Nonlocal incoherent solitons

Vector solitons in nonlocal optical media with pseudo spin-orbit-coupling

We numerically investigate the existence and stability of nonlocal vector solitons with pseudo spin-orbit-coupling (SOC). The pseudo SOC is realized by a framework based on the spatial-domain copropagation of two beams with mutually orthogonal polarizations and opposite transverse components of the carrier wave vectors in nonlocal optical media. The numerical results show that there are two kinds of solutions for vector solitons, one is central symmetric, and the other is noncentral symmetric. The solitons may exist below a certain threshold value of the effective SOC strength in the system.

Spectral long-range interaction of temporal incoherent solitons

We study the interaction of temporal incoherent solitons sustained by a highly noninstantaneous (Raman-like) nonlinear response. The incoherent solitons exhibit a nonmutual interaction, which can be either attractive or repulsive depending on their relative initial distance. The analysis reveals that incoherent solitons exhibit a long-range interaction in frequency space, which is in contrast with the expected spectral short-range interaction described by the usual approach based on the Raman-like spectral gain curve. Both phenomena of anomalous interaction and spectral long-range behavior of incoherent solitons are described in detail by a long-range Vlasov equation.

Abundant soliton solutions of general nonlocal nonlinear Schrödinger system with external field

Periodic and quasi-periodic breather multi-solitons solutions, the dipole-type breather soliton solution, the rogue wave solution, and the fission soliton solution of the general nonlocal Schrödinger equation are derived by using the similarity transformation and manipulating the external potential function. The stability of the exact solitary wave solutions with the white noise perturbation also is investigated numerically.

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.

Solitons in nonlocal nonlinear Kerr media with exponential response function

In this paper, we find some exact analytical solutions including bright soliton solution, dipole-mode soliton solution, double soliton solution and periodic solution when a slit laser beam propagates in Kerr-type nonlinear, nonlocal media with exponential response function. Furthermore, we address the energy flow is a monotonically growing function of d₂ and the Hamiltonian decreases while the energy flow increases. And we also obtain an Airy-like soliton by numerical method.

Incoherent soliton turbulence in nonlocal nonlinear media

The long-term behavior of a modulationally unstable nonintegrable system is known to be characterized by the soliton turbulence self-organization process: It is thermodynamically advantageous for the system to generate a large-scale coherent soliton in order to reach the ("most disordered") equilibrium state. We show that this universal process of self-organization breaks down in the presence of a highly nonlocal nonlinear response. A wave turbulence approach based on a Vlasov-like kinetic equation reveals the existence of an incoherent soliton turbulence process: It is advantageous for the system to self-organize into a large-scale, spatially localized, incoherent soliton structure.

Random-phase surface-wave solitons in nonlocal nonlinear media

We demonstrate, theoretically and experimentally, incoherent surface solitons in a noninstantaneous nonlocal nonlinear media. These incoherent surface waves are located at the interface between a nonlinear medium with long-range nonlocality and a linear dielectric medium (air).

Nonspecular total internal reflection of spatial solitons at the interface between highly birefringent media

We investigate total internal reflection of nonlocal spatial optical solitons at the interface between two differently oriented regions of a highly birefringent nematic liquid crystal. The solitons survive the interaction with an induced index mismatch and undergo nonspecular reflection, with an emerging angle differing appreciably from the incidence angle.

The Dynamics of Self-Trapped Beams of Incoherent White Light in a Free-Radical Photopolymerizable Medium

Detailed experimental studies of the dynamics of self-trapped beams of white light (400-800 nm) in a photosensitive organosiloxane medium are presented. Self-trapped white light beams with similar spatial profiles formed in the organosiloxane at intensities ranging across an order of magnitude (2.7-22.0 W.cm-2). Beam-profiling measurements showed that these spatially and temporally incoherent wave packets propagate without diffracting (broadening) by initiating free-radical polymerization of methacrylate groups and corresponding refractive index changes in the organosiloxane medium. Analyses of their temporal evolution showed that the intensity-dependent behavior of self-trapped white light is similar to that of self-trapped laser light despite the extreme differences in their phase structure and chromaticity; the self-trapped incoherent beams even show the complementary oscillations of width and intensity that is characteristic of self-trapped coherent light. Furthermore, the dynamics of the self-trapped white light beams was found to be strongly correlated to the kinetics of free-radical polymerization and corresponding rates of refractive index changes in the organosiloxane. These studies provide accessible photochemical routes to self-trapped incoherent wave packets, which are extremely difficult to generate in conventional nonlinear optical media that owe their responses to higher-order dielectric susceptibility tensors. This could enable the experimental verification of theoretical models developed for the nonlinear propagation of white light and stimulate research into more complex self-trapping phenomena such as the interactions of self-trapped incoherent beams and spontaneous pattern formation due to modulation instability in a uniform incoherent optical field. These findings also carry potential for the development of self-induced waveguide, optical solder and interconnect technology for incoherent light emitted by incandescent sources or LEDs.

Incoherent accessible white-light solitons in strongly nonlocal Kerr media

We present a theoretical investigation of incoherent accessible white-light solitons in strongly nonlocal medium with noninstantaneous Kerr nonlinearity. This soliton has elliptic Gaussian intensity profile and anisotropic spatiotemporal coherence properties. For this soliton to exist, the spatial coherence distance should be larger for lower frequencies and shorter for higher frequencies. When the incident power differs from the critical value, we demonstrate the periodic harmonic oscillations of the accessible white-light solitons.

Perturbative analysis of generally nonlocal spatial optical solitons

In analogy to a perturbed harmonic oscillator, we calculate the fundamental and some other higher order soliton solutions of the nonlocal nonlinear Schödinger equation (NNLSE) in the second approximation in the generally nonlocal case. Comparing with numerical simulations we show that soliton solutions in the second approximation can describe the generally nonlocal soliton states of the NNLSE more exactly than that in the zeroth approximation. We show that for the nonlocal case of an exponential-decay type nonlocal response the Gaussian-function-like soliton solutions cannot describe the nonlocal soliton states exactly even in the strongly nonlocal case. The properties of such nonlocal solitons are investigated. In the strongly nonlocal limit, the soliton's power and phase constant are both in inverse proportion to the fourth power of its beam width for the nonlocal case of a Gaussian function type nonlocal response, and are both in inverse proportion to the third power of its beam width for the nonlocal case of an exponential-decay type nonlocal response.

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.

Partially coherent accessible solitons in strongly nonlocal media

We study the propagation of incoherent accessible solitons in strongly nonlocal media with arbitrary response function. Based on the linear propagation equation and the mutual coherence function approach, we obtain an exact analytical solution of such incoherent accessible solitons. The solitons radius is related to the total power as well as the coherence characteristics of the incoherent beam. We find that there is not a threshold for incoherent solitons exist in strongly nonlocal media because the model is linear. Evolution behaviors of the solitons width and the coherence radius are also described when the solitons undergo linear harmonic oscillation.

Ultrashort solitons and kinetic effects in nonlinear metamaterials

We present a stability analysis of a modified nonlinear Schrödinger equation describing the propagation of ultrashort pulses in negative refractive index media. Moreover, using methods of quantum statistics, we derive a kinetic equation for the pulses, making it possible to analyze and describe partial coherence in metamaterials. It is shown that a unique short pulse soliton, which is found analytically, can propagate in the medium.

Nonlocal incoherent white-light solitons in logarithmically nonlinear media

The propagation properties of white-light solitons in spatially nonlocal media with a logarithmically nonlinearity are investigated theoretically. The existence curve of the stationary nonlocal incoherent soliton is obtained and the coherence characteristics of the soliton are also described. The evolution behaviors of the nonlocal white-light soliton are discussed in detail by both approximate analytical solution and numerical simulation when the solitons undergo periodic oscillation.

Soliton mobility in nonlocal optical lattices

We address the impact of nonlocality in the physical features exhibited by solitons supported by Kerr-type nonlinear media with an imprinted optical lattice. We discover that the nonlocality of the nonlinear response can profoundly affect the soliton mobility, hence all the related phenomena. Such behavior manifests itself in significant reductions of the Peierls-Nabarro potential with an increase in the degree of nonlocality, a result that opens the rare possibility in nature of almost radiationless propagation of highly localized solitons across the lattice.