Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Department of Engineering Physics

First Advisor

Jeffrey W. Grantham, PhD


Gradient index thin films provide greater flexibility for the design of optical coatings than the more conventional 'layer' films. In addition, gradient index films have higher damage thresholds and better adhesion properties. This dissertation presents an enhancement to the existing inverse Fourier transform gradient index design method, and develops a new optimal design method for gradient index films using a generalized Fourier series approach. The inverse Fourier transform method is modified to include use of the phase of the index profile as a variable in rugate filter design. 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. The optimal values of the design coefficients are determined using a sequential quadratic programming algorithm. 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 determine the minimum film thickness needed, as well as the index of refraction profile for the optimal film.

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