Some theoretical aspects of thin-film optics and their applications.

The principal focus of my report is on the theoretical study of the properties of spectral coefficients in a complex wave-number plane. The basic results of the study are described, and their application to the synthesis of a rugate filter and to inhomogeneous layer recognition problems are considered. General results concerning the existence of solutions to synthesis problems are also presented. The close analogy between synthesis problems in thin-film optics and optimal control problems is outlined, and some applications of Pontryagin's maximum principle are considered.