Dynamic spatial solitons

Stochastic theory of an optical vortex in nonlinear media

A stochastic theory is given of an optical vortex occurring in nonlinear Kerr media. This is carried out by starting from the nonlinear Schrödinger type equation which accommodates vortex solution. By using the action functional method, the evolution equation of vortex center is derived. Then the Langevin equation is introduced in the presence of random fluctuations, which leads to the Fokker-Planck equation for the distribution function of the vortex center coordinate by using a functional integral. The Fokker-Planck equation is analyzed for a specific form of pinning potential by taking into account an interplay between the strength of the pinning potential and the random parameters, diffusion and dissipation constants. This procedure is performed by several approximate schemes.

Optical spatial solitons: historical overview and recent advances

Solitons, nonlinear self-trapped wavepackets, have been extensively studied in many and diverse branches of physics such as optics, plasmas, condensed matter physics, fluid mechanics, particle physics and even astrophysics. Interestingly, over the past two decades, the field of solitons and related nonlinear phenomena has been substantially advanced and enriched by research and discoveries in nonlinear optics. While optical solitons have been vigorously investigated in both spatial and temporal domains, it is now fair to say that much soliton research has been mainly driven by the work on optical spatial solitons. This is partly due to the fact that although temporal solitons as realized in fiber optic systems are fundamentally one-dimensional entities, the high dimensionality associated with their spatial counterparts has opened up altogether new scientific possibilities in soliton research. Another reason is related to the response time of the nonlinearity. Unlike temporal optical solitons, spatial solitons have been realized by employing a variety of noninstantaneous nonlinearities, ranging from the nonlinearities in photorefractive materials and liquid crystals to the nonlinearities mediated by the thermal effect, thermophoresis and the gradient force in colloidal suspensions. Such a diversity of nonlinear effects has given rise to numerous soliton phenomena that could otherwise not be envisioned, because for decades scientists were of the mindset that solitons must strictly be the exact solutions of the cubic nonlinear Schrödinger equation as established for ideal Kerr nonlinear media. As such, the discoveries of optical spatial solitons in different systems and associated new phenomena have stimulated broad interest in soliton research. In particular, the study of incoherent solitons and discrete spatial solitons in optical periodic media not only led to advances in our understanding of fundamental processes in nonlinear optics and photonics, but also had a very important impact on a variety of other disciplines in nonlinear science. In this paper, we provide a brief overview of optical spatial solitons. This review will cover a variety of issues pertaining to self-trapped waves supported by different types of nonlinearities, as well as various families of spatial solitons such as optical lattice solitons and surface solitons. Recent developments in the area of optical spatial solitons, such as 3D light bullets, subwavelength solitons, self-trapping in soft condensed matter and spatial solitons in systems with parity-time symmetry will also be discussed briefly.

Stabilization of vector soliton complexes in nonlocal nonlinear media

We introduce vector soliton complexes in nonlocal Kerr-type nonlinear media. We discover that under proper conditions the combination of nonlocality and vectorial coupling has a remarkable stabilizing action on multihumped solitons. In particular, we find that stable bound states featuring several field oscillations in each soliton component do exist. This affords stabilization of vector soliton trains incorporating a large number of humps, a class of structures known to self-destroy via strong instabilities in scalar settings.

Multiband vector lattice solitons

We predict multiband vector solitons in nonlinear periodic systems, using photonic lattices as a prime example. The solitons consist of two optical fields arising from different bands of the transmission spectrum, which involve both bound state and radiation mode components.

Spatial vector solitons consisting of counterpropagating fields

We present the experimental observation of a spatial vector soliton formed by counterpropagation of coherent optical fields. This is to our knowledge the first observation of a vector soliton in which the induced waveguide (potential) is periodic in the propagation direction. This vector soliton induces a waveguide and a thick grating within the waveguide, which can be used as a tunable optical waveguide filter.

Symmetry-breaking instability of multimode vector solitons

We show experimentally that the two-component multimode spatial optical vector soliton, i.e., a two-hump self-guided laser beam, exhibits in Kerr media a sharp space-inversion symmetry-breaking instability. The experiment is performed in a CS2 planar waveguide using the orthogonal circular polarization states of light as the two components of the vector soliton.

Linear superposition principle for partially coherent solitons

The existence of a linear superposition principle is demonstrated for partially coherent solitons with identical intensity profiles that are supported by the same medium. Since such degenerate partially coherent solitons are generic for saturable as well as for Kerr-like nonlinear media, our results are relevant to any non-instantaneous nonlinear media. The proposed superposition principle suggests a physical interpretation of partially coherent solitons as generalized linear modes of their self-induced waveguides. The power of such a superposition principle is illustrated by identifying soliton structures with controllable coherence properties both in logarithmically saturable and in Kerr-like nonlinear media.

Collisions between (2+1)D rotating propeller solitons

We study theoretically the collisions between (2+1)D rotating-dipole-type bimodal solitons and find that such interactions exhibit many interesting exchanges of angular momentum.

Rotating propeller solitons

We demonstrate experimentally and theoretically (both analytically and numerically) a new type of spatial soliton: a rotating "propeller" soliton. This is a composite soliton made of a rotating dipole component jointly trapped with a bell-shaped component. We observe as much as 239 degrees of rotation over 13 mm of propagation (6.5 diffraction lengths).

Interactions between two-dimensional composite vector solitons carrying topological charges

We present a comprehensive study of interactions (collisions) between two-dimensional composite vector solitons carrying topological charges in isotropic saturable nonlinear media. We numerically study interactions between such composite solitons for different regimes of collision angle and report numerous effects which are caused solely by the "spin" (topological charge) carried by the second excited mode. The most intriguing phenomenon we find is the delayed-action interaction between interacting composite solitons carrying opposite spins. In this case, two colliding solitons undergo a fusion process and form a metastable bound state that decays after long propagation distances into two or three new solitons. Another noticeable effect is spin-orbit coupling in which angular momentum is being transferred from "spin" to orbital angular momentum. This phenomenon occurs at angles below the critical angle, including the case when the initial soliton trajectories are in parallel to one another and lie in the same plane. Finally, we report on shape transformation of vortex component into a rotating dipole-mode solitons that occurs at large collision angles, i.e., at angles for which scalar solitons of all types simply go through one another unaffected.

Dynamic soliton-like modes

Incoherent optical spatial solitons require noninstantaneous nonlinearity, i.e., the local intensity fluctuation of the solitons must be faster than the medium can respond. Observing partially incoherent bicomponent solitons, we find that there exists a threshold speed. When the fluctuation of the soliton intensity, resulting from the time-varying interference of its constituent modes, is below the threshold, the soliton beam and its induced waveguide oscillate violently. Just above the threshold, the soliton-induced waveguide is observed to be dragged by the soliton beam.

Delayed-action interaction and spin-orbit coupling between solitons

We report on new fundamental phenomena in soliton interactions: delayed-action interaction and "spin"-orbit coupling upon collision between two-dimensional composite solitons carrying topological charges.

Observation of two-dimensional multimode solitons

We present the first experimental observation of (2+1) -dimensional multimode (composite) solitons. A single-hump component and a double-hump (dipole-type) component are jointly self-trapped as a composite soliton in a biased photorefractive crystal.

Observation of bound states of interacting vector solitons

We report experimental observation of bound states formed by two well-separated vector spatial solitons as the result of a force balance between vector-soliton components. We also demonstrate a link between such soliton bound states and two-hump, two-mode solitons, along with the induced coherence effect observed for incoherently interacting solitons.

Composite multihump vector solitons carrying topological charge

We propose composite solitons carrying topological charge: multicomponent two dimensional [ (2+1)D] vector (Manakov-like) solitons for which at least one component carries topological charge. These multimode solitons can have a single hump or exhibit a multihump structure. The "spin" carried by these multimode composite solitons suggests 3D soliton interactions in which the particlelike behavior includes spin, in addition to effective mass, linear, and angular momenta.

Multicomponent two-dimensional solitons carrying topological charges

We propose multihump N-component two-dimensional vector solitons for which each constituent carries a different topological charge. These new structures exhibit a unique triple-point phase diagram that is completely absent in the two-component limit.

Optical Spatial Solitons and Their Interactions: Universality and Diversity

Spatial solitons, beams that do not spread owing to diffraction when they propagate, have been demonstrated to exist by virtue of a variety of nonlinear self-trapping mechanisms. Despite the diversity of these mechanisms, many of the features of soliton interactions and collisions are universal. Spatial solitons exhibit a richness of phenomena not found with temporal solitons in fibers, including effects such as fusion, fission, annihilation, and stable orbiting in three dimensions. Here the current state of knowledge on spatial soliton interactions is reviewed.

Asymmetric partially coherent solitons in saturable nonlinear media

We investigate theoretically properties of partially coherent solitons in optical nonlinear media with slow saturable nonlinearity. We have found numerically that such a medium can support spatial solitons which are asymmetric in shape and are composed of only a finite number of modes associated with the self-induced waveguide. It is shown that these asymmetric spatial solitons can propagate many diffraction lengths without changes, but that collisions change their shape and may split them apart.

Multicomponent photorefractive cnoidal waves: stability, localization, and soliton asymptotics

An algorithm of building up a different class of stable self-consistent multicomponent periodical solutions of the nonlinear Schrödinger equation--multicomponent cnoidal waves--has been formulated by the example of a nonlinear wave propagating through a photorefractive crystal with a drift nonlinear response. Exact analytical expressions, describing distribution of light field in the components, have been obtained for solutions, which include up to three mutually incoherent components. It has been shown that such cnoidal waves are stable and their spatial structure is robust to collisions with the same cnoidal waves and to stochastic perturbations of the components' intensity distributions in a sufficiently wide range of changing spatial period.

Partially coherent solitons of variable shape in a slow Kerr-like medium: exact solutions

We carry out a theoretical investigation of the properties of partially coherent solitons for media which have a slow Kerr-like nonlinearity. We find exact solutions of the Nth-order Manakov equations in a general form. These describe partially coherent solitons (PCSs) and their collisions. In fact, the exact solutions allow us to analyze important properties of PCSs such as stationary profiles of the spatial beams and effects resulting from their collisions. In particular, we find, analytically, the number of parameters that control the soliton shape. We present profiles which are symmetric as well as those which are asymmetric. We also find that collisions allow the profiles to remain stationary but cause their shapes to change.

Rotating vector solitary waves in isotropic fibers

The properties of elliptically polarized solitary waves in isotropic optical fibers are investigated. Two families of polarized solitary pulses are identified, but only one of them is shown to be stable. These pulses are characterized by a fixed polarization pattern that rotates at a constant rate as the pulse propagates down the fiber. The evolution of the polarization of these pulses is important for the operation of short-pulse fiber lasers and other nonlinear devices.

Spatial solitons of Maxwell's equations

Spatial solitons of Maxwell's equations propagating in an isotropic Kerr material differ significantly from the classical soliton of the nonlinear Schrödinger equation unless the electric field is linearly polarized along a geometric axis of the soliton intensity pattern. In general the polarization state changes continuously as the beam propagates, with a period of millimeters for highly nonlinear materials. This effect is due to the form birefringence of the soliton-induced waveguide. Equivalently, a soliton of Maxwell's equations is composed of both the TE and TM modes of the axially uniform waveguide it induces. Modal beating leads to the polarization dynamics.