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The special theory of relativity teaches us that, although distinct inertial frames perceive the same dynamical laws, space and time intervals differ in value. We revisit the problem of time contraction using the paradigmatic model of a…
We consider a system composed of a mobile slab and the electromagnetic field. We assume that the slab is made of a material that has the following properties when it is at rest: it is linear, isotropic, non-magnetizable, and ohmic with zero…
We investigate the motion of a massive particle constrained to move along a path consisting of two line segments on a vertical plane under an arbitrary conservative force. By fixing the starting and end points of the track and varying the…
Fermat's principle applied to a flat metric in the plane yields the phase of a Bessel function in the periodic domain for a constant index of refraction. Gravitational forces cause the index of refraction to vary and lead to a modified…
The colliding between an ultra-intense laser pulse with a high energy electron beam is not only an important source for high-brightness gamma-rays but also a powerful approach to exploit new physics in the exotic strong-field QED regime. In…
Compared to traditional electromagnetic stealth (ES) materials, which are effective only within specific frequencies and orientations, intelligent reflecting surface (IRS) technology introduces a novel paradigm for achieving dynamic and…
We motivate then formulate a novel variant of the near-field reflector problem and call it the near-field reflector problem with spatial restrictions. Let $O$ be an anisotropic point source of light and assume that we are given a bounded…
Reflection of light from surfaces is a very common, but complex phenomenon not only in science and technology, but in every day life. The underlying basic optical principles have been developed within the last five centuries using visible…
In this work is elaborated the wording of Fermat`s principle for electromagnetic waves spreading in materials with negative index of refractions (MNR). The recent experiments with such material has confirmed their main characteristics,…
A unique perspective approach based on an analogy method is presented to solve the ray equation in a model of a continuous inhomogeneous medium, which has a spherically symmetric distribution. Basically, in the standard undergraduate…
In this paper, we investigate the use of intelligent reflecting surfaces (IRSs) to relax the line-of-sight requirement of free space optical (FSO) systems. Considering a Gaussian laser beam, we first design a phase-shift distribution across…
This paper considers the question of characterizing the behavior of waves reflected by a fractional singularity of the wave speed profile, i.e., of the form \[ c(x_1, x_2, x_3) = c_0 \left(1 + \left( \frac{x_1}{\ell}\right)_{+}^\alpha…
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 the following geometric optics problem: Construct a system of two reflectors which transforms a spherical wavefront generated by a point source into a beam of parallel rays. This beam has a prescribed intensity distribution. We…
Special Relativity (SR) kinematics is derived from very intuitive assumptions. Contrary to standard Einstein's derivation, no light signal is used in the construction nor it is assumed to exist. Instead we postulate the existence of two…
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 prove a general ergodic-theoretic result concerning the return time statistic, which, properly understood, sheds some new light on the common sense phenomenon known as {\it the law of series}. Let \proc be an ergodic process on finitely…
We have defined slowness (or reciprocal velocity) corresponding to v as cc/v, where c is the speed of light and v is the corresponding velocity. Velocity and slowness are images of each other. Reciprocal symmetric law of addition of…
We derive certain constraints on the reflection matrix for reflection from a plane, nonmagnetic, optically anisotropic surface using a reciprocity theorem stated long ago by van de Hulst in the context of scattering of polarized light. The…
We prove a version of Sylvester's law of inertia for the Reflection Equation Algebra (=REA). We will only be concerned with the REA constructed from the $R$-matrix associated to the standard $q$-deformation of $GL(N,\mathbb{C})$. For $q$…