Solitons in complex optical lattices

We present an overview of our recent results in the area of soliton excitation and control in optical lattices induced by different types of nondiffracting beams featuring unique symmetries. Optical lattices offer the possibility to engineer and to control the diffraction of light beams in media with transversally modulated optical properties, to manage the corresponding reflection and transmission bands, and to form specially designed defects. Consequently, they afford the existence of a rich variety of new families of nonlinear stationary waves and solitons, lead to new rich dynamical phenomena, and offer novel conceptual opportunities for all-optical shaping, switching and routing of optical signals encoded in soliton formats. In this overview, we consider different types of solitons, including fundamental, multipole, and vortex solitons in reconfigurable lattices optically induced by nondiffracting radially symmetric and azimuthally modulated single Bessel beams, soliton control in networks, couplers, and switches induced by several mutually coherent or incoherent Bessel beams, we address soliton properties in three-dimensional Bessel lattices, as well as in lattices produced by Mathieu and parabolic optical beams.     

Rotary solitons in bessel optical lattices

We introduce solitons supported by Bessel photonic lattices in cubic nonlinear media. We show that the cylindrical geometry of the lattice, with several concentric rings, affords unique soliton properties and dynamics. In particular, in addition to the lowest-order solitons trapped in the center of the lattice, we find soliton families trapped at different lattice rings. Such solitons can be set into controlled rotation inside each ring, thus featuring novel types of in-ring and inter-ring soliton interactions.     

中空圆柱形边界条件下非线性介质中的晶格孤子

本文采用自相似方法求解中空圆柱形边界贝塞尔晶格中变系数非线性薛定谔方程, 得到了与数值模拟解一致的解析解, 表明由非衍射贝塞尔光束诱导的光子晶格可支持稳定的自相似孤子簇. 精确解ψ_mn是n+2层, 2m极的多极孤立波, 其形状及大小在传播过程中保持不变. 关键词： 空间光孤子 贝塞尔晶格 边界 自相似     

Higher-order surface solitons in one-dimensional Bessel optical lattices

We demonstrate the existence of higher-order solitons occurring at an interface separating two one-dimensional (1D) Bessel optical lattices with different orders or modulation depths in a defocusing medium. We show that, in contrast to homogeneous waveguides where higher-order solitons are always unstable, the Bessel lattices with an interface support branches of higher-order structures bifurcating from the corresponding linear modes. The profiles of solitons depend remarkably on the lattice parameters and the stability can be enhanced by increasing the lattice depth and selecting higher-order lattices. We also reveal that the interface model with defocusing saturable Kerr nonlinearity can support stable multi-peaked solitons. The uncovered phenomena may open a new way for soliton control and manipulation.     

Interfering Bessel beams for optical micromanipulation

We examine the properties of interfering high-order Bessel beams. We implement an experimental setup that allows us to realize these interferograms, using interfering Laguerre-Gaussian beams and an axicon. We demonstrate the use of such beams for controlled rotation of microscopic particles in optical tweezers and rotators. The self-healing properties of interfering Bessel beams allow the simultaneous manipulation and rotation of particles in spatially separated sample cells.     

Shaping soliton properties in Mathieu lattices

We address basic properties and stability of two-dimensional solitons in photonic lattices induced by the nondiffracting Mathieu beams. Such lattices allow for smooth topological transformation of radially symmetric Bessel lattices into quasi-one-dimensional periodic ones. The transformation of lattice topology drastically affects the properties of ground-state and dipole-mode solitons, including their shape, stability, and transverse mobility.     

Highly asymmetric soliton complexes in parabolic optical lattices

We introduce multipole soliton complexes in optical lattices induced by nondiffracting parabolic beams. Despite the symmetry breaking dictated by the curvature of the lattice channels, we find that complex, asymmetric higher-order states can be stable. The unique topology of parabolic lattices affords new types of soliton motion: single solitons launched into the lattice with nonzero transverse momentum perform periodic oscillations along parabolic paths.     

Tailoring light structures using an off-axis double axicon holographic pattern

We propose a new method for tailoring light structures using a double axicon holographic pattern. The light structure can be tailored using pairs of Bessel modes with different angular momentum indices, and changed into an optical wheel by combining two copropagating Bessel beams. We also demonstrated that the optical wheel obtained from a pair of Bessel beams had rotation feature over the propagation distance by introducing different axial wavenumbers between the two modes.     

Surface solitons supported by one-dimensional composite Bessel optical lattices

We address the existence of surface solitons at an interface in a defocusing cubic medium with an imprinted one-dimensional （1D） composite Bessel optical lattice. This setting is composed of two Bessel lattices with different orders and different modulation depths, separated beside both sides of an interface. Stability analysis and numerical propagation simulations prove that solitons supported by the model are dynamically stable in the entire domain of their existence. The order of lattice determines the shape of soliton, and the amplitude of soliton depends on the lattice modulation depth. The experimental realization of the scheme is also proposed. Our results may provide another effective way of controlling the shapes of surface solitons and thus their evolutions by introducing a new freedom degree.     

Internal oscillation of vector solitons and necklace solitons

Internal modes and internal oscillation of vector solitons associated with photoisomerization and necklace solitons in Bessel lattices are researched. While white noise gives rise to the unsmoothness of the vector solitons, the perturbation of internal modes results in the long-distance quasi-periodic oscillation of soliton shape. Internal modes of two-dimensional necklace solitons in Bessel lattices have both real and imaginary parts, which is different with the internal modes of one-dimensional solitons which have only real part.     

Dynamic optical manipulation with a higher-order fractional bessel beam generated from a spatial light modulator

Higher-order Bessel beams have been demonstrated to have the ability to trap and rotate low- and high-index particles simultaneously [Phys. Rev. A 66, 063402 (2002)]. The rotation and trapping is caused by the presence of orbital angular momentum arising from its azimuthal phase variation (that changes at integer multiples of 2pi) and the concentric rings of the Bessel mode. We demonstrate for the first time to our knowledge a branch from the family of higher-order Bessel beams that has fractional azimuthal variation at its beam axis. This new family of laser beams has the ability to perform dynamic optical manipulation with dynamic control of a spatial light modulator. Furthermore, we take the opportunity to explore the propagation characteristics of higher-order Bessel beams for which the azimuthal phase changes at noninteger multiples of 2pi.     

Observation of discrete solitons and soliton rotation in optically induced periodic ring lattices

We report the first experimental demonstration of ring-shaped photonic lattices by optical induction and the formation of discrete solitons in such radially symmetric lattices. The transition from discrete diffraction to single-channel guidance or nonlinear self-trapping of a probe beam is achieved by fine-tuning the lattice potential or the focusing nonlinearity. In addition to solitons trapped in the lattice center and in different lattice rings, we demonstrate controlled soliton rotation in the Bessel-like ring lattices.     

深光晶格势阱中凝聚体的扭结包络隙孤子

发展准离散多尺度法结合紧束缚近似,解析地研究了局陷于光晶格势阱中凝聚体的非线性动力学性质.结果发现,系统中出现稳定的对称包络孤子外,还可观察到一种新的非线性元激发:扭结包络隙孤子.有趣的是,该隙孤子并不传播且局域在初始位置,其幅度可通过光晶格势阱的晶格常数和势阱深度来调控.相应的实验方案是:通过改变形成光晶格势阱的两交叉耦合激光束之间的夹角和(或)激光光强来调控扭结包络隙孤子的幅度.     

Rotation of laser beams with zero of the orbital angular momentum

We show that among the multitude of rotating light beams whose complex amplitude can be represented as a linear superposition of the Laguerre-Gaussian (LG) modes with definite numbers there are light beams with zero orbital angular momentum (OAM) and vice versa, multi-mode LG beams that show no rotation and are lacking the radially symmetric intensity distribution can possess the non-zero OAM. Also, we give examples of the rotating light beams with zero OAM, represented as a superposition of the Bessel and new hypergeometric modes. Using an SLM, we generate a rotating Bessel beam with zero OAM for the first time.     

Gaussian-induced rotation in periodic photonic lattices

We numerically investigate time-dependent rotation of counterpropagating mutually incoherent self-trapped Gaussian beams in periodic optically induced fixed photonic lattices. We demonstrate the relation between such rotation and less confined discrete solitonic solutions.     

Numerical Simulation of SRS of Cylindrical Wave Beams

A method for numerical simulation of stimulated Raman scattering of cylindrical wave beams in a nonlinear medium has been developed. The features of the spatial structure formation of interacting wave fields in the regime of conservation of azimuthal angular distributions of amplitudes have been investigated. The radial intensity profiles of diffracting light beams in the near-field zone and their angular spectra in the far-field zone corresponding to different stages of energy exchange in the process of amplification from the noise in the barium nitrate crystal have been calculated. It has been shown that in the field of Bessel beams waveguide structures of the soliton type with a peak intensity of the self-channeling Stokes component significantly exceeding the initial pumping intensity are formed. A comparison of the conversion efficiencies under pumping by Gaussian and Bessel light beams has been made.     

Nonlinear beam interactions in semi-infinite waveguide arrays

The interactions between coherent beams launched near the interface of one-dimensional semi-infinite Kerr-type nonlinear waveguide arrays have been theoretically investigated. We have explored the effect of the input intensities, the relative phase of the optical beams, and the modulation of the refractive index of the optical lattices on nonlinear beam interaction dynamics. For in-phase beams with different incident intensities, the highly-localized spatial soliton was dragged in a discrete fashion by a low-intensity diffracting beam. Anomalous fusion of two out-of-phase beams, and energy exchange between the excited channels were observed at high intensities. The possibility of employing nonlinear interactions for optical signal re-addressing, all-optical switching is also discussed.     

向列型液晶中的非局域孤子

 在两种极限情况下求得了向列型液晶中（1+1）D空间光孤子的精确解析解。对非局域非线性项作近似计算,获得了光束的演化方程。在弱非局域情况下,直接积分得出单峰孤子解;强非局域情况下,用贝塞尔函数表示明孤子的解析解,本征值个数与峰的个数一致,预示了多峰明孤子的存在;这些结果与其它文献的精确数值解一致。并把所得解与双曲近似解析解进行了比较。     

利用空间诱导色散补偿介质色散

研究了超短脉冲贝塞尔光束在色散介质中的传输特性 ,指出空间诱导色散效应可以用来补偿介质色散作用 ,从而可以在色散介质中实现无衍射无色散的类时空孤子波的传输。用理论推导和数值模拟的方法得到的具有反常色散性质的空间诱导色散可以有效地补偿介质色散。数值模拟的结果表明 ,由于超短脉冲贝塞尔光束的无衍射无色散传输距离受到高阶色散效应和贝塞尔光束空间受限两方面的限制 ,无衍射无色散传输只能在有限距离内近似实现。通过增加脉冲长度可以减小高阶色散效应的影响。在传输距离小于衍射距离时 ,空间诱导色散效应可以很好地描述脉冲演化和色散补偿过程     

Rotating optical soliton clusters

We introduce the concept of soliton clusters--multisoliton bound states in a homogeneous bulk optical medium--and reveal a key physical mechanism for their stabilization associated with a staircaselike phase distribution that induces a net angular momentum and leads to cluster rotation. The ringlike soliton clusters provide a nontrivial generalization of the concepts of two-soliton spiraling, optical vortex solitons, and necklace-type optical beams.