Transmittance constraints in serial decompositions of depolarizing Mueller matrices: the arrow form of a Mueller matrix.

The passivity of the linear components in the main approaches for serial decompositions of depolarizing Mueller matrices [J. Opt. Soc. Am. A13, 1106 (1996); J. Opt. Soc. Am. A26, 1109 (2009)] is dealt with, and it is found that it is not always possible to perform such decompositions in terms of passive components. A compact form of Mueller matrix ("arrow matrix") associated with any given Mueller matrix, which retains, in a condensed manner, the physical properties relative to transmittance, diattenuation, polarizance, and depolarization, is presented.