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It is noted that the Jones-matrix formalism for polarization optics is a six-parameter two-by-two representation of the Lorentz group. It is shown that the four independent Stokes parameters form a Minkowskian four-vector, just like the…
It is well known that there exists a four dimensional complex vector associated with a nondepolarizing Mueller matrix. In this note it is shown that this complex vector, which is isomorphic to the Jones matrix, can be obtained from the…
We review the well-known polarization optics matrix methods, i.e., Jones and Stokes-Mueller calculus, and show how they can be formulated in terms of four-dimensional (4d) rotations of the four independent electromagnetic field quadratures.…
The paper discusses the role played by Mueller and Jones formalisms in polarization optics, by addressing the following aspects: restriction to the SU(2) symmetry, non-relativistic Stokes 3-vectors; Cartan 2-spinors in polarization optics;…
The Stokes Mueller polarimetry is generalized to include nonlinear optical processes such as second- and third-harmonic generation, sum- and difference-frequency generations. The overall algebraic form of the polarimetry is preserved, where…
It is shown that the Stokes-Mueller formalism can be reformulated in terms of quaternions, and the quaternion approach is more suitable for the formalism of Mueller-Jones states that we have recently described. In terms of quaternions it…
It is shown that the two-by-two Jones-matrix formalism for polarization optics is a six-parameter two-by-two representation of the Lorentz group. The attenuation and phase-shift filters are represented respectively by the three-parameter…
In polarization optics unitary and non-unitary operations can be carried out by the Jones matrix. $\mathbf{Z}$ matrix is the $4\times 4$ analogue of the Jones matrix and the Mueller matrix of a nondepolarizing optical medium can be written…
Despite the virtues of Jones and Mueller formalisms for the representation of the polarimetric properties, for some purposes in both Optics and SAR Polarimetry, the concept of coherency vector associated with a nondepolarizing medium has…
In the study of polarized light, there are two basic notions: the Stokes vectors and the matrices which preserve them, called Mueller matrices. The set of Stokes vectors forms a cone: the Future Light Cone. In this work we will see that the…
In polarization optics, an important role play Mueller matrices -- real four-dimensional matrices which describe the effect of action of optical elements on the polarization state of the light, described by 4-dimensional Stokes vectors. An…
We present an approach to fully characterize the polarization of general vector light beams. When attempting to generalize the notion of Stokes parameters to nonparaxial light beams in momentum space, we find that the Jones function that…
Group-theoretical analysis of arbitrary polarization devices is performed, based on the theory of the Lorentz group. In effective "non-relativistic" Mueller case, described by 3-dimensional orthogonal matrices, results of the one…
In the context of applying the Lorentz group theory to polarization optics in the frames of Stokes-Mueller formalism, some properties of the Lorentz group are investigated. We start with the factorized form of arbitrary Lorentz matrix as a…
The Mueller-Stokes formalism which governs conventional polarization optics is formulated for plane waves, and thus the only qualification one could demand of a $4\times 4$ real matrix $M$ in order that it qualifies to be the Mueller matrix…
Modern digital crosscorrelators permit the simultaneous measurement of all four Stokes parameters. However, the results must be calibrated to correct for the polarization transfer function of the receiving system. The transfer function for…
It was generally assumed that the Stokes parameters are complete characterization for the state of polarization of a plane light wave so that their counterparts in quantum optics, called the Stokes operators, represent the polarization of…
Stokes Muller formalism is important to understand the optical properties of materials by measuring the change in the polarization state of light upon scattering. The formalism can be extended to nonlinear scattering processes involving two…
The Stokes formalism of polarization physics has astounding structural parallels with the formalism used for relativity theory in Minkowski spacetime. The structure and symmetry properties of the Mueller matrices are the same as those for…
The work defines the general form of the Jones vector and establishes the Jones matrix for polarizers, wave plates, Faraday rotators, Q-plates, and spiral phase plates. We establish the generalized Jones calculus for vortex, vector, and…