A Simple Necessary and Sufficient Condition on Physically Realizable Mueller Matrices

Abstract Development of simple tools to test physical realizability of measured or computed Mueller matrices is the subject of this paper. In particular, the overpolarization problem, i.e., the problem of ensuring that the output degree of polarization does not exceed unity is solved by finding an easily implementable necessary and sufficient condition. With G being the Lorentz metric, it states that a given matrix M is not overpolarizing if and only if the spectrum of GM T GM is real and an eigenvector associated with the largest eigenvalue is a physical Stokes vector. This result is used to characterize some M classes of special interest, and is used to test several examples from recent literature.