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Ellipses, parabolas and hyperbolas all have beautiful reflective properties. However, an intuitive explanation for why they have those properties has been lacking. There exist many mathematical proofs, but they tend to involve several…
A relatively efficient scheme to generate energetic $\gamma$-ray is all-optical Compton scattering based on wakefield acceleration and plasma mirror where planar or concave solid target is usually employed to reflect driving pulse. For flat…
This paper develops a rigorous mathematical framework for light propagation by constructing the optical phase space with its symplectic structure and the extended phase space with its contact structure. We prove that light rays in…
We propose and substantiate experimentally the cascaded rotational Doppler effect for interactions of spinning objects with light carrying angular momentum. Based on the law of parity conservation for electromagnetic interactions, we reveal…
Circularly polarized (CP) $\gamma$-ray sources are versatile for broad applications in nuclear physics, high-energy physics and astrophysics. The laser-plasma based particle accelerators provide accessibility for much higher flux…
The effect of vacuum polarization on the propagation of photons in curved spacetime is studied in scalar QED. A compact formula is given for the full frequency dependence of the refractive index for any background in terms of the Van…
This paper discusses the observed at rotation curves of galaxies in the context of noncommutative geometry. The energy density of such a geometry is diffused throughout a region due to the uncertainty encoded in the coordinate commutator.…
We consider $N$ circles of equal radii, $r$, having their centers randomly placed within a square domain $\mathcal{D}$ of size $L \times L$ with periodic boundary conditions ($\mathcal{D} \in \mathbb{R}^2$). When two or more circles…
We present the first numerical radiative transfer simulation of multiple light scattering in dust configurations containing aligned non-spherical (spheroidal) dust grains. Such models are especially important if one wants to explain the…
Reflections from hypersurfaces act by symplectomorphisms on the space of oriented lines with respect to the canonical symplectic form. We consider an arbitrary $C^{\infty}$-smooth hypersurface $\gamma\subset\mathbb R^{n+1}$ that is either a…
Let $P$ be a convex polytope in the Euclidean space $\E^n$. Consider the group $G_P$ generated by reflections in the facets of $P$. We say that $P$ {\it generates a reflection group $G_P$}. In the present paper, we list all Euclidean…
We systematically investigate the generation of optical chirality patterns by applying the superposition of two waves in three scenarios, namely plane waves in free space, evanescent waves of totally reflected light at dielectric interface…
The process of gravitational collapse excites the fields propagating in the background geometry and gives rise to thermal radiation. We demonstrate by explicit calculations that the density matrix corresponding to such radiation actually…
We consider stochastic differential equations with (oblique) reflection in a $2$-dimensional domain that has a cusp at the origin, i..e. in a neighborhood of the origin has the form $\{(x_1,x_2):0<x_1\leq\delta_0,\psi_1(x_1)<x_2<\psi_…
We proved earlier that every measurable function on the circle, after a uniformly small perturbation, can be written as a power series (i.e. a series of exponentials with positive frequencies), which converges almost everywhere. Here we…
We present an elementary analysis of the effects on light reflected from a uniformly moving mirror by using the photon picture of light and the conservation laws for energy and momentum of the system photon-mirror. Such a dynamical approach…
We have developed a relativistic model for pulsar radio emission and polarization by taking into account of detailed geometry of emission region, rotation and modulation. The sparks activity on the polar cap leads to plasma columns in the…
We systematically investigate the self-assembly of anisotropic cone-shaped particles decorated by ring-like attractive patches. We demonstrate that the self-assembled clusters, which arise due to the conical particle's anisotropic shape…
In this work, I have derived the equation of the curve obtained on reflection of a point object in an arbitrary curved mirror if the object and the mirror are placed on the 2D Cartesian plane. I have used only the basic laws of reflection…
We develop a model for the reflection and transmission of plane waves by an isotropic layer sandwiched between two uniaxial crystals of arbitrary orientation. In the laboratory frame, reflection and transmission coefficients corresponding…