Control of spatiotemporal disorder in parametrically excited surface waves

Interacting surface waves, parametrically excited by two commensurate frequencies, yield a number of nonlinear states. Near the system's bicritical point, a state, highly disordered in space and time, results from competition between nonlinear states. Experimentally, this disordered state can be rapidly stabilized to a variety of nonlinear states via open-loop control with a small-amplitude third frequency excitation, whose temporal symmetry governs the temporal and the spatial symmetry of the selected nonlinear state. This technique also excites rapid switching between nonlinear states.     

Control and characterization of spatio-temporal disorder in parametrically excited surface waves

The nonlinear interactions of parametrically excited surface waves have been shown to yield a rich family of nonlinear states. When the system is driven by two commensurate frequencies, a variety of interesting superlattice type states are generated via a number of different 3-wave resonant interactions. These states occur either as symmetry-breaking bifurcations of hexagonal patterns composed of a single unstable mode or via nonlinear interactions between the two different unstable modes generated by the two forcing frequencies. Near the system’s bicritical point, a well-defined region of phase space exists in which a highly disordered state, both in space and time, is observed. We first show that this state results from the competition between two distinct nonlinear super-lattice states, each with different characteristic temporal and spatial symmetries. After characterizing the type of spatio-temporal disorder that is embodied in this disordered state, we will demonstrate that it can be controlled. Control to either of its neighboring nonlinear states is achieved by the application of a small-amplitude excitation at a third frequency, where the spatial symmetry of the selected pattern is determined by the temporal symmetry of the third frequency used. This technique can also excite rapid switching between different nonlinear states.     

Spatial solitons in an optical lattice with varying diffraction and spatially inhomogeneous nonlinearity

In this paper, we present the (1+1)-dimensional inhomogeneous nonlinear Schrödinger (NLS) equation that describes the propagation of optical waves in nonlinear optical systems exhibiting optical lattice, inhomogeneous nonlinearity and varying diffraction at the same time. A series of interesting properties of spatial solitons are found from the numerical calculations, such as the stable propagation in the a nonperiodic optical lattice induced by periodic diffraction variations and periodic nonlinearity variations. Finally, the interaction of neighboring spatial solitons in a nonperiodic optical lattice is discussed, and the results reveal that two spatial solitons can propagate periodically and separately in the optical lattice without interaction.     

Attraction of nonlocal dark optical solitons

We study the formation and interaction of spatial dark optical solitons in materials with a nonlocal nonlinear response. We show that unlike in local materials, where dark solitons typically repel, the nonlocal nonlinearity leads to a long-range attraction and formation of stable bound states of dark solitons.     

Observation of dipole-like gap solitons in self-defocusing waveguide lattices

We observe dipole-like gap solitons in two-dimensional waveguide lattices optically induced with a self-defocusing nonlinearity. Under appropriate conditions, two mutually coherent input beams excited in neighboring lattice sites evolve into a self-trapped state, whose spatial power spectrum and stability depend strongly on the initial excitation conditions. Our experimental observations are compared with numerical simulations.     

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.     

Spatial solitons in optically induced gratings

We study experimentally nonlinear localization effects in optically induced gratings created by interfering plane waves in a photorefractive crystal. We demonstrate the generation of spatial bright solitons similar to those observed in arrays of coupled optical waveguides. We also create pairs of out-of-phase solitons, which resemble twisted localized states in nonlinear lattices.     

Elliptic incoherent solitons in saturable nonlinear media

We identify elliptic incoherent spatial solitons in isotropic saturable nonlinear media. These solitary states are possible, provided that their correlation function is anisotropic. The propagation dynamics of this new class of solitons are investigated by use of numerical simulations. We find that, during a collision event of two such elliptic solitons, their intensity ellipse rotates, and at the same time their centers of gravity tend to revolve around each other.     

Correlations due to localization in quantum eigenfunctions of disordered microwave cavities

Statistical properties of experimental eigenfunctions of quantum chaotic and disordered microwave cavities are shown to demonstrate nonuniversal correlations due to localization. Varying energy E and mean free path l enable us to experimentally tune from localized to delocalized states. Large level-to-level inverse participation ratio ( I2) fluctuations are observed for the disordered billiards, whose distribution is strongly asymmetric about . The spatial density autocorrelations of eigenfunctions are shown to spatially decay exponentially and the decay lengths are experimentally determined. All the results are quantitatively consistent with calculations based upon nonlinear sigma models.     

Soliton complexes and flat-top nonlinear modes in optical lattices

We describe a continuous analog of the quasirectangular flat-top nonlinear modes earlier found for discrete nonlinear models. We show that these novel nonlinear modes can be understood as multi-soliton complexes with either in-phase or out-of-phase neighboring solitons trapped by the periodic potential of the lattice. We demonstrate a link between the flat-top states and the truncated nonlinear Bloch waves, and discuss how these nonlinear localized modes can be monitored experimentally in photonics and Bose–Einstein condensates. PACS 42.65.Tg; 42.65.Jx; 03.75.Lm     

Laguerre and Hermite soliton clusters in nonlocal nonlinear media

We introduce novel classes of higher-order spatial optical solitons in analogy with Laguerre-Gaussian and Hermite-Gaussian linear eigenmodes. We reveal that stable higher-order optical solitons can exist in nonlocal nonlinear media in the various forms of soliton necklaces and soliton matrices. Modulational instability can lead to nontrivial transformations between energetically close solitons with different symmetries through the intermediate states resembling generalized Hermite-Laguerre-Gaussian modes.     

Dissipative solitons compounds in a fiber laser. Analogy with the states of the matter

We investigate experimentally ordered and disordered pattern formation of solitons in a double-clad fiber laser. We point out an analogy between the different states of matter and the states of a set of dissipative solitons. In particular, we have identified a gas, a supersonic gas flow, a liquid, a polycrystal and a crystal of solitons. The different states are obtained only by adjustment of the intracavity phase plates.     

空间相位调制对强非局域空间光孤子的影响

利用空间相位调制技术和数值分析的方法，讨论了高斯光束在强非局域非线性平板波导中的传输问题，发现只要介质的响应具有对称性,光束就会有相同的演化规律，可控的空间相位调制参数不仅能让光束自偏转还能实现分束，其全新特性在全光开关及分光器上有潜在的应用价值. 关键词： 强非局域空间光孤子 空间相位调制 光偏转 光开关     

Suppression of spatial chaos via noise-induced growth of arrays of spatial solitons

Domain walls with oscillatory tails are commonplace in models of spatially extended nonlinear optical devices. Their interaction and locking at discrete distances lead to asymptotically stable spatial disorder. We show that noise in the presence of domain walls with oscillatory tails can suppress spatial disorder by privileging highly correlated dynamical states consisting of arrays of spatial solitons.     

Bright spatial solitons on a partially incoherent background

We present the first observation of incoherent antidark spatial solitons in noninstantaneous nonlinear media. This new class of soliton states involves bright solitons on a partially incoherent background of infinite extent. In the case where the nonlinearity is of the Kerr type, their existence is demonstrated analytically by means of an exact solution. Computer simulations and experiments indicate that these incoherent antidark solitons can propagate in a stable fashion provided that the spatial coherence of their background is reduced below the incoherent modulation instability threshold.     

First principle theory for cavity solitons in semiconductor microresonators

Cavity solitons are similar to spatial solitons, appearing as localized bright dots in the transverse intensity profile of the electromagnetic field, but they arise in dissipative systems. In this paper we consider a broad-area vertical-cavity semiconductor microresonator, driven by an external coherent field, at room temperature. The active material is constituted by a Multiple Quantum Well GaAs/AlGaAs structure (MQW). We present a set of nonlinear dynamical equations for the electric field and the carrier density valid for both a passive and an active (i.e. with population inversion) configuration. The complex nonlinear susceptibility is derived on the basis of a full many-body theory, with the Coulomb enhancement treated in the Padé approximation. The linear stability analysis of the homogeneous steady states is performed with a generalised approach, and numerical simulations demonstrating the existence of spatial patterns and cavity solitons in experimentally achievable parameter regions are given for the two configurations. Received 18 January 2001     

Nonlinear theory of transverse perturbations of quasi-one-dimensional solitons

An averaged variational principle is applied to analyze the nonlinear effect of transverse perturbations (including diffraction) on quasi-one-dimensional soliton propagation governed by various wave equations. It is shown that parameters of the spatiotemporal solitons described by the cubic Schrödinger equation and the Yajima-Oikawa model of interaction between long-and short-wavelength waves satisfy the spatial quintic nonlinear Schrödinger equation for a complex-valued function composed of the amplitude and eikonal of the soliton. Three-dimensional solutions are found for two-component “bullets” having long-and short-wavelength components. Vortex and hole-vortex structures are found for envelope solitons and for two-component solitons in the regime of resonant long/short-wave coupling. Weakly nonlinear behavior of transverse perturbations of one-dimensional soliton solutions in a self-defocusing medium is described by the Kadomtsev-Petviashvili equation. The corresponding rationally localized “lump” solutions can be considered as secondary solitons propagating along the phase fronts of the primary solitons. This conclusion holds for primary solitons described by a broad class of nonlinear wave equations.     

Collisions of Two Spatial Solitons in Inhomogeneous Nonlinear Media

Collisions of spatial solitons occurring in the nonlinear Schröinger equation with harmonic potential are studied, using conservation laws and the split-step Fourier method. We find an analytical solution for the separation distance between the spatial solitons in an inhomogeneous nonlinear medium when the light beam is self-trapped in the transverse dimension. In the self-focusing nonlinear media the spatial solitons can be transmitted stably, and the interaction between spatial solitons is enhanced due to the linear focusing effect (and also diminished for the linear defocusing effect). In the self-defocusing nonlinear media, in the absence of self-trapping or in the presence of linear self-defocusing, no transmission of stable spatial solitons is possible. However, in such media the linear focusing effect can be exactly compensated, and the spatial solitons can propagate through.     

五阶非线性对啁啾超短脉冲间相互作用的影响

基于包含五次复系数的高阶Ginzburg Landau方程为模型,采用分步傅里叶方法数值研究了啁啾类超短脉冲间的相互作用。结果表明:相邻孤子之间的相互作用对五阶非线性效应非常敏感,即使参数改变很小的值,也会改变其传输特性。适当地选择五阶非线性参数值,能够很好地抑制孤子间的相互作用,提高光纤传输的比特率。当相邻孤子的初始间距为6.8,五阶非线性参数值取-0.001时,可以实现2个孤子长距离的保型传输。最后讨论了五阶非线性作用下多孤子之间的相互作用及抑制。     

Bright and dark spatial solitons in metallic nanowire arrays

We investigate the formation and propagation of bright and dark three-dimensional unstaggered spatial solitons with cylindrical symmetry in a nonlinear nanowire metamaterial. The metamaterial is formed by metallic nanowires embedded in a Kerr-type dielectric host and is modeled using an effective medium approach. Unlike conventional Kerr media, the metamaterial supports bright solitons when the host is a self-defocusing material and dark solitons when the host is a self-focusing material. Our numerical calculations show that the confinement of the spatial-solitons results from the interplay of the host nonlinear response strength and the hyperbolic dispersion of the photonic states in the nanowire array. Subwavelength solitary beams may be observed for sufficiently strong nonlinearities.