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We present a theoretical analysis of the connection between classical polarization optics and quantum mechanics of two-level systems. First, we review the matrix formalism of classical polarization optics from a quantum information…

We demonstrate a method for general linear optical networks that allows one to factorize any SU($n$) matrix in terms of two SU($n-1)$ blocks coupled by an SU(2) entangling beam splitter. The process can be recursively continued in an…

The polarization process when polarizers act on an optical field is studied. We give examples for two kinds of polarizers. The first kind presents an anisotropic absorption - as in a polaroid film - and the second one is based on total…

The photon-induced process of electron-positron pair creation in a strong homogeneous magnetic field, provided that the polarization of particles is arbitrary, has been considered. The polarization of a photon is described in terms of the…

We present a moment expansion method for the systematic characterization of the polarization properties of quantum states of light. Specifically, we link the method to the measurements of the Stokes operator in different directions on the…

By using complex quaternion, which is the system of quaternion representation extended to complex numbers, we show that the laws of electromagnetism can be expressed much more simply and concisely. We also derive the quaternion…

Group elements of SU(2) are expressed in closed form as finite polynomials of the Lie algebra generators, for all definite spin representations of the rotation group. The simple explicit result exhibits connections between group theory,…

It is shown that the reflection 2Cat --> 2Preord of the category of all 2-categories into the category of 2-preorders determines a monotone-light factorization system on 2Cat and that the light morphisms are precisely the 2-functors…

We have described a novel way to determine the Mueller matrix of any optical element by using projection method. For this purpose, we have used two universal SU(2) gadgets for polarization optics to obtain projection matrix directly from…

Our earlier work [J. Opt. 19. (2017) 0905603] showed that, in contrast to the four parameters of the traditional Stokes vector description of the statistics of the partially polarized light, the complete second-order statistics of the…

Analogous to the famous Euler angle parametrization in three-dimensional Euclidean space, a reflection-free Lorentz transformation in (2+1)-dimensional Minkowski space can be decomposed into three simple parts. Applying this decomposition…

An alternative method to the density matrix formalism for the derivation of general expressions of the interaction of polarized atoms with polarized photons and electrons is presented. The expression for the cross-section describing the…

For a general-form polarization biphoton qutrit, physically corresponding to a pair of arbitrarily polarized photons in a single frequency and wavevector mode, we explicitly find polarization Schmidt modes. A simple method is suggested for…

We prove a factorization theorem for heavy-to-light form factors. Our result differs in several important ways from previous proposals. A proper separation of scales gives hard kernels that are free of endpoint singularities. A general…

The Stokes parameters have been found in the framework of quantum electrodynamics for the description of polarization of radiation emitted by relativistic positrons channeled between (110) planes in Si crystal. The degree of polarization,…

We use group theoretic ideas and coset space methods to deal with problems in polarization optics of a global nature. These include the possibility of a globally smooth phase convention for electric fields for all points on the Poincar\'{e}…

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…

A new formalism of beam-optics and polarization has been recently presented, based on an exact matrix representation of the Maxwell equations. This is described in Part-I and Part-II. In this Part, we present the application of the above…

In this tutorial, exponentiation and factorization (decomposition) formulas are derived and discussed for common matrix operators that arise in studies of classical dynamics, linear and nonlinear optics, and special relativity. To…

Light front formalism for composite systems is presented. Derivation of equations for bound state and scattering problems are given. Methods of constructing of elastic form factors and scattering amplitudes of composite particles are…