Related papers: Two-vector representation of a nondepolarizing Mue…
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…
Via a non degenerate symmetric bilinear form we identify the coadjoint representation with a new representation and so we induce on the orbits a simplectic form. By considering Hamiltonian systems on the orbits we study some features of…
We use categorical method and birational geometry to study moduli spaces of quiver representations. From certain "representable" functor, we construct a birational transformation from the moduli space of representations of one quiver to…
A relative position 4-vector is constructed for two spin-zero particles. Some advantages of this relative position over Bakamjian-Thomas are pointed out. The centre-of-mass (CM) and relative positions and momenta are an explicit realisation…
We study moduli spaces of (semi-)stable representations of one-point extensions of quivers by rigid representations. This class of moduli spaces unifies Grassmannians of subrepresentations of rigid representations and moduli spaces of…
We use polarization operators known from quantum theory of angular momentum to expand the $N \times N$ dimensional density operators. Thereby, we construct generalized Bloch vectors representing density matrices. We study their properties…
Transmission matrices are valuable tools to describe and control light transport through scattering media. There are only a few cases where the transmission matrix can be compared to microscopic theories. Here we measure the…
We establish a connection between certain unique models, or equivalently unique functionals, for representations of p-adic groups and linear characters of their corresponding Hecke algebras. This allows us to give a uniform evaluation of…
Lie algebra is a hidden mathematical structure behind various quantum systems realised in nature. Here, we consider $SU(2)$ wavefunctions for polarisation states of coherent photons emitted from a laser source, and discuss the relationship…
In this work, oriented for students with knowledge of basics of linear algebra, we demonstrate, how the use of polar decomposition allows one to understand metric properties of non-degenerate linear operators in $R^2$.
In this survey one discusses the notion of the Poincar\'e series of multi-index filtrations, an alternative approach to the definition, a method of computation of the Poincar\'e series based on the notion of integration with respect to the…
A representation of solutions of the wave equation with two spatial coordinates in terms of localized elementary ones is presented. Elementary solutions are constructed from four solutions with the help of transformations of the affine…
In polarization optics, various topological constructs, namely Poincar\'e spheres of different orders, are used to represent uniform and structured polarization distributions. Similarly, there are also structured polarization optical…
The generalized theory of Stokes Mueller polarimetry is employed to develop the third-order optical polarimetry framework for third-harmonic generation (THG). The outgoing and incoming radiations are represented by 4-element and 16-element…
The properties of metric perturbations are determined in the context of an expanding Universe governed by a modified theory of gravity with a non-minimal coupling between curvature and matter. We analyse the dynamics of the 6 components of…
Complete polarimeters deliver the full polarization transfer matrix of a medium that relates input polarization states to output polarization states. In order to interpret the Mueller matrix of a luminescent medium at the emission…
Designing a single element for all polarization transformations on a Poincar\'e sphere is impossible due to practical limitations and hence a combination of few standard wave-plates are used to construct a gadget. With this gadget it is…
In this work, we develop a hybrid-order Poincar\'{e} sphere to describe the evolution of polarization states of wave propagation in inhomogeneous anisotropic media. We extend the orbital Poincar\'{e} sphere and high-order Poincar\'{e}…
Forward models for the Mueller Matrix (MM) components of materials with relative magnetic permeability tensor {\mu} \neq 1 are studied. 4x4 matrix formalism is employed to produce general solutions for the complex reflection coefficients…
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;…