Related papers: Two theorems on the outer product of input and out…
Lax representation in terms of $2\times 2$ matrices is constructed for a separable multiply--periodic system splitting on two tori. Hyperelliptic Kleinian functions and their reduction to elliptic functions are used.
Linear polarimetric transformations of light polarization states by the action of material media are fully characterized by the corresponding Mueller matrices, which contain in an implicit and intricate manner all measurable information on…
Inspecting three-dimensional partially polarized light fields we show that there is no unambiguous correspondence between the three-dimensional field and coherence matrix (or light beam tensor). Therefore, it is needed to clarify the…
Constructive methods for matrices of multihomogeneous (or multigraded) resultants for unmixed systems have been studied by Weyman, Zelevinsky, Sturmfels, Dickenstein and Emiris. We generalize these constructions to mixed systems, whose…
Modern datasets are often in the form of matrices or arrays,potentially having correlations along each set of data indices. For example, data involving repeated measurements of several variables over time may exhibit temporal correlation as…
Using a quantum electrodynamical approach, we derive the scattering phase matrices for polarized radiation involving forbidden line transitions and in the presence of an external magnetic field. The case of (J=0->2->0) scattering is…
Up till now, the Jones vector is, strictly speaking, only a notion about the state of polarization of plane electromagnetic waves though it is generally applied to paraxial fields approximately. Here we generalize it to non-paraxial fields.…
The Jost function formalism is extended with use of the complex potential in this paper. We derive the Jost function by taking into account the dual state which is defined by the complex conjugate the complex Hamiltonian. By using the…
We apply the method of [arXiv:1705.07610] to compute the Stokes matrices of non-resonant confluent hypergeometric differential equations. We discuss the ambiguity of the presentation of the Stokes matrices regarding different choices. The…
This paper presents a method for expressing the determinant of an N {\times} N complex block matrix in terms of its constituent blocks. The result allows one to reduce the determinant of a matrix with N^2 blocks to the product of the…
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…
While the Lorentz group serves as the basic language for Einstein's special theory of relativity, it is turning out to be the basic mathematical instrument in optical sciences, particularly in ray optics and polarization optics. The beam…
We discuss a new mechanism leading to a matrix product form for the stationary state of one-dimensional stochastic models. The corresponding algebra is quadratic and involves four different matrices. For the example of a…
The Mueller Matrix Polar Decomposition method decomposes a Mueller matrix into a diattenuator, a retarder, and a depolarizer. Among these elements, the retarder, which plays a key role in medical and material characterization, is modelled…
A fast multichannel Stokes/Mueller polarimeter with no mechanically moving parts has been designed to have close to optimal performance from 430-2000 nm by applying a genetic algorithm. Stokes (Mueller) polarimeters are characterized by…
Positive-definite matrices materialize as state transition matrices of linear time-invariant gradient flows, and the composition of such materializes as the state transition after successive steps where the driving potential is suitably…
We develop an abstract look at linear optical networks from the viewpoint of combinatorics and permanents. In particular we show that calculation of matrix elements of unitarily transformed photonic multi-mode states is intimately linked to…
We experimentally implement an optical algorithm for integration of a real-valued bivariate func- tion. A user-defined function is encoded in the position-dependent phase of one of the polarization components of an optical beam. The…
Binary constrained flows of soliton equations admitting $2\times 2$ Lax matrices have 2N degrees of freedom, which is twice as many as degrees of freedom in the case of mono-constrained flows. For their separation of variables only N pairs…
We study the extended Bose--Hubbard model describing an ultracold gas of dipolar molecules in an optical lattice, taking into account all on-site and nearest-neighbor interactions, including occupation-dependent tunneling and pair tunneling…