# Conventions and formulas for using the Mueller-Stokes calculus in ellipsometry

## Abstract

An analysis of the compatability of ellipsometry conventions with the Mueller-Stokes calculus has shown that for the two approaches to be consistent, modifications to the 1968 Nebraska ellipsometry conventions are necessary. A sign convention is proposed which specifies the ellipticity angle and the fourth Stokes parameter to be positive when the tip of the instantaneous electric-field vector describes a right-handed helix in space. Polarization of this type will be designated as right-handed and represented by a point on the northern half of the Poincaré sphere. The consequences of using this convention, along with the previously adopted ei(ωt+δ) convention for the electric field, are seen in the relationships among several representations of polarization state. These include the magnitudes and phases of the electric-field components, the Jones vector, coherency matrix, Stokes parameters, Poincaré sphere, polarization ratio, ellipsometric parameters ψ and Δ, and the azimuth and ellipticity of the polarization ellipse. The formalism for converting the Jones matrix into the matrix that transforms the coherency vector or the Stokes vector (Mueller matrix) is described. Mueller matrices for a linear retarder and an isotropic reflecting surface and the description of a compensator-analyzer polarimeter are given. © 1980.