Related papers: Ray and caustic structure of Ince-Gauss beams
The aim of the present review is to introduce the reader to some of the physical notions and of the mathematical methods that are relevant to the study of nonlinear waves in Bose-Einstein Condensates (BECs). Upon introducing the general…
We present an ab-initio numerical investigation of the internal conical refraction of structured light beams in a biaxial crystal. Starting from the solutions of the Fresnel equation, a theoretical analysis is developed without assuming any…
In this study, we consider a beam summation method adapted from the semiclassical regime of quantum mechanics to study the classical properties of thin light bundles in gravity. In Newtonian paraxial optics, this method has been shown to…
We present a quantum mechanical analysis of the orbital angular momentum of a class of recently discovered elliptically-symmetric stable light fields --- the so-called Ince-Gauss modes. We study, in a fully quantum formalism, how the…
A centred system forms the coherent image of the optical field on a spherical cap, taken as an object, on another spherical cap, whose vertex and curvature center are the respective paraxial images of the vertex and center of the object…
Here we consider the problem of small oscillations of a rotating inviscid incompressible fluid. From a mathematical point of view, new exact solutions to the two-dimensional Poincar\'e-Sobolev equation in a class of domains including…
We consider an ultracold quantum degenerate gas in an optical lattice inside a cavity. This system represents a simple but key model for "quantum optics with quantum gases," where a quantum description of both light and atomic motion is…
We investigate the waveguiding properties of the optical interference pattern of two counter-propagating Laguerre-Gaussian beams. The number, helicity, radius, pitch, depth and frequencies of transverse confinement of the waveguides are…
We investigate the structure of the generalized Weierstrass semigroups at several points on a curve defined over a finite field. We present a description of these semigroups that enables us to deduce properties concerned with the…
The differential energy spectrum of cosmic rays from Cherenkov radiation measurements in EAS in the energy range of 10^15-10^20eV has been compared with an anomalous diffusion model for the particles in interstellar space having fractal…
Collapse of an intense (2+1)-dimensional wave packet in a medium with cubic nonlinearity and a two-dimensional dispersion of an order higher than parabolic is studied both theoretically and experimentally. The carrier waves are microwave…
Classical beams of light with non-uniform polarization patterns (e.g. radially and azimuthally polarized doughnut beams) may exhibit quantum-like features as, for instance, inseparability. We establish an exact correspondence between…
We present a single-scattering formalism for incoherent resonant light scattering by dilute quantum gas systems such as the atomic-trap Bose-Einstein condensates. We show that resonant scattering gives access to more information than the…
It is shown on the examples of Moore and Gosper curves that two spatially shifted or twisted, pre-asymptotic space-filling curves can produce large-scale superstructures akin to moir\'e patterns. To study physical phenomena emerging from…
Coupled beam optics can be geometrically described in terms of invariant eigenmode planes of a stable symplectic ``one-turn'' map $\mathcal M\in Sp(4)$. We show that the non-uniqueness of symplectically normalized bases within each…
The Higher-Order Poincar\'e Sphere (HOPS) provides a powerful geometrical tool for representing vector beams as points on the surface of a unitary sphere. Since a particular position on the surface represents any spatial mode regardless of…
It has been a persistent question at least for a decade where the gravitational lens caustics are in the radial direction: whether in front of the lensing mass, behind the lensing mass, or on the plane normal to the line of sight that…
We present a fully relativistic analysis of Bessel beams revealing some noteworthy features that are not explicit in the standard description. It is shown that there is a reference frame in which the field takes a particularly simple form,…
The two-mode Bose-Hubbard model in the mean-field approximation is revisited emphasizing a geometric interpretation where the system orbits appear as intersection curves of a (Bloch) sphere and a cylinder oriented parallel to the mode axis,…
Mathematically representing the shape of an object is a key ingredient for solving inverse rendering problems. Explicit representations like meshes are efficient to render in a differentiable fashion but have difficulties handling topology…