Related papers: Paraxial beam propagation from Airy-type initial c…
We study nonlinear elliptic equations for operators corresponding to non-stable L\'evy diffusions. We include a sum of fractional Laplacians of different orders. Such operators are infinitesimal generators of non-stable (i.e., non…
In this work we present a model for the paraxial propagation of vector beams. Of particular importance is the appearance of a new transverse momentum term proportional to the linear polarization angle gradient imparted to the beam during…
Diffractionless propagation of optical beams through atomic vapors is investigated. The atoms in the vapor are operated in a three-level Raman configuration. A suitably chosen control beam couples to one of the transitions, and thereby…
It is well known that phase function methods allow for the numerical solution of a large class of oscillatory second order linear ordinary differential equations in time independent of frequency. Unfortunately, these methods break down in…
We scrutinize the geometrical properties of light propagation inside a nonlinear medium modeled by a fully covariant electromagnetic theory in $2+1$-dimensions. After setting the nonlinear constitutive relations, the phase velocity and the…
We consider the Cauchy problem for one-dimensional dispersive equations with a general nonlinearity in the periodic setting. Our main hypotheses are both that the dispersive operator behaves for high frequencies as a Fourier multiplier by $…
Quantum light propagation through turbulent atmosphere has become a subject of intensive research, spanning both theoretical and experimental studies. This interest is driven by its important applications in free-space quantum…
New solid-state physics based approach is developed for analysis of the paraxial light propagation in two-dimensional (2D) photonic lattices of coupled dielectric waveguides or microcavities. In particular, using Maxwell's equations, a…
Ninety years after their prediction, quantum vacuum nonlinearities in macroscopic electromagnetic fields still await a direct experimental verification in the laboratory. A particularly promising route towards their first measurement is the…
We experimentally generate an Airy beam with polarization structure while keeping its original amplitude and phase profile intact. This class of Airy beam preserves the acceleration properties. By monitoring their initial polarization…
Controlling light propagation through complex media plays a significant role in a wide range of applications ranging from astronomical observations to microscopy. Although, several advances have been made based on adaptive optics, optical…
We present a rigorous and quantum-consistent description of dispersive non-Hermitian optical bilayers in the framework of the canonical quantization scheme. Then we investigate the propagation of a normally incident squeezed coherent state…
We study the behavior of the fermion propagator in an external time dependent potential in 0+1 dimension. We show that, when the potential has upto quadratic terms in time, the propagator can be expressed in terms of generalized Airy…
We consider an evolution equation with the Caputo-Dzhrbashyan fractional derivative of order $\alpha \in (1,2)$ with respect to the time variable, and the second order uniformly elliptic operator with variable coefficients acting in spatial…
Tightly-focused laser beams, or optical tweezers, are essential for analogue and digital quantum simulation with neutral atoms and trapped ions. Despite this, most of the current intuition and theoretical treatment utilizes the paraxial…
We study the propagation, observation and control properties of the 1-d wave equation on a bounded interval discretized in space using the quadratic classical finite element approximation. A careful Fourier analysis of the discrete wave…
The paper presents an ab initio account of the paraxial complex geometrical optics (CGO) in application to a scalar Gaussian beam propagation and diffraction in a 3D smoothly inhomogeneous medium. The paraxial CGO deals with quadratic…
Using the very basic physics principles, we have studied the implications of quantum corrections to classical electrodynamics and the propagation of electromagnetic waves and pulses. The initial nonlinear wave equation for the…
Operator-sum representations of quantum channels can be obtained by applying the channel to one subsystem of a maximally entangled state and deploying the channel-state isomorphism. However, for continuous-variable systems, such schemes…
A wave near an isolated turning point is typically assumed to have an Airy function profile with respect to the separation distance. This description is incomplete, however, and is insufficient to describe the behavior of more realistic…