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The problem of synthesizing absorbing layered media having low reflection over a wide spectral range is formulated. The properties of the reflection coefficient of such media at high and low frequencies are investigated. A number of conclusions are drawn regarding the dependence of the reflecting properties of a layered medium with absorption on its parameters. A method for the numerical solution of this synthesis problem is given. Examples of the synthesis of broadband absorbing layered media are given.

A general formulation of the problem of synthesizing optical coatings in the case of oblique incidence of a plane electromagnetic wave is given, and the necessary optimality conditions are analyzed. Examples of the synthesis using prepared programs are presented.

The link between the amplitudes and phases of spectral coefficients is investigated and a theorem concerning the uniqueness of the parameters of a laminar medium which are recovered using spectral data is obtained. A theorem concerning th necessary and sufficient conditions for the phase of the spectral transfer coefficients to be constant, and a theorem concerning the transformation of the paramters of a laminar medium which corresponds to a transformation of the phase of the transfer coefficient without changing its amplitude are proved. These theorems are important for problems of the synthesis of laminar media.

The problem of the synthesis of a laminar medium with specified amplitude and phase properties of the spectral transfer coefficient is considered. A theorem concerning the solvability of this problem is proved. A new way of representing the operator for the direct problem is introduced which expresses the spectral characteristics of a laminar medium in terms of its wave impedance. A method of constructing particular solutions of the synthesis problem is proposed on the basis of this representation. The basis of the method is given: theorems concerning the eixstence, uniqueness, and stability of the solution are proved.

ON the basis of the idea of regularization, a correct formulation is given of the problem of synthesizing multilayer optical systems with a given transmittance. Examples are given of the synthesis of some important practical systems.