Optimization of conventional ellipsometric setups for determining the dielectric tensor of arbitrarily anisotropic systems

We present a general theoretical development to optimize the setup of a conventional ellipsometer to determine dielectric tensors of arbitrarily anisotropic systems. Typical conventional ellipsometers permit changing several variables: angle of incidence, azimuth angle of the sample, and the azimuth angles of the polarizer, compensator, or analyzer. We illustrate the optimization with two examples, one using a rotating analyzer ellipsometer where we show that our theory requires changing at least one less variable than required by the Jones matrix approach. In the second example, a new ellipsometric approach is proposed to determine the dielectric tensors and film thicknesses of an arbitrarily anisotropic system. With this approach, only the sample is rotated and all other parts are fixed. Numerical calculations were performed to simulate several common multi-layer structures. Potential applications for in situ quality monitoring of MBE growth or of space growth are also discussed.