Thin-film coatings--a transmission ellipsometric function approach: I. Nonnegative transmission systems, polarization devices, coatings, and closed-form design formulas.

The transmission ellipsometric function (TEF) of a film-substrate system relates the polarization change, upon transmission, of an electromagnetic wave obliquely incident on, and transmitted through, a film-substrate system. The behavior of the TEF depends on the category of the film-substrate system: negative, zero, or positive. The category is determined by the sign of [equation in text]: negative for a negative film-substrate system, zero for a zero system, and positive for a positive system. We discuss the behavior of the TEFs of the two transparent nonnegative film-substrate systems, zero and positive. We describe the TEF as two successive transformations and analyze its behavior as the angle of incidence and film thickness of the film-substrate system are changed. We use the constant-angle-of-incidence contours and constant- thickness contours to analyze and utilize that behavior. From the analysis and understanding of the behavior of the TEF, and from the definition of a polarization device as a film-substrate system that introduces prescribed polarization changes, we discuss the design of all possible types of polarization devices using either of the two systems. We present a design formula for each. We also present a general formula that is used for the design of any of the devices. Thin-film coatings are treated as polarization devices for the purposes of our discussion. We conclude with a brief discussion of suggested practical modifications to, and simplifications of, ellipsometric memory, which is an interesting application of polarization devices for which there is a patent pending.

Design of reflection retarders by use of nonnegative film-substrate systems.

A reflection-type film-substrate retarder is an optical device that changes the relative phase but not the relative amplitude of light upon reflection from a film-substrate system. While there are several such device designs based on the common negative film-substrate system, very little has been done with the other two categories of systems, zero and positive. The system category is determine by the relationship between the refractive indices of the ambient N0, film N1 and substrate N2. If N1 < square root of N0N2, the system is negative; if N1 = square root of N0N2, the system is zero; and if N1 > square root of N0N2, the system is positive. The design procedure and characteristics of zero-system reflection retarders are discussed. The polarization and ellipsometric properties of the positive system preclude the existence of a reflection retarder. First, a brief characterization of the zero and positive systems by means of constant-angle-of-incidence contours and constant-thickness contours of the ellipsometric function is presented and discussed. Then an algorithm outlining the design procedures is presented, and the characteristics of the obtained designs are optimized, analyzed, and discussed. The exact retarder is valid for a single wavelength at a set angle of incidence. The design tolerance to changes in the design parameters is analyzed and discussed. In general, N1 < or = square root of N1N2 is the condition to be satisfied to realize reflection-type retarders with film-substrate systems.