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In the diffraction pattern produced by a half-plane sharp edge when it obstructs the passage of a laser beam, two characteristic regions are noticeable. There is a central region, where it can be noticed the diffraction of laser light in…
We report on the successful operation of an analogue computer designed to factor numbers. Our device relies solely on the interference of classical light and brings together the field of ultrashort laser pulses with number theory. Indeed,…
Theory of the Linear photogalvanic effect is developed for direct optical transitions between surface states of three-dimensional topological insulators. The photocurrent governed by the orientation of the polarization plane of light and…
The last stage of evolution toward the stationary Kolmogorov spectrum of hydrodynamic turbulence is studied using the Leith model. This evolution is shown to manifest itself as a reflection wave in the wavenumber space propagating from the…
Many naturally-occuring models in the sciences are well-approximated by simplified models, using multiscale techniques. In such settings it is natural to ask about the relationship between inverse problems defined by the original problem…
We suggest a novel type of photonic structures where the strength of diffraction can be managed in a very broad frequency range. We introduce optimized arrays of curved waveguides where light beams experience wavelength-independent normal,…
Refraction at the interface between two materials is fundamental to the interaction of light with photonic devices and to the propagation of light through the atmosphere at large. Underpinning the traditional rules for the refraction of an…
In the Hilbert space $H$, the inverse problem of determining the right-hand side of the abstract subdiffusion equation with the fractional Caputo derivative is considered. For the forward problem, a non-local in time condition $u(0)=u(T)$…
Although the pattern formation on polymer gels has been considered as a result of the mechanical instability due to the volume phase transition, we found a macroscopic surface pattern formation not caused by the mechanical instability. It…
The Markovian diffusion theory is generalized within the framework of the special theory of relativity using a modification of the mathematical calculus of diffusion on Riemannian manifolds (with definite metric) to describe diffusion on…
We study the spatio-temporal pattern of the near-field intensity correlations generated by parametric scattering processes in a planar optical cavity. A generalized Bogolubov-de Gennes model is used to compute the second order field…
L\'evy flights for light have been demonstrated in disordered systems with and without optical gain, and remained unobserved in ordered ones. In the present letter, we investigate, numerically and experimentally, L\'evy flights for light in…
The influence of the relativistic motion of the reference frame on the light reflection law is investigated. The method is based on applying the relativistic aberration affect for three light signals: incident, normal and reflected rays.…
Distributed order fractional Langevin-like equations are introduced and applied to describe anomalous diffusion without unique diffusion or scaling exponent. It is shown that these fractional Langevin equations of distributed order can be…
We discuss several qualitative properties of the solutions of reaction-diffusion systems and equations of the form $u_t = \epsilon^2 D \Delta u + f(u,x,\epsilon t)$, that are used in modeling pattern formation. We analyze the diffusion…
After an introduction to the problem of cosmological structure formation, we develop gauge invariant cosmological perturbation theory. We derive the first order perturbation equations of Einstein's equations and energy momentum…
Recent advances in twistor theory are applied to geometric optics in ${\Bbb{R}}^3$. The general formulae for reflection of a wavefront in a surface are derived and in three special cases explicit descriptions are provided: when the…
We discuss quantum interference phenomena in a system consisting from a laser driven three-level ladder-type emitter possessing orthogonal transition dipoles and embedded in a leaking optical resonator. The cavity mean-photon number…
We first review classical results on cloaking and mirage effects for electromagnetic waves. We then show that transformation optics allows the masking of objects or produces mirages in diffusive regimes. In order to achieve this, we…
An explicit form for the geodesic equations that would describe diffracted light rays is obtained and the Levi-Civita connection that enters into it is shown to be a sum of contributions from the metric of the ambient space, the index of…