Related papers: Nonlinear Bessel beams
Non-separable superpositions of polarization and spatial modes in Gaussian beams have shown rich patterns of spatially-variable polarization encoded in the transverse mode of the light, with the potential for many applications. In this work…
In our analysis, we show that Howell et al.'s nonlinear beam theory does not depict a representation of the Euler-Bernoulli beam equation, nonlinear or otherwise. The authors' nonlinear beam theory implies that one can bend a beam in to a…
The interactions between copropagating ring-Airy beams in a (2+1)-dimensional Kerr medium are numerically investigated for the first time. It is shown that two overlapping ring-Airy beams in such a medium produce controllable regions of…
We give explicit criteria for the reflectionlessness, transparency, and invisibility of a finite-range potential in the presence of an incoherent (intensity-dependent) nonlinearity that is confined to the range of the potential. This allows…
In this work we study the initial boundary value problem associated with the coupled Schr\"odinger equations {with quadratic nonlinearities, that appears in nonlinear optics}, on the half-line. We obtain local well-posedness for data {in…
Scattering resonances play a crucial role in understanding wave behavior in various physical systems. While significant progress has been made in analyzing resonances in high-contrast and nonlinear media, a general characterization of…
We start a study of various nonlinear PDEs under the effect of a modulation in time of the dispersive term. In particular in this paper we consider the modulated non-linear Schr\"odinger equation (NLS) in dimension 1 and 2 and the…
The nonlinear dynamics of collisionless Alfven trains, including resonant particle effects is studied using the kinetic nonlinear Schroedinger (KNLS) equation model. Numerical solutions of the KNLS reveal the dynamics of Alfven waves to be…
We obtain the characteristic equation for the nonlinear Born-Infeld electrodynamics. This equation has the form of the characteristic equation for the linear electrodynamics in some effective Riemann space. The effective metric include the…
Recent studies have shown that line profile distortions are commonly observed in gravitationally lensed quasar spectra. We investigate the effect of gravitational microlensing on quasar broad emission line profiles and their underlying…
Dispersive shock waves (DSWs) of the defocusing radial nonlinear Schr\"odinger (rNLS) equation in two spatial dimensions are studied. This equation arises naturally in Bose-Einstein condensates, water waves and nonlinear optics. A unified…
We develop a diagrammatic theory for transport of waves in disordered media with weak nonlinearity. We first represent the solution of the nonlinear wave equation as a nonlinear Born series. From this, we construct nonlinear ladder and…
A new class of nonparaxial accelerating optical waves is introduced. These are beams with a Bessel-like profile that are capable of shifting laterally along fairly arbitrary trajectories as the wave propagates in free space. The concept…
We analytically and numerically study the temporal intensity pattern emerging from the linear or nonlinear evolutions of a single or double phase jump in an optical fiber. The results are interpreted in terms of interferences of the…
In this paper we study the noncompact star-type graph with perturbed radial Schrodinger equation on each ray and the matching conditions of some special form at the vertex. The results include the uniqueness theorem and constructive…
We investigate the optical response induced by a d.c. current flowing in a nonmagnetic material that lacks inversion symmetry. In this class of materials, the flowing current experiences a nonlinear Hall effect and induces a nonequilibrium…
According to a recent experiment, the instantaneous electronic Kerr effect in air exhibits a strong intensity dependence, the nonlinear refractive index switching sign and crossing over from a self-focusing to a de-focusing nonlinearity. A…
Bessel beams are known for their property of maintaining propagation-invariant transverse intensity distribution. The true Bessel beams has unlimited energy, however the experimental realization of limited energy Bessel-like beams provides…
We address the question of whether the presence of Kerr nonlinearity in multiple-scattering optical media offers any advantage with respect to the design of physical unclonable functions. Our results suggest that under certain conditions,…
Dynamics of wavepackets in fractional Schrodinger equation is still an open problem. The difficulty stems from the fact that the fractional Laplacian derivative is essentially a nonlocal operator. We investigate analytically and…