Design of Gradient Index Optical Thin Films.
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH
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This dissertation develops an enhancement to existing inverse Fourier transform gradient index design methods, and develops a new optimal design method for gradient index films using a generalized Fourier series approach. 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 side lobes into desired wavelength regions. A new method of gradient index thin film design using generalized Fourier series extends the domain of problems for which gradient index solutions can be found. The method is analogous to existing techniques for layer based coating design, but adds the flexibility of gradient index films. A subset of the coefficients of a generalized Fourier series representation of the gradient index of refraction profile are used as variables in a nonlinear constrained optimization formulation. This method is particularly well suited for the design of coatings for laser applications, where only a few, widely separated wavelength requirements exist. The generalized Fourier series method is extended to determined the minimum film thickness needed, as well as the index of refraction profile for the optimal film.
- Lasers and Masers