Related papers: Binary Representations of ABCD Matrices
The various non-linear transformations incurred by the rays in an optical system can be modelled by matrix products up to any desired order of approximation. Mathematica software has been used to find the appropriate matrix coefficients for…
By bivariate irreducible representations of ${\rm Sp}(2r)$, we mean irreducible representations with highest weights containing at most two nonzero entries, using the usual identification of dominant weights for complex symplectic Lie…
The Poincar\'e sphere is a graphical representation in a three-dimensional space for the polarization of light. Similarly, an optical element with spatially varying birefringence can be represented by a surface on a four-dimensional…
In this paper, an algorithm for construction of multiple sets of two dimensional (2D) or matrix unipolar (optical) orthogonal codes has been proposed. Representations of these 2D codes in difference of positions representation (DoPR) have…
This work provides a quaternioinc reprsentation for real symplectic matrices in dimension four, analogous to the pair of unit quaternions representation for special orthogonal matrices. In the process of finding formulae for this…
Contemporary presentation of the version 1 demonstrates briefly the development of our investigations and our future goals. The improved free of difficulties in interpretation and printing errors version is presented. The 256-dimensional…
We use group or representation theory and scattering matrix calculations to derive analytical results for the band structure topology and the scattering parameters, applicable to any chiral photonic crystal with body-centered cubic symmetry…
The analysis of strong lensing images usually involves an external convergence and shear, which are meant to model the effect of perturbations along the line of sight, on top of the main lens. Such a description of line-of-sight…
A wide range of numerical and semi-analytical approaches has been developed for optical modeling of photonic-crystal surface-emitting lasers (PCSELs). However, a systematic framework for comparing their predictive capabilities and…
Lorentz's group represented by the hypercomplex system of numbers, which is based on dirac matrices, is investigated. This representation is similar to the space rotation representation by quaternions. This representation has several…
We define a special matrix multiplication among a special subset of $2N\x 2N$ matrices, and study the resulting (non-associative) algebras and their subalgebras. We derive the conditions under which these algebras become alternative…
Aberration compensation with emphasis on the generalized spherical aberration components is discussed for plane-symmetric and anamorphic optical systems. A narrow field-of-view double-plane symmetric telescope objective containing…
We investigate binary lenses with $1/r^n$ potentials in the asymmetric case with two lenses with different indexes $n$ and $m$. These kinds of potentials have been widely used in several contexts, ranging from galaxies with halos described…
It has been recently shown that the lens equation for a binary gravitational lens, which is apparently a coupled system, can be reduced to a real fifth-order (quintic) algebraic equation. Some algebraic properties of the real quintic…
It is usually assumed that the ellipticity power spectrum measured in weak lensing observations can be expressed as an integral over the underlying matter power spectrum. This is true at second order in the gravitational potential. We…
We present a comprehensive and self-contained discussion of the use of the transfer matrix to study propagation in one-dimensional lossless systems, including a variety of examples, such as superlattices, photonic crystals, and optical…
We present formal expressions for the optical scalars in terms of the curvature scalars in the weak gravitational lensing regime at second order in perturbations of a flat background without mentioning the extension of the lens or their…
The standard weak lensing formalism assumes that the lensing map relating the observed image of a source to its intrinsic shape depends only on the deflection angle. We show that this description is incomplete beyond linear perturbation…
The boundary-value problem of the reflection and transmission of a plane wave due to a slab of an electro-optic structurally chiral material (SCM) is formulated in terms of a 4x4 matrix ordinary differential equation. The SCM slab can be…
We extend the existing skew polynomial representations of matrix algebras which are direct sum of matrix spaces over division rings. In this representation, the sum-rank distance between two tuples of matrices is captured by a weight…