Jones-matrix analysis with Pauli matrices: application to ellipsometry

Abstract

The coherency matrix formalism based on Pauli matrices is applied to analyze a general ellipsometer that is described by Jones matrices. Here the Jones matrices are represented as sums of appropriate coefficients times the Pauli matrices and the identity matrix, and intensities are represented as traces of coherency matrices. This approach allows us not only to treat partial polarizations explicitly but also to take advantage of various identities to reduce to algebra the operations necessary for system analysis. A general expression is obtained for the intensity transmitted through a polarizer-sample-compensator-analyzer (PSCA) ellipsometer. This general expression is applied to an ideal PSCA ellipsometer, and then the results are reduced to describe several simpler but commonly used configurations. The results provide insight regarding general capabilities and limitations and allow us to compare different ellipsometer systems directly. Finally, this expression is extended to include artifacts, the explicit representation of which allows a complete determination of their defects.