Mueller matrix symmetry for both reciprocal and nonreciprocal metamaterials

Mueller matrices relate the Stokes parameters of the incident and emerging light, providing useful information about the radiative properties and other characteristics of the medium. Determining all elements of the 4 × 4 Mueller matrix requires complete polarimetry, which is often challenging to perform. Partial polarimetry, on the other hand, uses simpler optical components in generating and/or analyzing states of polarization, thereby measuring only a subset of the Mueller matrix. However, it may determine the full Mueller matrix under specific symmetry conditions. The present study develops a symmetry classification scheme to categorize the Mueller matrix of materials. It is shown that the symmetry of the Mueller matrix is directly determined from the information of symmetries of the sample's optical properties. Numerical calculations of various measurement scenarios, structures, and materials (with or without Lorentz reciprocity) are carried out to validate the methodology. This study offers an insightful understanding of Mueller matrix symmetry and practical guidance for simplified ellipsometry measurements.