Related papers: Computing aberration coefficients for plane-symmet…
The onset of transformation optics has opened avenues for designing of a plenitude of applications related to propagation of electromagnetic waves in anisotropic media. In this paper, an algorithm is proposed using a coordinate…
We develop some calculation schemes to determine dynamics of a wide class of integrable quantum-optical models using their symmetry adapted reformulation in terms of polynomial Lie algebras $su_{pd}(2)$. These schemes, based on "diagonal"…
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 present an algorithm to fair a given planar curve by a log-aesthetic curve (LAC). We show how a general LAC segment can be uniquely characterized by seven parameters and present a method of parametric approximation based on this fact.…
We propose an effective route to fully control the phase of plane waves reflected from electrically (optically) thin sheets. This becomes possible using engineered artificial full-reflection layers (metamirrors) as arrays of electrically…
We carry out the group classification of the class of two-dimensional shallow water equations with variable bottom topography using an optimized version of the method of furcate splitting. The equivalence group of this class is found by the…
Invariant affine reflection algebras are the last and the most general known extension of affine Kac-Moody Lie algebras, introduced in recent years. We develop a method known as "affinization" to the class of invariant affine reflection…
The multi-plane phase retrieval method provides a budget-friendly and effective way to perform phase imaging, yet it often encounters alignment challenges due to shifts along the optical axis in experiments. Traditional methods, such as…
Aberration and radiation pressure reflected by a moving mirror are examples of the Klein and Poincar\'e models of hyperbolic geometry, respectively. Reflection at a moving mirror produces a two-way Dopper shift. Its one-way counterpart,…
We propose a method to monochromatize multiple orders of high harmonics by using a proper designed multilayer mirror. Multilayer mirrors designed by our concept realize the perfect extraction of a single-order harmonic from multiple-order…
Geometric optics is often described as tracing the paths of non-diffracting rays through an optical system. In the paraxial limit, ray traces can be calculated using ray transfer matrices (colloquially, ABCD matrices), which are 2x2…
In this work, we consider Lie algebras L containing a subalgebra isomorphic to sl3 and such that L decomposes as a module for that sl3 subalgebra into copies of the adjoint module, the natural 3-dimensional module and its dual, and the…
A technique is presented for producing synthetic images from numerical simulations whereby the image resolution is adapted around prominent features. In so doing, adaptive image ray-tracing (AIR) improves the efficiency of a calculation by…
Q1: Why deploy N wavefront sensors on a three mirror anastigmat (TMA) and not N + 1? Q2: Why measure M Zernike coefficients and not M + 1? Q3: Why control L rigid body degrees of freedom (total) on the secondary and tertiary and not L + 1?…
Neutron and X-ray reflectometry are important methods for studying thin multilayer systems. The Parratt method and the method of characteristic matrices, also referred to as transfer matrices, are used for simulation, evaluation of…
We investigate a certain class of solvable metric Lie algebras. For this purpose a theory of twofold extensions associated to an orthogonal representation of an abelian Lie algebra is developed. Among other things, we obtain a…
We study a Lie algebra $\mathcal A_{a_1,\ldots,a_{n-1}}$ of deformed skew-symmetric $n \times n$ matrices endowed with a Lie bracket given by a choice of deformed symmetric matrix. The deformations are parametrized by a sequence of real…
This paper is dedicated to method for spectral and polarization selective optical systems properties investigations for accurate analysis of nonclassical diffraction gratings properties: aspherical surfaces, variable grating step, variable…
The recent years have given rise to a large number of techniques for "looking around corners", i.e., for reconstructing occluded objects from time-resolved measurements of indirect light reflections off a wall. While the direct view of…
We propose the method for obtaining invariants of arbitrary representations of Lie groups that reduces this problem to known problems of linear algebra. The basis of this method is the idea of a special extension of the representation…