## Abstract

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 determined by the relationship between the refractive indices of the ambient ${N}_{0}$, film ${N}_{1}$, and substrate ${N}_{2}$. If ${N}_{1}<\sqrt{{N}_{0}{N}_{2}}$, the system is negative; if ${N}_{1}=\sqrt{{N}_{0}{N}_{2}}$, the system is zero; and if ${N}_{1}>\sqrt{{N}_{0}{N}_{2}}$, 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, ${N}_{1}\u2a7d\sqrt{{N}_{1}{N}_{2}}$ is the condition to be satisfied to realize reflection-type retarders with film–substrate systems.

© 2005 Optical Society of America

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