Related papers: Using Rolling Circles to Generate Caustic Envelope…
Given any light position S in the complex projective plane P^2 and any algebraic curve C of P^2 (with any kind of singularities), we consider the incident lines coming from S (i.e. the lines containing S) and their reflected lines after…
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.…
Given a point S and any irreducible algebraic curve C in P^2 (with any type of singularities), we consider the caustic of reflection defined as the Zariski closure of the envelope of the reflected lines from the point S on the curve C. We…
One can often see caustic by reflection in nature, but it is rather hard to understand the way of how caustic arise and which geometric properties of a mirror surface define the geometry of the caustic. The caustic by reflection has…
Euler used intrinsic equations expressing the radius of curvature as a function of the angle of inclination to find curves similar to their evolutes. We interpret the evolute of a plane curve optically, as the caustic (envelope) of light…
A point source of light is placed inside an oval. The $n$-th caustic by reflection is the envelope of the light rays emanating from the light source after $n$ reflections off the curve. We show that each of these caustics, for a generic…
We are interested in the study of caustics by reflection of irreducible algebraic planar curves (in the complex projective plane). We prove the birationality of the caustic map (for a generic light position). We also give simple formulas…
We study the formation of images in a reflective sphere in three configurations using caustics of the field of light rays. The optical wavefront emerging from a source point reaching a subject following passage through the optical system…
We present an approach for the study and design of reflectors with rotational or translational symmetry that redirect light from a point source into any desired radiant intensity distribution. This method is based on a simple conformal map…
Given a reflection group $G$ acting on a complex vector space $V$, a reflection map is the composition of an embedding $X \hookrightarrow V$ with the orbit map $V\to\mathbb C^p$ that maps a $G$-orbit to a point. Reflection maps can be very…
A novel scheme is proposed to generate uniform relativistic electron layers for coherent Thomson backscattering. A few-cycle laser pulse is used to produce the electron layer from an ultra-thin solid foil. The key element of the new scheme…
Structured {\gamma} rays, particularly cylindrical vector {\gamma} rays, offer promising tools for sub-nuclear imaging and polarization-sensitive probes in fundamental research and applications, but conventional optical methods face great…
We propose an original method for determining suitable refracting profiles between two media to solve two related problems: to produce a given wave front from a single point source after refraction at the refracting profile, and to focus a…
We analyze spin scattering in ballistic transport of electrons through a ripple at a normal incidence of an electron flow. The model of a ripple consists of a curved graphene surface in the form of an arc of a circle connected from the…
Given a point S (the light position) in P^3 and an algebraic surface Z (the mirror) of P^3, the caustic by reflection of Z from S is the Zariski closure of the envelope of the reflected lines got by reflection of the incident lines (Sm) on…
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…
We prove that the focal set generated by the reflection of a point source off a translation invariant surface consists of two sets: a curve and a surface. The focal curve lies in the plane orthogonal to the symmetry direction containing the…
Caustics occur in diverse physical systems, spanning the nano-scale in electron microscopy to astronomical-scale in gravitational lensing. As envelopes of rays, optical caustics result in sharp edges or extended networks. Caustics in…
We consider the polarization arising from scattering in an envelope illuminated by a central anisotropic source. Spherical harmonics are used to describe both the light source anisotropy and the envelope density distribution functions of…
Coherent backscattering is a coherence effect in the propagation of waves through disordered media involving two or more scattering events. Here, we report on the observation of coherent backscattering from individual atoms and their mirror…