Related papers: Geometrical aspects of first-order optical systems
The method of images, when applied to an opto-mechanical Fabry-Perot resonator with a heavy, charged mirror, and a light, charged mirror that can be driven into motion, reveals that the highest order images can move relativistically when…
The purpose of this paper is twofold. In the first part we concentrate on hyperplane sections of algebraic schemes, and present results for determining when Gr\"obner bases pass to the quotient and when they can be lifted. The main…
A general family of structured Gaussian beams naturally emerges from a consideration of families of rays. These ray families, with the property that their transverse profile is invariant upon propagation (except for cycling of the rays and…
We introduce a numerical procedure which permits to drastically accelerate the design of multimode photonic crystal resonators. Specifically, we demonstrate that the optical response of an important class of such nanoscale structures is…
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 describe a generalized formalism, addressing the fundamental problem of reflection and transmission of complex optical waves at a plane dielectric interface. Our formalism involves the application of generalized operator matrices to the…
The beam transfer matrix, often called the $ABCD$ matrix, is a two-by-two matrix with unit determinant, and with three independent parameters. It is noted that this matrix cannot always be diagonalized. It can however be brought by rotation…
For the purpose of understanding second-order scalar PDEs and their hydrodynamic integrability, we introduce G-structures that are induced on hypersurfaces of the space of symmetric matrices (interpreted as the fiber of second-order jet…
We construct a canonical irreducible representation for the orthofermion algebra of arbitrary order, and show that every representation decomposes into irreducible representations that are isomorphic to either the canonical representation…
We present a full formalism for the calculation of the linear and second-order optical response for semiconductors and insulators. The expressions for the optical susceptibilities are derived within perturbation theory. As a starting point…
We reelaborate on the basic properties of lossless multilayers. We show that the transfer matrices for these multilayers have essentially the same algebraic properties as the Lorentz group SO(2,1) in a (2+1)-dimensional spacetime, as well…
The subject of this introductory course is transverse dynamics of charged particle beams in linear approximation. Starting with a discussion of the most important types of magnets and defining their multipole strengths, the linearized…
Optics are bidirectional data accessors that capture data transformation patterns such as accessing subfields or iterating over containers. Profunctor optics are a particular choice of representation supporting modularity, meaning that we…
General high-order rogue wave solutions for the (1+1)-dimensional Yajima-Oikawa (YO) system are derived by using Hirota's bilinear method and the KP-hierarchy reduction technique. These rogue wave solutions are presented in terms of…
We review the theory of first BGG operators and study how to approach them and find their solution on homogeneous geometries. We provide many new examples of parabolic geometries that admit solutions of first BGG operators with many…
The problem of diagonalizing a class of complicated matrices, to be called ultrametric matrices, is investigated. These matrices appear at various stages in the description of disordered systems with many equilibrium phases by the technique…
- An algorithm for calculating the radiation field of a charged point particle performing a spiral motion in an infinite cylindrical waveguide with a multilayer side wall is found. The number of layers and their filling is arbitrary. The…
Based on diffraction theory and the propagation of the light, Fourier optics is a powerful tool allowing the estimation of a visible-range imaging system to transfer the spatial frequency components of an object. The analyses of the imaging…
I develop the formalism that allows calculation of beam envelopes through a linear accelerator given its on-axis electric field. Space charge can naturally be added using Sacherer formalism. A complicating feature is that the reference…
Six families of generalized hypergeometric series in a variable $x$ and an arbitrary number of parameters are considered. Each of them is indexed by an integer $n$. Linear recurrence relations in $n$ relate these functions and their product…