Related papers: Ray and caustic structure of Ince-Gauss beams
It is shown that the kinematic equations governing steady motions of an ideal fibre-reinforced fluid in a curved stratum may be expressed entirely in terms of the intrinsic Gauss equation, which assumes the form of a partial differential…
Quantum universal invariants of general N-beam Gaussian fields are investigated from the point of view of fields' intensity moments. A method that uniquely links these invariants, including the global and marginal fields' purities, to…
We report on a new class of exact solutions of the scalar Helmholtz equation obtained by carefully engineering the form of the angular spectrum of a Bessel beam. We consider in particular the case in which the angular spectrum of such…
This paper explores the topologies of caustics observed in instruments that employ charged particles, such as electron and ion microscopes. These geometrical figures are studied here using catastrophe theory. The application of this…
General properties of linear propagation of discretized light in homogeneous and curved waveguide arrays are comprehensively investigated and compared to those of paraxial diffraction in continuous media. In particular, general laws…
I investigate the caustics produced by the fall of collisionless dark matter in and out of a galaxy in the limit of negligible velocity dispersion. The outer caustics are spherical shells enveloping the galaxy. The inner caustics are rings.…
Bessel beams are renowned members of a wide family of non-diffracting (propagation-invariant) fields. We report on experiments showing that non-diffracting fields are also immune to diffusion. We map the phase and magnitude of structured…
We study the problem of gravitational lensing by binary galaxies, idealized as two isothermal spheres. In a wide binary, each galaxy possesses individual tangential, nearly astroidal, caustics and roundish radial caustics. As the separation…
Two Kerr-squeezed optical beams can be combined in a beamsplitter to produce non-Gaussian continuous-variable entangled states. We characterize the non-Gaussian nature of the output by calculating the third-order cumulant of quadrature…
We deduce a set of circularly polarized Gaussian laser beam modes via a separation-of-variables solution to the Helmholtz wave equation in oblate spheriodal coordinates. On transforming to cylindrical coordinates these become the well-known…
All the components of cosmic rays have 'structure' in their energy spectra at some level, ie deviations from a simple power law, and their examination is relevant to the origin of the particles. Emphasis, here, is placed on the large-scale…
We consider a Bose-Einstein condensate (BEC), which is characterized by long-range and anisotropic dipole-dipole interactions and vanishing s-wave scattering length, in a double-well potential. The properties of this system are investigated…
New phenomena of collective light scattering are observed when an elongated Bose-Einstein condensate is pumped by two non-interfering beams counterpropagating along its long axis. In the limit of small Rayleigh scattering rates, the…
Vector modes represent the most general state of light in which, the spatial and polarisation degrees of freedom are coupled in a non-separable way. Crucially, while polarisation is limited to a bi-dimensional space, the spatial degree of…
On a Riemannian manifold with a positive lower bound on the Ricci tensor, the distance of isoperimetric sets from geodesic balls is quantitatively controlled in terms of the gap between the isoperimetric profile of the manifold and that of…
Phase-space procedure based on coherent state representation is proposed for investigation of reflection and transmission of light beams at a curved dielectric boundary. Numerical simulations of reflection and transmission of light at…
A space curve is determined by conformal arc-length, conformal curvature, and conformal torsion, up to M\"obius transformations. We use the spaces of osculating circles and spheres to give a conformally defined moving frame of a curve in…
In this Letter we propose the concept of the evanescent Airy beam. We analyze the structure of the ideal evanescent Airy beam, which initial profile has the Airy form, while the spectral decomposition consists of only evanescent partial…
In many physical situations involving diverse length scales, waves or rays representing them travel through media characterized by spatially smooth, random, modest refactive index variations. "Primary" diffraction (by individual…
Although acoustics is one of the disciplines of mechanics, its "geometrization" is still limited to a few areas. As shown in the work on nonlinear propagation in Reissner beams, it seems that an interpretation of the theories of acoustics…