Related papers: Information structure and general characterization…
We give uniqueness theorem and reconstruction algorithm for the nonlinearized problem of finding the dielectric anisotropy f of the medium from non-overdetermined polarization tomography data. We assume that the medium has uniform…
Motivated by new technologies for designing and tailoring metamaterials, we seek properties for certain classes of nonlinear optical materials that allow room for a reversibly controlled opacity-to-transparency phase transition through the…
We develop a model based on a multiple scattering theory to describe the diffusion of polarized light in disordered media exhibiting short-range structural correlations. Starting from exact expressions of the average field and the field…
We present a photonic wave packet construction which is immune against the decoherence effects induced by the action of the Lorentz group. The amplitudes of a pure quantum state representing the wave packet remain invariant irrespective of…
We describe a basic correspondence between linear algebraic structures within vector embeddings in artificial neural networks and conditional independence constraints on the probability distributions modeled by these networks. Our framework…
Elementary methods are used to examine some nontrivial mathematical issues underpinning the Lorentz transformation. Its eigen-system is characterized through the exponential of a $G$-skew symmetric matrix, underlining its unconnectedness at…
Sensing light's polarization and wavefront direction enables surface curvature assessment, material identification, shadow differentiation, and improved image quality in turbid environments. Traditional polarization cameras utilize multiple…
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…
We explore the set of unitary matrices characterized by a given structure in the context of their applications in the field of Quantum Information. In the first part of the Thesis we focus on classification of special classes of unitary…
We study the normal form of multipartite density matrices. It is shown that the correlation matrix (CM) separability criterion can be improved from the normal form we obtained under filtering transformations. Based on CM criterion the…
For a multivariate normal distribution, the sparsity of the covariance and precision matrices encodes complete information about independence and conditional independence properties. For general distributions, the covariance and precision…
Companion matrices of the second type are characterized by properties that involve bilinear maps.
Realistic applications in metal detection involve multiple inhomogeneous conducting permeable objects and the aim of this paper is to characterise such objects by polarizability tensors. We show that, for the eddy current model, the leading…
Top polarisation measurements at the LHC are often performed using template methods. I discuss the role of quantum interference between polarisation states - which is mostly overlooked in the literature. Furthermore, I argue which is the…
When the sizes of photonic nanoparticles are much smaller than the excitation wavelength, their optical response can be efficiently described with a series of polarizability tensors. Here, we propose a universal method to extract the…
A unification of characteristic mode decomposition for all method-of-moment formulations of field integral equations describing free-space scattering is derived. The work is based on an algebraic link between impedance and transition…
In this paper, we study spectral properties of generalized weighted Hilbert matrices. In particular, we establish results on the spectral norm, determinant, as well as various relations between the eigenvalues and eigenvectors of such…
We consider emission of a photon by an electron in the field of a strong laser wave. Polarization effects in this process are important for a number of physical problems. We discuss a probability of this process for linearly polarized laser…
Many polarisation techniques have been harnessed for decades in biological and clinical research, each based upon measurement of the vectorial properties of light or the vectorial transformations imposed on light by objects. Various…
By using finite resolution measurements it is possible to simultaneously obtain noisy information on two non-commuting polarization components of a single photon. This method can be applied to a pair of entangled photons with polarization…