Related papers: Using Rolling Circles to Generate Caustic Envelope…
Spiral waves in excitable media possess both wave-like and particle-like properties. When resonantly forced (forced at the spiral rotation frequency) spiral cores travel along straight trajectories, but may reflect from medium boundaries.…
First geometric calculus alongside its description of equiangular spirals, reflections and rotations is introduced briefly. Then single and double reflections at such a spiral are investigated. It proves suitable to distinguish incidence…
We theoretically show that a single free electron in circular/spiral motion radiates an electromagnetic wave possessing helical phase structure and carrying orbital angular momentum. We experimentally demonstrate it by double-slit…
The radiation arising under uniform motion of non-relativistic charged particle by (or through) perfectly conducting sphere is considered. The rigorous results are obtained using the method of images known from electrostatics.
In this article, we attempt to study the possible link between the dynamics of a circle map and the caustics of its iterations. The attention is on a geometrically defined off-center reflections, which, coincidentally, is also a…
Intuitively, an envelope of a family of curves is a curve that is tangent to a member of the family at each point. Here we use envelopes of families of circles to study objects from matrix theory and hyperbolic geometry. First we explore…
We show theoretically that a directional dipole wave can be perfectly reflected by a single point-like oscillating dipole. Furthermore, we find that in the case of a strongly focused plane wave up to 85 % of the incident light can be…
Caustics are optical phenomena which occur when a family of rays creates an envelope of divergent intensity. Here we show that caustic surfaces also appear when a real or complex field is mapped to its order parameter manifold. We study…
We use geometrical optics and the caustic-touching theorem to study, in an exact way, the change in the topology of the image of an object obtained by reflections on an arbitrary smooth surface. Since the procedure that we use to compute…
Designing freeform surfaces to control light based on real-world illumination patterns is challenging, as existing caustic lens designs often assume oversimplified point or parallel light sources. We propose representing surface light…
We construct a subset $A$ of the unit disc with the following properties. (i) The set $A$ is the finite union of disjoint line segments. (ii) The shadow of $A$ is arbitrarily close to the shadow of the unit disc in "most" directions. (iii)…
We demonstrate, both theoretically and experimentally, that arbitrary scatterers preserving parity-time-duality ($\mathcal{P}\cdot\mathcal{T}\cdot\mathcal{D}$) symmetry inherently produce a backscattered wave whose electric field is the…
We propose a simple yet efficient method for generating in-plane hollow beams with a nearly-full circular light shell without the contribution of backward propagating waves. The method relies on modulating the phase in the near field of a…
The beamed radio emission from relativistic plasma (particles or bunches), constrained to move along the curved trajectories, occurs in the direction of velocity. We have generalized the coherent curvature radiation model to include the…
In this paper, on envelopes created by circle families in the plane, all four basic problems (existence problem, representation problem, problem on the number of envelopes, problem on relationships of definitions) are solved.
It is shown that the infall of collisionless dark matter onto isolated galaxies produces a series of caustic rings in the halo dark matter distribution. The properties of these caustics are investigated. The density profile of the caustic…
Emission lines formed in the circumstellar envelopes of several type of stars can be modeled using first principles of line formation. We present simple ways of calculating line emission profiles formed in circumstellar envelopes having…
The high gradient of magnification across the source during both small impact parameter events and caustic crossings offers a unique opportunity for determining the surface brightness profile of the source. Furthermore, models indicate that…
This work seeks to present an investigation about the trajectories followed by rays of light passing through refractive index gradients that was entirely carried by high school students. Such trajectories are curved, therefore contradicting…
An exact formulation of the propagation of a monochromatic wave packet impinging upon a transparent, homogeneous, isotropic and parallel slab at oblique incidence is presented. Approximate formulas are derived for low divergence Gaussian…