584 research outputs found
Optical vortices in dispersive nonlinear Kerr type media
The applied method of slowly varying amplitudes of the electrical and magnet
vector fields give us the possibility to reduce the nonlinear vector
integro-differential wave equation to the amplitude vector nonlinear
differential equations. It can be estimated different orders of dispersion of
the linear and nonlinear susceptibility using this approximation. The critical
values of parameters to observe different linear and nonlinear effects are
determinate. The obtained amplitude equation is a vector version of 3D+1
Nonlinear Schredinger Equation (VNSE) describing the evolution of slowly
varying amplitudes of electrical and magnet fields in dispersive nonlinear Kerr
type media. We show that VNSE admit exact vortex solutions with classical
orbital momentum and finite energy. Dispersion region and medium
parameters necessary for experimental observation of these vortices, are
determinate.
PACS 42.81.Dp;05.45.Yv;42.65.TgComment: 24 page
Nonlinear vortex light beams supported and stabilized by dissipation
We describe nonlinear Bessel vortex beams as localized and stationary
solutions with embedded vorticity to the nonlinear Schr\"odinger equation with
a dissipative term that accounts for the multi-photon absorption processes
taking place at high enough powers in common optical media. In these beams,
power and orbital angular momentum are permanently transferred to matter in the
inner, nonlinear rings, at the same time that they are refueled by spiral
inward currents of energy and angular momentum coming from the outer linear
rings, acting as an intrinsic reservoir. Unlike vortex solitons and dissipative
vortex solitons, the existence of these vortex beams does not critically depend
on the precise form of the dispersive nonlinearities, as Kerr self-focusing or
self-defocusing, and do not require a balancing gain. They have been shown to
play a prominent role in "tubular" filamentation experiments with powerful,
vortex-carrying Bessel beams, where they act as attractors in the beam
propagation dynamics. Nonlinear Bessel vortex beams provide indeed a new
solution to the problem of the stable propagation of ring-shaped vortex light
beams in homogeneous self-focusing Kerr media. A stability analysis
demonstrates that there exist nonlinear Bessel vortex beams with single or
multiple vorticity that are stable against azimuthal breakup and collapse, and
that the mechanism that renders these vortexes stable is dissipation. The
stability properties of nonlinear Bessel vortex beams explain the experimental
observations in the tubular filamentation experiments.Comment: Chapter of boo
Transverse Patterns in Nonlinear Optical Resonators
The book is devoted to the formation and dynamics of localized structures
(vortices, solitons) and extended patterns (stripes, hexagons, tilted waves) in
nonlinear optical resonators such as lasers, optical parametric oscillators,
and photorefractive oscillators. The theoretical analysis is performed by
deriving order parameter equations, and also through numerical integration of
microscopic models of the systems under investigation. Experimental
observations, and possible technological implementations of transverse optical
patterns are also discussed. A comparison with patterns found in other
nonlinear systems, i.e. chemical, biological, and hydrodynamical systems, is
given. This article contains the table of contents and the introductory chapter
of the book.Comment: 37 pages, 14 figures. Table of contents and introductory chapter of
the boo
Vortex solitons in dispersive nonlinear Kerr type media
We have investigated the nonlinear amplitude vector equation governing the
evolution of optical pulses in optical and UV region. We are normalizing this
equation for the cases of different and equal transverse and longitudinal size
of optical pulses, of week and strong dispersion. This gives us the possibility
to reduce the amplitude equation to different nonlinear evolution equations in
the partial cases. For some of these nonlinear equations exact vortex solutions
are found. Conditions for experimental observations of these vortices are
determined.Comment: 28 pages, 9 figures, Late
Introduction: Localized Structures in Dissipative Media: From Optics to Plant Ecology
Localised structures in dissipative appears in various fields of natural
science such as biology, chemistry, plant ecology, optics and laser physics.
The proposed theme issue is to gather specialists from various fields of
non-linear science toward a cross-fertilisation among active areas of research.
This is a cross-disciplinary area of research dominated by the nonlinear optics
due to potential applications for all-optical control of light, optical
storage, and information processing. This theme issue contains contributions
from 18 active groups involved in localized structures field and have all made
significant contributions in recent years.Comment: 14 pages, 0 figure, submitted to Phi. Trasaction Royal Societ
Korteweg-de Vries description of Helmholtz-Kerr dark solitons
A wide variety of different physical systems can be described by a relatively small set of universal equations. For example, small-amplitude nonlinear Schrödinger dark solitons can be described by a Korteweg-de Vries (KdV) equation. Reductive perturbation theory, based on linear boosts and Gallilean transformations, is often employed to establish connections to and between such universal equations. Here, a novel analytical approach reveals that the evolution of small-amplitude Helmholtz–Kerr dark solitons is also governed by a KdV equation. This broadens the class of nonlinear systems that are known to possess KdV soliton solutions, and provides a framework for perturbative analyses when propagation angles are not negligibly small. The derivation of this KdV equation involves an element that appears new to weakly nonlinear analyses, since transformations are required to preserve the rotational symmetry inherent to Helmholtz-type equations
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