter with a figure of merit of 4.17. Mortlett's wavelet is used as the basis of the wavelet design technique. A single wavelet yields a single reflection band, similar to the classical rugate filter. Sidelobe suppression is an inherent property of the method, but matching layers are needed for passband ripple suppression. The optical density of the high reflection filter is larger for a filter designed with this method than for the equivalent classical rugate filter. The figure of merit of 1.75 for the high-reflectance filter is the best for any of the designs. Flip-flop refinement is a brute force approach to filter design. The layers of a starting design are flipped between two values of refractive index, the change in figure of merit evaluated and the best case saved. This process is repeated for a fixed number of iterations. It is computationally intensive and lacks ripple suppression characteristics. The flip-flop method does not compare well with any of the other techniques. It yields filters with the worst figures of merit for most of the design examples. However, it was applied successfully to the anti-reflection coating. The peak ripple for the anti-reflection filter in the 400 nm to 1100 nm wavelength band is 9.62 % compared to the inverse Fourier transform's 57.30 %. The genetic algorithm operates on the principle of "survival of the fittest". It is a stochastic procedure and yields quasi-random refractive index profiles. It excels with the antireflection coating. The peak ripple in the passband of the anti-reflection coating is 3.29%. The figure of merit for the anti-reflection coating designed with the genetic algorithm is 2.09