The widely-used Jones and Mueller differential polarization calculi allow non-depolarizing deterministic polarization interactions, known to be elements of the SO + (1, 3) Lorentz group, to be described in an efficient way. In this Letter, a stochastic differential Jones formalism is shown to provide a clear physical insight on light depolarization, which arises from the interaction of polarized light with a random medium showing fluctuating anisotropic properties. Based on this formalism, several intrinsic depolarization metrics naturally arise to efficiently characterize light depolarization in a medium, and an irreversibility property of depolarizing transformations is finally established.PACS numbers: 42.25.Ja; 42.25.Bs; 78.20.Bh; 89.70.Cf; 02.20.Sv In the field of polarimetry, Jones and Stokes/Mueller formalisms have always appeared as dual and often exclusive approaches, whose specific characteristics have been exploited for diverse applications. On the one hand, the description of field coherence in the Jones calculus, which relates the input and output 2-dimensional complex electric field through E out = JE in , justifies its use in ellipsometry [1,2], optical design [3-6], spectroscopy [6], astronomy [7] or radar (PolSar) [8]. On the other hand, Mueller calculus is widely used in biophotonics [9,10], material characterization [11,12] or teledetection [13], as it is based on optical field observables (intensity measurements), relating the input and output 4-dimensional real Stokes vector through s out = Ms in . As a consequence, these approaches fundamentally differ in their capacity to characterize depolarizing light-matter interactions (i.e., non-deterministic polarization transformations yielding a partial randomization of the input electric field). As Jones already pointed out in one of his seminal papers [14], Jones matrices are unable to directly describe depolarizing media, which can however be grasped in the Mueller formalism via depolarizing Mueller matrices. This discrepancy between both standpoints takes part in the debate, still topical in the scientific community, about the physical origin of light depolarization in media [15][16][17][18][19][20][21][22][23]. In this Letter, we show that the differential polarization formalism, which naturally arises from group theory, provides new physical insight on depolarizing light-matter interactions. This approach allows us to define intrinsic depolarization metrics, and to demonstrate an irreversibility property for depolarizing transformations, as a counterpart to the well-known invariance property verified by deterministic interactions.In the specific situation of a deterministic polarization transformation, there is a clear one-to-one relationship (recalled in Fig. 1) between a 2 × 2 complex Jones matrix J and the corresponding 4 × 4 real-valued nondepolarizing Mueller-Jones matrix M nd [24,25]. Interestingly, when one considers normalized unit-determinant matrices, both descriptions appear to be isomorphic representations of the same 6-dimensi...
