Related papers: Singular Mueller matrices
Orthogonal Mueller matrices can be considered either as corresponding to retarders or to generalized transformations of the polarization basis for the representation of Stokes vectors, so that they constitute the only type of Mueller…
Polarization is a basic property of light and is fundamentally linked to the internal geometry of a source of radiation. Polarimetry complements photometric, spectroscopic, and imaging analyses of sources of radiation and has made possible…
Let X be a singular affine normal variety with coordinate ring R and assume that there is an R-order admitting a stability structure such that the scheme of relevant semistable representations is smooth, then we construct a partial…
We show that polarization singularities, generic for any complex vector field but so far mostly studied for electromagnetic fields, appear naturally in inhomogeneous yet monochromatic sound and water-surface (e.g., gravity or capillary)…
It has become obvious that certain singular phenomena cannot be explained by a mere investigation of the configuration space, defined as the solution set of the loop closure equations. For example, it was observed that a particular 6R…
We investigate theoretical properties of beams of light with non-uniform polarization patterns. Specifically, we determine all possible configurations of cylindrically polarized modes (CPMs) of the electro-magnetic field, calculate their…
Our goal here is to see the space of matrices of a given size from a geometric and topological perspective, with emphasis on the families of various ranks and how they fit together. We pay special attention to the nearest orthogonal…
The centralizer algebra of a matrix consists of those matrices that commute with it. We investigate the basic representation-theoretic invariants of centralizer algebras, namely their radicals, projective indecomposable modules, injective…
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;…
Polarization independent Mie scattering of building blocks is foundational for constructions of optical systems with robust functionalities. Conventional studies for such polarization independence are generally restricted to special states…
We describe the evolution of a paraxial electromagnetic wave characterizing by a non-uniform polarization distribution with singularities and propagating in a weakly anisotropic medium. Our approach is based on the Stokes vector evolution…
We present a symmetry-based theory of the depolarization induced by subwavelength metal hole arrays. We derive the Mueller matrices of hole arrays with various symmetries (in particular square and hexagonal) when illuminated by a…
Mueller and Jones matrices have been thoroughly studied as mathematical tools to describe the manipulation of the polarization state of classical light. In particular, the most general physical transformation on the polarization state has…
Analysis of the singularities of the polarization field of CMB, where polarization is equal to zero, is presented. It is found that the classification of the singular points differs from the usual three types known in the ordinary…
The Pauli channel acting on 2 x 2 matrices is generalized to an n-level quantum system. When the full matrix algebra M is decomposed into pairwise complementary subalgebras, then trace-preserving linear mappings from M to M are constructed…
In recent years, there has been a mounting interest in better methods of measuring nanoscale objects, especially in fields such as nanotechnology, biomedicine, cleantech, and microelectronics. Conventional methods have proved insufficient,…
A nonlinear scattering transform is studied for the two-dimensional Schrodinger equation at zero energy with a radial potential. First explicit examples are presented, both theoretically and computationally, of potentials with nontrivial…
The polarization of the light scattered by an optically dense, random solution of dielectric nanoparticles shows peculiar properties when the scatterers exhibit strong electric and magnetic polarizabilities. While the distribution of the…
We study linear polarization due to scattering of light on a cloudlet of particles, taking into account the radiation drag and the gravitational pull exerted on them by a central body. Effects of special and general relativity are included…
The polarization of a coherent depolarized incident light beam passing through a disordered medium is investigated. The local polarization of the scattered far field and the probability density function are calculated and show an excellent…