Depolarizing differential Mueller matrices

Abstract

The evolution of a polarized beam can be described by the differential formulation of Mueller calculus. The nondepolarizing differential Mueller matrices are well known. However, they only account for 7 out of the 16 independent parameters that are necessary to model a general anisotropic depolarizing medium. In this work we present the nine differential Mueller matrices for general depolarizing media, highlighting the physical implications of each of them. Group theory is applied to establish the relationship between the differential matrix and the set of transformation generators in the Minkowski space, of which Lorentz generators constitute a particular subgroup.

Physical model of differential Mueller matrix for depolarizing uniform media

“…Six generators G [1][2][3][4][5][6] are the well known generators of SO(3,1) the proper orthochronous Lorentz group and G 0 is the identity matrix. These generators and their relations are described in Appendix A.…”

“…So there must be a relationship between the off-diagonal coefficients d [7][8][9][10][11][12] physically representing the uncertainties of the respective elementary polarization properties d [1][2][3][4][5][6] and the diagonal anisotropic depolarizations d [13][14][15] . In order to solve this problem Germer [10] proposes a very interesting approach to ensure that the parameterization will only lead to physical Mueller matrices.…”

Polarization gating based on Mueller matrices

“…Instead of this, only the measurement of the experimental Mueller matrix of the sample is required with our method. Secondly, Mueller measurements not only allow building a more general analytical expression, but also give access to extra channels of data processing, such as those provided by the different product Mueller matrix decompositions schemes [21][22][23] or even further, by applying recently developed methods as those based on the differential Mueller matrix [21,[23][24][25][26].…”

Enhanced depolarization contrast in polarization-sensitive optical coherence tomography

“…where * is the complex conjugate, 2 i  denotes the variance and , i j  the covariance, with the subscripts xy, 45, and C referring to the complex propagation constant that completely characterizes anisotropy in the x-y, ±45°, and circular directions, respectively [21]. The DDI, denoted as P  , is given by the Frobenius norm of the previous matrix: P    .…”