| Holographic mirrors have wavelength-selection properties and thus qualify as a class of interference filters. Two theoretical methods for analyzing such structures are developed. The first method uses Hill's matrix method to yield closed-forms solutions in terms of the Floquet-Bloch waves within a periodic structure. A process is developed for implementing this solution method on a computer, using sparse-matrix memory allocation, numerical root-finding algorithms, and inverse-iteration techniques. It is demonstrated that Hill's matrix method is valid for the analysis of finite and multi-periodic problems. The second method of theoretical analysis is a transfer-matrix technique, which is herein termed thin-film decomposition. It is shown that the two methods of solution yield results that differ by, at worst, a fraction of a percent. Using both calculation techniques, a number of example problems are explored. Of key importance is the construction of a set of curves that are useful for the design and characterization of holographic interference filters. In addition to the theoretical development, methods are presented for the fabrication of holographic interference filters using DuPont HRF-800X001 photopolymer. Central to the exposure system is a frequency-stabilized, tunable dye laser. The types of filters fabricated include single-tone reflection filters, two types of multitone reflection filters, and reflection filters for infrared wavelengths. These filters feature index profiles that are not easily attainable through other fabrication methods. As a supplement to the body of the dissertation, the computer algorithms developed to implement Hill's matrix method and thin-film decomposition are also included as an appendix. Further appendices provide more information on Floquet's theorem and Hill's matrix method. A final appendix presents a design for an infrared laser spectrophotometer. |
