General criterion for the physical realizability of the differential Mueller matrix

In this Letter, we derive a general criterion for the physical realizability of the differential Mueller matrix m of a depolarizing continuous medium. The criterion is based on checking the positive semidefiniteness of a 3×3 restriction of the coherency matrix of the G-symmetric component of m and turns out be a close analogue of the well-known criterion of Cloude for a Mueller matrix to be physically realizable. The related aspects of local and global, as well as Stokes and physical (or Cloude), realizabilities are discussed comparatively. The practical application of the criterion, in connection with the above types of realizabilities, is illustrated on experimental Mueller matrices from the literature.