Related papers: Ray and caustic structure of Ince-Gauss beams
We develop the paraxial approximation for electromagnetic fields in arbitrary isotropy-broken media in terms of the ray-wave tilt and the curvature of materials Fresnel wave surfaces. We obtain solutions of the paraxial equation in the form…
Given any smooth plane curve {\alpha}(s)representing a mirror that reflects light the usual way and any radiant light source at a point in the plane, the reflected light will produce a caustic envelope. For such an envelope, we show that…
Analogous coherent states are deduced from classical optical fields on curved surface in this paper. The Gaussian laser beam, as a fundamental mode, cannot be adequately simulated by coherent states due to their inherent diffraction in flat…
Airy beams are known for displaying shape invariance and self-acceleration along the transverse direction while they propagate forwards. Although these properties could be associated with the beam coherence, it has been revealed that they…
Under the introduction of any interface in its trajectory, an optical beam experiences polarization-dependent deflections in the longitudinal and transverse directions with respect to the plane of incidence. The physics of such optical beam…
A Gaussian beam method is presented for the analysis of the energy of the high frequency solution to the mixed problem of the scalar wave equation in an open and convex subset, with initial conditions compactly supported in this set, and…
We study the geometry of fanning curves in the Grassmann manifold of n-dimensional subspaces of $\mathbb{R}^{kn}$; we construct a complete system of invariants which solve the congruence problem. The geometry of the invariants themselves…
Canonical principal parameters are introduced for surfaces in $\mathbb R^3$ without umbilical points. It is proved that in these parameters the surface is determined (up to position in space) by a pair of invariants satisfying a partial…
Taxonomy of radio pulsar profiles is mostly based on a system of Ptolemaic artificiality, consisting of separated rings and a core, arbitrarily located at disparate altitudes in the magnetosphere. Diversity of observed profile shapes…
Information geometry is an emergent branch of probability theory that consists of assigning a Riemannian differential geometry structure to the space of probability distributions. We present an information geometric investigation of gases…
Gravitational waves provide a unique window into gravity, cosmology, and high-energy physics, enabling the exploration of fundamental phenomena across a wide range of scales. This review presents a coherent and pedagogical framework that…
Geometry is wavy: even at the purely geometric level (no particular theory chosen), curvature satisfies a covariant quasilinear wave equation. In Riemannian geometry equipped with the Levi-Civita connection, the Riemann curvature tensor…
Structure of mean pulsar radiation patterns is discussed within the nested-cones and patchy beam models. Observational predictions of both these models are analyzed and compared with available data on pulsar waveforms. It is argued that…
The 3D Airy beam (AiB) is thoroughly explored from a wave-theory point of view. We utilize the exact spectral integral for the AiB to derive local ray-based solutions that do not suffer from the limitations of the conventional parabolic…
The exact elastodynamic scattering theory is constructed to describe the spectral properties of two- and more-cylindrical cavity systems, and compared to an elastodynamic generalization of the semi-classical Gutzwiller unstable periodic…
Using all available multi-component radio pulse profiles for pulsars with medium to long periods and good polarisation data, we have constructed a two-dimensional image of the mean radio beamshape. This shows a peak near the centre of the…
Explicit and compact expressions describing the reflection and the transmission of a Gaussian beam by anisotropic parallel plates are given. Multiple reflections inside the plate are taken into account as well as arbitrary optical axis…
This paper investigates the global structures of periodic orbits that appear in Rayleigh-B\'enard convection, which is modeled by a two-dimensional perturbed Hamiltonian model, by focusing upon resonance, symmetry and bifurcation of the…
By analogy to the three dimensional optical bottle beam, we introduce the plasmonic bottle beam: a two dimensional surface wave which features a lattice of plasmonic bottles, i.e. alternating regions of bright focii surrounded by low…
When the gravitational lensing potential can be approximated by that of circularly symmetric system affected by weak perturbations, it is found that the shape of the resulting (tangential) caustics is entirely specified by the local…