Transmission ellipsometry, circular birefringence, and circular dichroism in the Mueller-matrix formalism

A theoretical framework is presented to describe absorption spectroscopy (AS), spectroscopic ellipsometry (SE), circular birefringence (CB), and circular dichroism (CD) in the Mueller-matrix formalism. Relations between Mueller-matrix elements and the conventional experimental parameters absorption coefficient α, transmission ratio ρt=tanΨteiΔt, polarization rotation β, and ellipticity angle ϵ in AS, SE, CB, and CD, respectively, are presented. If only one of the effects, linear birefringence, circular birefringence, linear dichroism, or circular dichroism, is present, simplified Mueller-matrix descriptions are readily available. In these cases, measurement data are straightforward to interpret, and it is shown that a Mueller-matrix instrument cannot match performance for very small β or ϵ. If several anisotropic effects are present, it is shown that instruments designed for CB- or CD-spectroscopy may deliver false results, and a measurement of the full Mueller matrix is then advantageous and sometimes necessary to avoid erroneous results due to information mixing. In more complex samples, differential decomposition of a Mueller matrix provides a complete separation of all anisotropic effects and, in addition, enables detection of depolarization.