Related papers: Caustics of wave fronts reflected by a surface
A formalism for describing an all-sky map of the polarization of the cosmic microwave background is presented. The polarization pattern on the sky can be decomposed into two geometrically distinct components. One of these components is not…
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…
This short note revisits the classical result that the complete caustic by refraction of a circle is the evolute of Cartesian ovals. We provide additional details to the statement and geometric proof of this fact, as presented in G.…
In this paper, scattering of incident plane waves from rough surfaces have been modeled in a fractional space. It is shown how wave scattering from a rough surface, could be a simple reflection problem in a fractional space. In the integer…
The propagation of a light ray in thin layer (film) within geometrical optics is considered. It is assumed that the ray is captured inside the layer due to reflecting walls or total internal reflection (in the case of a dielectric layer).…
A nonrelativistic quantum mechanical particle moving freely on a curved surface feels the effect of the nontrivial geometry of the surface through the kinetic part of the Hamiltonian, which is proportional to the Laplace-Beltrami operator,…
Wave scattering from two-dimensional self-affine Dirichlet and Neumann surfaces is studied for the purpose of using the intensity scattered from them to obtain the Hurst exponent and topothesy that characterize the self-affine roughness. By…
When thermal energies are weak, two dimensional lamellar structures confined on a curved substrate display complex patterns arising from the competition between layer bending and compression in the presence of geometric constraints. We…
The mechanism of wavefront reconstruction by a geometric-optical reflection of reconstructing light from surfaces with constant phase differences between the object and reference waves used to record the interference fringe structure in the…
A body of literature has developed concerning "cloaking by anomalous localized resonance". The mathematical heart of the matter involves the behavior of a divergence-form elliptic equation in the plane, $\nabla\cdot (a(x)\nabla u(x)) =…
The first order equation relating object and image location for a mirror of arbitrary conic-sectional shape is derived. It is also shown that the parabolic reflecting surface is the only one free of aberration and only in the limiting case…
Within classical optics, one may add microscopic "roughness" to a macroscopically flat mirror so that parallel rays of a given angle are reflected at different outgoing angles. Taking the limit (as the roughness becomes increasingly…
We consider in a simple and general way elastic waves in isotropic and anisotropic media, their polarization, speeds, reflection from interfaces with mode conversion, and surface waves. Reflection of quasi transverse waves in anisotropic…
The geometry of a light wavefront evolving in the 3--space associated with a post-Newtonian relativistic spacetime from a flat wavefront is studied numerically by means of the ray tracing method. For a discretization of the bidimensional…
Phase delays, spectral, orientation, and angular dependences of radiation refraction in metamaterial targets have been experimentally studied within the millimeter-wave range. It has been shown that angular and spectral dependences have a…
Wave scattering from rough surfaces in addition the inverse scattering is an interesting approach to obtain the surface topography properties in various fields. Analytical expression in wave scattering from some known rough surfaces, not…
Refraction is the predominant mechanism causing spatially inhomogeneous surface gravity wave fields. However, the complex interplay between depth- and current-induced wave refraction remains poorly understood. Assuming weak currents and…
A caustic is a mathematical concept describing the beam formation when the beam envelope is reflected or refracted by a manifold. While caustics are common in a wide range of physical systems, caustics typically exhibit a reciprocal wave…
We show that periodically doped, flat surfaces can act as reflective diffraction gratings for atomic and molecular matter waves. The diffraction element is realized by exploiting that charged dopants locally suppress quantum reflection from…
Motivated by a recent experiment on acoustic lenses, we perform numerical calculations based on a multiple scattering technique to investigate the focusing of acoustic waves with sonic crystals formed by rigid cylinders in air. The focusing…