Related papers: Revisiting 2x2 matrix optics: Complex vectors, Fer…
The systematization of the purely Lagrangean approach to constrained systems in the form of an algorithm involves the iterative construction of a generalized Hessian matrix W taking a rectangular form. This Hessian will exhibit as many left…
Review of a matrix method used in optics of thin films for the calculation of reflectance, transmittance, absorptance, the electric field distribution inside the stack and the photonic dispersion considering the stack as perfect…
In this paper we introduce a generating vector-operator acting on the class of functions $L_2([a,a+2l])$. This operator produces (for arbitrarily fixed $[a,a+2l]$) infinite number of new generation $L_2$-systems. Every element of the…
We consider a family {P} of determinantal point processes arising in representation theory and random matrix theory. The processes live on the one-dimensional lattice and their correlation kernels correspond to projection operators in the…
Starting from Rodrigues formula we present a general construction of raising and lowering operators for orthogonal polynomials of continuous and discrete variable on uniform lattice. In order to have these operators mutually adjoint we…
We consider how vectorial aspects (polarization) of light propagation can be implemented, and its origin, within a Feynman path integral approach. A key part of this scheme is in generalising the standard optical path length integral from a…
This paper extends three results from classical finite frame theory over real or complex numbers to binary frames for the vector space ${\mathbb Z}_2^d$. Without the notion of inner products or order, we provide an analog of the…
The joint design of the optical system and the downstream algorithm is a challenging and promising task. Due to the demand for balancing the global optimal of imaging systems and the computational cost of physical simulation, existing…
The Dirac-Bergmann algorithm is a recipe for converting a theory with a singular Lagrangian into a constrained Hamiltonian system. Constrained Hamiltonian systems include gauge theories -- general relativity, electromagnetism, Yang Mills,…
We present the gauge-invariant formalism of cosmological weak lensing, accounting for all the relativistic effects due to the scalar, vector, and tensor perturbations at the linear order. While the light propagation is fully described by…
It is well known that Maxwell equations can be expressed in a unitary Schrodinger-Dirac representation for homogeneous media. However, difficulties arise when considering inhomogeneous media. A Dyson map points to a unitary field qubit…
We construct a class of representations of the quadratic R-matrix algebra, given by the reflection equation with the spectral parameter, in terms of certain ordinary difference operators. These operators turn out to act as parameter…
We introduce the notion of a confluent Vandermonde matrix with quaternion entries and discuss its connection with Lagrange-Hermite interpolation over quaternions. Further results include the formula for the rank of a confluent Vandermonde…
Fractional integral operators connected with real-valued scalar functions of matrix argument are applied in problems of mathematics, statistics and natural sciences. In this article we start considering the case of a Gauss hypergeometric…
A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one…
In this article we consider the action of affine group and time rescaling on planar quadratic differential systems. We construct a system of representatives of the orbits of systems with at least five invariant lines, including the line at…
We report on progress for the analytical calculation of the two-loop corrections to top quark pair production at hadron colliders. For the light fermionic corrections in the gluon channel, we discuss the analytical solution for the master…
Diffractive optical information processors have demonstrated significant promise in delivering high-speed, parallel, and energy efficient inference for scaling machine learning tasks. Training, however, remains a major computational…
In this work, we present the theoretical and experimental study of the propagation of Airy beams when passing through two convex lenses with different focal distances. The theoretical analysis is presented from a matrix optical model for an…
We present a new perspective on gravitational lensing. We describe a new extension of the weak lensing formalism capable of describing strongly lensed images. By integrating the non-linear geodesic deviation equation, the amplification…