Characterizing dielectric tensors from angle-of-incidence Mueller matrix images

Abstract

Biaxial ellipsometry is a technique that measures the dielectric tensor and thickness of a biaxial substrate, single-layer thin film, or multi-layer structure. The dielectric tensor of a biaxial material consists of the real and imaginary parts of the three orthogonal principal indices (n x + ik x , n y + ik y and n z + ik z ) and three Euler angles (Θ, Φ, ∆) to describe its orientation. The method utilized in this work measures an angle-of-incidence Mueller matrix from a Mueller matrix imaging polarimeter equipped with a pair of microscope objectives with low polarization aberrations. The dielectric tensors for multilayer samples are determined from multi-spectral angle-of-incidence Mueller matrix images in either a transmission or reflection mode using an appropriate dispersion model. Given approximate a priori knowledge of the dielectric tensor and film thickness, a Jones matrix image is first calculated by solving Maxwell's equations at each surface which is then transformed into a Mueller matrix image. An optimization algorithm then finds the best fit dielectric tensor based on matching the measured and calculated angle-of-incidence Mueller matrix images. One use for this application is to more accurately determine the dielectric tensors of biaxial films used in liquid crystal displays.