Discrete diffraction and waveguiding of optical beams in a cascade-induced lattice

Regularities of anisotropic discrete diffraction in a cascade-induced lattice formed by two crossed pump waves in a quadratically nonlinear medium have been studied. The transition from diffraction of a signal beam in free space to discrete diffraction with further capture into a waveguide in a defocusing lattice with an increase in the pump wave intensity has been traced. Diffraction-free propagation of a tilted beam is described.     

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.     

Controlled generation of momentum states in a high-finesse ring cavity

A Bose-Einstein condensate in a high-finesse ring cavity scatters the photons of a pump beam into counterpropagating cavity modes, populating a bi-dimensional momentum lattice. A high-finesse ring cavity with a sub-recoil linewidth allows to control the quantized atomic motion, selecting particular discrete momentum states and generating atom-photon entanglement. The semiclassical and quantum model for the 2D collective atomic recoil lasing (CARL) are derived and the superradiant and good-cavity regimes discussed. For pump incidence perpendicular to the cavity axis, the momentum lattice is symmetrically populated. Conversely, for oblique pump incidence the motion along the two recoil directions is unbalanced and different momentum states can be populated on demand by tuning the pump frequency.     

Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices

We investigate both experimentally and theoretically the interaction between a light beam and a photonic lattice optically induced with partially coherent light. We demonstrate a clear transition from two-dimensional discrete diffraction to discrete solitons in such a partially coherent lattice and show that the nonlinear interaction process is associated with a host of new phenomena including lattice dislocation, lattice deformation, and creation of structures akin to optical polarons.     

Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains

We demonstrate anisotropic enhancement of discrete diffraction and formation of discrete-soliton trains in an optically induced photonic lattice. Such discrete behavior of light propagation was observed when a one-dimensional stripe beam was launched appropriately into a two-dimensional lattice created with partially coherent light. Our experimental results are corroborated with numerical simulations.     

光诱导光子晶格结构中新型的离散空间光孤子

离散孤子标志着从线性到非线性，从连续到非连续，从相干到非相干，人们对孤子认识的一个飞越．文章简要回顾了近期在二维光致光子晶格结构中有关空间离散光孤子的研究，包括基模离散孤子、类矢量离散孤子、离散偶极孤子、离散涡旋孤子和离散孤子串等．在非线性光折变晶体里用部分相干光诱导的波导阵列中，对每一种离散孤子，都清楚地观测到光从二维的离散衍射状态到自囚禁形成离散孤子的转变过程，获得的结果将对其他离散非线性系统中类似现象的研究有所启发．     

Anisotropic diffraction and elliptic discrete solitons in two-dimensional waveguide arrays

We demonstrate that both the linear (diffraction) and the nonlinear dynamics of two-dimensional waveguide arrays are considerably more complex and versatile than their one-dimensional counterparts. The discrete diffraction properties of these arrays can be effectively altered, depending on the propagation Bloch k-vector within the first Brillouin zone of the lattice. In general, this diffraction behavior is anisotropic and therefore permits the existence of a new class of discrete elliptic solitons in the nonlinear regime.     

Light propagation in double-periodic nonlinear photonic lattices in lithium niobate

Single- and double-periodic one-dimensional photonic lattices are formed in lithium niobate using both titanium in-diffusion and holographic grating recording. We investigate linear band structures and diffraction properties of such superlattices and observe a decrease of discrete diffraction with increasing modulation depth of the second superimposed lattice. In weakly modulated superlattices with tailored diffraction properties, our results demonstrate the formation of discrete solitons having a propagation constant inside the extra mini-gap formed inside the Brillouin zone. PACS 42.65.Tg; 42.70.Qs; 42.82.Et     

Discrete diffraction on a cascade-induced periodic lattice

A method for cascade generation of a periodic lattice in a medium with quadratic nonlinearity is proposed. Such a lattice is induced as a result of interference of two or four crossed fundamental-frequency waves. Numerical simulation of the discrete diffraction of a signal beam coupled to one of the lattice waveguides is performed. With an increase in the modulation depth of the refractive index, the signal wave is trapped in the waveguide.     

Reconfigurable 3D photonic lattices by optical induction for optical control of beam propagation

We report on our recent theoretical and experimental studies of three-dimensional (3D) photonic lattice structures which are established in a bulk nonlinear crystal by employing different optical induction techniques. These 3D photonic lattices bring about new opportunities for controlling the flow of light via coupling engineering originated from the lattice modulation along the beam propagation direction. By fine tuning the lattice parameters, we observe a host of unusual behaviors of beam propagation in such reconfigurable 3D lattices, including enhanced discrete diffraction, light tunneling inhibition—better known as coherent destruction of tunneling (CDT), anomalous diffraction, negative refraction, as well as CDT-based image transmission. In addition, we propose and demonstrate a new way of creating 3D ionic-type photonic lattices by controlled Talbot effect.     

Nonexponential decay via tunneling in tight-binding lattices and the optical zeno effect

An exactly-solvable model for the decay of a metastable state coupled to a semi-infinite, tight-binding lattice, showing large deviations from exponential decay in the strong coupling regime, is presented. An optical realization of the lattice model, based on discrete diffraction in a semi-infinite array of tunneling-coupled optical waveguides, is proposed to test nonexponential decay and for the observation of an optical analog of the quantum Zeno effect.     

液态急冷Fe-12.6at%B合金中的六角亚稳相

本文利用X射线粉末照相法及透射电子显微镜选区电子衍射法,唯一地确定了作者在液态急冷Fe-12.6at％B合金中发现的新亚稳相具有六角点阵。其点阵参数为α=5.501? c=7.213?,c/α=1.311。 关键词：     

平顶光端面抽运DPL中热效应对输出功率的影响

用平顶光束描述由多根光纤紧密排列耦合并经透镜整形后的抽运光分布，给出了平顶光束的光强分布，对晶体热效应引起的热致衍射损耗随抽运功率和抽运光束半径的变化规律进行了数值计算，讨论了晶体热效应引起的热致衍射损耗对基横模高斯光束输出功率的影响，并实验验证了基横模高斯光束输出功率随抽运功率的变化规律．结果表明：热致衍射损耗使基横模高斯光束输出功率明显降低．随着抽运光束半径的增大，热致衍射损耗减小，对基横模高斯光束输出功率的影响就减小；抽运功率越大，热致衍射损耗越大，对基横模高斯光束输出功率的影响就越大．     

Two new integrable lattice hierarchies associated with a discrete Schrödinger nonisospectral problem and their infinitely many conservation laws

In this Letter, by means of using discrete zero curvature representation and constructing opportune time evolution problems, two new discrete integrable lattice hierarchies with n-dependent coefficients are proposed, which relate to a new discrete Schrödinger nonisospectral operator equation. The relation of the two new lattice hierarchies with the Volterra hierarchy is discussed. It has been shown that one lattice hierarchy is equivalent to the positive Volterra hierarchy with n-dependent coefficients and another lattice hierarchy with isospectral problem is equivalent to the negative Volterra hierarchy. We demonstrate the existence of infinitely many conservation laws for the two lattice hierarchies and give the corresponding conserved densities and the associated fluxes formulaically. Thus their integrability is confirmed.     

New integrable lattice hierarchies

In this Letter we give a new integrable four-field lattice hierarchy, associated to a new discrete spectral problem. We obtain our hierarchy as the compatibility condition of this spectral problem and an associated equation, constructed herein, for the time-evolution of eigenfunctions. We consider reductions of our hierarchy, which also of course admit discrete zero curvature representations, in detail. We find that our hierarchy includes many well-known integrable hierarchies as special cases, including the Toda lattice hierarchy, the modified Toda lattice hierarchy, the relativistic Toda lattice hierarchy, and the Volterra lattice hierarchy. We also obtain here a new integrable two-field lattice hierarchy, to which we give the name of Suris lattice hierarchy, since the first equation of this hierarchy has previously been given by Suris. The Hamiltonian structure of the Suris lattice hierarchy is obtained by means of a trace identity formula.     

一种新型模拟晶体的设计

微波布拉格衍射实验中点阵模拟晶体是一种常用模型,对此的研究已趋于成熟,也形成了比较完善的理论体系。本文在研究了用点阵模拟晶体发生微波布拉格衍射的基础上,结合布拉格衍射实验原理,设计一种线阵模拟晶体来替代点阵模拟晶体。利用微波分光仪进行了不同线阵面间距和不同微波频率入射的布拉格衍射实验,并将实验结果与微波布拉格衍射理论计算结果进行了分析比较和符合性的验证。     

An integrable coupling family of Merola-Ragnisco-Tu lattice systems, its Hamiltonian structure and related nonisospectral integrable lattice family

An integrable coupling family of Merola-Ragnisco-Tu lattice systems is derived from a four-by-four matrix spectral problem. The Hamiltonian structure of the resulting integrable coupling family is established by the discrete variational identity. Each lattice system in the resulting integrable coupling family is proved to be integrable discrete Hamiltonian system in Liouville sense. Ultimately, a nonisospectral integrable lattice family associated with the resulting integrable lattice family is constructed through discrete zero curvature representation.     

Two-Dimensional Breather Lattice Solutions and Compact-Like Discrete Breathers and Their Stability in Discrete Two-Dimensional Monatomic β-FPU Lattice

We restrict our attention to the discrete two-dimensional monatomic β-FPU lattice. We look for two- dimensional breather lattice solutions and two-dimensional compact-like discrete breathers by using trying method and analyze their stability by using Aubry＇s linearly stable theory. We obtain the conditions of existence and stability of two-dimensional breather lattice solutions and two-dimensional compact-like discrete breathers in the discrete two- dimensional monatomic β-FPU lattice.     

Two new discrete integrable systems

In this paper,we focus on the construction of new(1+1)-dimensional discrete integrable systems according to a subalgebra of loop algebra A 1.By designing two new(1+1)-dimensional discrete spectral problems,two new discrete integrable systems are obtained,namely,a 2-field lattice hierarchy and a 3-field lattice hierarchy.When deriving the two new discrete integrable systems,we find the generalized relativistic Toda lattice hierarchy and the generalized modified Toda lattice hierarchy.Moreover,we also obtain the Hamiltonian structures of the two lattice hierarchies by means of the discrete trace identity.     

Novel spatial solitons in light-induced photonic bandgap structures

The study of wave propagation in periodic systems is at the frontiers of physics, from fluids to condensed matter physics, and from photonic crystals to Bose-Einstein condensates. In optics, a typical example of periodic system is a closely-spaced waveguide array, in which collective behavior of wave propagation exhibits many intriguing phenomena that have no counterpart in homogeneous media. Even in a linear waveguide array, the diffraction property of a light beam changes due to evanescent coupling between nearby waveguide sites, leading to normal and anomalous discrete diffraction. In a nonlinear waveguide array, a balance between diffraction and self-action gives rise to novel localized states such as spatial “discrete solitons” in the semi-infinite (or total-internal-reflection) gap or spatial “gap solitons” in the Bragg reflection gaps. Recently, in a series of experiments, we have “fabricated” closely-spaced waveguide arrays (photonic lattices) by optical induction. Such photonic structures have attracted great interest due to their novel physics, link to photonic crystals, as well as potential applications in optical switching and navigation. In this review article, we present a brief overview on our experimental demonstrations of a number of novel spatial soliton phenomena in light-induced photonic bandgap structures, including self-trapping of fundamental discrete solitons and more sophisticated lattice gap solitons. Much of our work has direct impact on the study of similar discrete phenomena in systems beyond optics, including sound waves, water waves, and matter waves (Bose-Einstein condensates) propagating in periodic potentials.