Related papers: Transforming nondepolarizing Mueller matrices into…
A topologically ordered phase on a torus possesses degenerate ground states that transform nontrivially under the modular transformations of the torus, generated by Dehn twists. Representation of modular transformations on the ground states…
A modeling methodology and matrix formalism is presented that permits analysis of arbitrarily complex interferometric waveguide systems, including polarization and backreflection effects. Considerable improvement results from separation of…
Mueller polarized bi-directional scattering distribution functions (pBSDFs) are 4x4 matrix-valued functions which depend on acquisition geometry. The most popular pBSDF is a weighted sum between a Fresnel matrix and an ideal depolarizer.…
We demonstrate a polarimetry technique based on geometric phase measurements. The technique can be used to obtain either the polarization state of a light beam or the properties of a polarizing optical system. On the one hand, we apply our…
Higher order tensor inversion is possible for even order. We have shown that a tensor group endowed with the Einstein (contracted) product is isomorphic to the general linear group of degree $n$. With the isomorphic group structures, we…
Mueller matrices are defined with respect to appropriate Cartesian reference frames for the representation of the states of polarization of the input and output electromagnetic waves. The polarimetric quantities that are invariant under…
The direct transition-matrix approach to determination of the electric polarizabilities of quantum bound systems developed in my recent work is applied to study the electric multipole polarizabilities of a two-particle bound complex with a…
We derive transformation formulas for the generalized polarization tensors under rigid motions and scaling in three dimensions, and use them to construct an infinite number of invariants under those transformations. These invariants can be…
It is shown that a complex normal projective variety has non-positive Kodaira dimension if it admits a non-isomorphic quasi-polarized endomorphism. The geometric structure of the variety is described by methods of equivariant lifting and…
Schur decompositions and the corresponding Schur forms of a single matrix, a pair of matrices, or a collection of matrices associated with the periodic eigenvalue problem are frequently used and studied. These forms are upper-triangular…
The ability to control light polarization state is critically important for diverse applications in information processing, telecommunications, and spectroscopy. Here, we propose that a stack of anisotropic van der Waals materials can…
We present a variational approach to a general Lienard-type equation in order to linearize it and, as an example, the Van der Pol oscillator is discussed. The new equation which is almost linear is factorized. The point symmetries of the…
The asymptotic performance of a polar code under successive cancellation decoding is determined by the exponent of its polarizing matrix. We first prove that the partial distances of a polarizing matrix constructed from the Kronecker…
The modification of the rotating vector model in the case of magnetars are calculated. Magnetars may have twisted magnetic field compared with normal pulsars. The polarization position angle of magnetars will change in the case of a twisted…
Advances in vectorial polarisation-resolved imaging are bringing new capabilities to applications ranging from fundamental physics through to clinical diagnosis. Imaging polarimetry requires determination of the Mueller matrix (MM) at every…
We introduce a novel approach that employs techniques from noncommutative Poisson geometry to comprehend the algebra of invariants of two $n\times n$ matrices. We entirely solve the open problem of computing the algebra of invariants of two…
Combining elements of twistor-space, phase space and Clifford algebras, we propose a framework for the construction and quantization of certain (quadric) varieties described by Lorentz-covariant multivector coordiantes. The correspondent…
In this note we mainly study the fine Jordan-Chevalley decomposition: a refinement of the classical Jordan-Chevalley decomposition of a matrix and we pay a particular attention to the field of the coefficients of the matrix. Moreover we…
We outline a program to classify domain walls (DWs) and vector solitons in the 1D two-component coupled nonlinear Schrodinger (CNLS) equation with general coefficients. The CNLS equation is reduced first to a complex ordinary differential…
For any real diagonalizable matrix with complex eigenvalues we provide a real, coordinate free decomposition with a clear geometric interpretation.