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.
A new method for the design of antireflection coatings is described in which a linearly constrained quadratic programming optimization procedure is used to find an inhomogeneous layer solution that, for a given overall thickness of the layer, corresponds to the global optimum for the problem. The refractive-index profile of this solution is then approximated by a two-material multilayer system that serves as a starting design for further numerical refinement. We present the theoretical basis for this method and discuss the effect of the various approximnations made on the solution. Four different antireflection problems are solved to illustrate this new method.
We introduce two parameters, large-scale and small-scale rms roughness, to take into account the interface properties of thin films and multilayers in the calculation of their specular reflectance and transmittance. A theoretical motivation for the introduction of these two parameters instead of a standard single rms roughness is provided. Experimental power spectral density functions of several samples are used to illustrate ways in which the parameters introduced can be evaluated.
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