Oscillation of spatial solitons in a waveguide with a symmetrical refractive index profile

Dynamics of (1+1)D spatial solitons in a Kerr medium with a transversely symmetrical refractive index profile is investigated. Propagation of solitons is analysed theoretically by using an effective-particle approach. Analytical results show that the soliton oscillates periodically with a variable acceleration. The expression of oscillatory period is derived by introducing a concept of `average acceleration'. Both acceleration and oscillatory period are determined by the parameters of the input soliton and the waveguide. Propagations of solitons are simulated numerically and good agreement is obtained between the theoretical and numerical results.     

Discrete soliton collisions in a waveguide array with saturable nonlinearity

We study the symmetric collisions of two mobile breathers/solitons in a model for coupled wave guides with a saturable nonlinearity. The saturability allows the existence of mobile breathers with high power. Three main regimes are observed: breather fusion, breather reflection and breather creation. The last regime seems to be exclusive of systems with a saturable nonlinearity, and has been previously observed in continuous models. In some cases a “symmetry breaking” can be observed, which we show to be an numerical artifact.     

Tunable soliton self-bending in optical lattices with nonlocal nonlinearity

We address the phenomenon of soliton self-bending in Kerr-type nonlocal nonlinear media with an imprinted transverse periodic modulation of the linear refractive index. We show that the imprinted optical lattice makes possible to control the mobility of soliton by varying the depth and the frequency of the linear refractive index modulation.     

Gap soliton in a waveguide array with a saturating defocusing nonlinearity

We investigate radiation of the solitary waves in the first band gap of the waveguide array with a defocusing nonlinearities of different types (Kerr nonlinearity and saturating nonlinearity). We confirm recent findings that gap solitons (GSs) are unstable for their eigenfrequencies around the middle of the band gap for Kerr nonlinearity. The instability is mediated by four-wave mixing process and appears in the form of radiation of solitons into mode continua of the upper and lower bands. We find that this soliton radiation is reduced (and even suppressed completely) in case of a saturating nonlinearity, resulting in substantial stabilization of the GSs.     

强非局域空间光孤子在铅玻璃材料中的传输特性

本文研究了矩形和圆形截面铅玻璃介质中强非局域空间光孤子的传输特性.基于镜像法,光束在铅玻璃中的传输被分成独立的两个过程,即孤子的形成和孤子的整体偏转.孤子的形成不依赖于边界,它来源于入射源光束本身形成的折射率分布的作用,所以形成孤子的临界功率只与材料的性质和入射光束束宽有关.孤子的整体偏转在本质上来源于边界的作用,其偏转力在数值上等同于所有镜像光束与源光束之间的作用力.截面圆形和截面矩形的边界分别"镜像"出一个和无穷多个镜像光束,进而导致不同边界条件下孤子不同的偏转轨迹.文中解析求得的孤子的临界功率以及两 关键词： 空间光孤子 强非局域 镜像法 铅玻璃     

强非局域介质中高斯型损耗空间光孤子

 利用变分法研究了1+1维傍轴高斯光束在含有小损耗的强非局域非线性介质中的传输特性，得到了光束各参量的演化方程、束宽的演化规律和一个临界功率。在介质损耗足够小的前提下，当光束初始功率等于临界功率时，得到了一个束宽随传输距离缓慢展宽的准空间光孤子——损耗空间光孤子；当光束初始功率小于临界功率时，光束束宽则按雅可比椭圆正弦函数和椭圆余弦函数作准周期展宽变化；当光束初始功率大于临界功率时，光束束宽将从按雅可比椭圆正弦函数和椭圆余弦函数作准周期压缩变化过渡到按雅可比椭圆正弦函数和椭圆余弦函数准周期展宽变化。     

Collective spontaneous emission in a waveguide with a near-zero refractive index

The optimum conditions for observing superradiance and subradiance effects in an ensemble of two-level atoms, placed in a waveguide cladding with a metamaterial with near-zero refractive index, are discussed.     

Optical solitons supported by finite waveguide lattices with diffusive nonlocal nonlinearity

We investigate the properties of fundamental, multi-peak, and multi-peaked twisted solitons in three types of finite waveguide lattices imprinted in photorefractive media with asymmetrical diffusion nonlinearity. Two opposite soliton self-bending signals are considered for different families of solitons. Power thresholdless fundamental and multi-peaked solitons are stable in the low power region. The existence domain of two-peaked twisted solitons can be changed by the soliton self-bending signals. When solitons tend to self-bend toward the waveguide lattice, stable two-peaked twisted solitons can be found in a larger region in the middle of their existence region. Three-peaked twisted solitons are stable in the lower (upper) cutoff region for a shallow (deep) lattice depth. Our results provide an effective guidance for revealing the soliton characteristics supported by a finite waveguide lattice with diffusive nonlocal nonlinearity.     

Families of spatial solitons in a two-channel waveguide with the cubic-quintic nonlinearity

We present eight types of spatial optical solitons which are possible in a model of a planar waveguide that includes a dual-channel trapping structure and competing (cubic-quintic) nonlinearity. The families of trapped beams include “broad” and “narrow” symmetric and antisymmetric solitons, composite states, built as combinations of broad and narrow beams with identical or opposite signs (“unipolar” and “bipolar” states, respectively), and “single-sided” broad and narrow beams trapped, essentially, in a single channel. The stability of the families is investigated via the computation of eigenvalues of small perturbations, and is verified in direct simulations. Three species-narrow symmetric, broad antisymmetric, and unipolar composite states-are unstable to perturbations with real eigenvalues, while the other five families are stable. The unstable states do not decay, but, instead, spontaneously transform themselves into persistent breathers, which, in some cases, demonstrate dynamical symmetry breaking and chaotic internal oscillations. A noteworthy feature is a stability exchange between the broad and narrow antisymmetric states: in the limit when the two channels merge into one, the former species becomes stable, while the latter one loses its stability. Different branches of the stationary states are linked by four bifurcations, which take different forms in the model with the strong and weak coupling between the channels.     

Spatiotemporal collapse in a nonlinear waveguide with a randomly fluctuating refractive index

Analytical results, based on the virial theorem and the Furutsu-Novikov theorem, of the spatiotemporal evolution of a pulse in a nonlinear waveguide with a randomly fluctuating refractive index are presented. For initial conditions in which total collapse occurs in a homogeneous waveguide, random fluctuations postpone the collapse. Sufficiently large-amplitude and short-wavelength fluctuations can cause an initially localized pulse to spread instead of contracting. We show that the disorder can be applied to induce a high degree of controllability of the spatiotemporal extent of the pulses in the nonlinear waveguide.     

Internal modes of solitons in media with a saturable nonlinearity of the refractive index

The theoretical analysis and calculation of internal modes (eigenmodes of small perturbations) of 1D, 2D, and 3D optical solitons in transparent media with a saturable nonlinearity of the refractive index are performed. Corrections that are nonlinear in the amplitude of perturbations and lead to the radiative damping of internal modes are found. The damping is shown to become weaker with increasing dimensionality of a solition.     

Nonadiabatic Landau-Zener tunneling in waveguide arrays with a step in the refractive index

Landau-Zener tunneling is discussed in connection with optical waveguide arrays. Light injected in a specific band of the Bloch spectrum in the propagation constant can be transmitted to another band, changing its physical properties. This can be achieved using two coupled waveguide arrays with different refractive indices. The step in the refractive index causes wave "acceleration" and thus induces strongly nonadiabatic Landau-Zener tunneling. Theoretically, the analysis is performed by considering a Schr?dinger equation in a periodic potential with a step. The region of physical parameters where this phenomenon can occur is analytically determined and a realistic experimental setup is suggested. Its application could allow the realization of light filters.     

强非局域光晶格中空间孤子的脉动传播

根据强非局域结构中空间孤子的演化方程——非局域非线性薛定谔方程,采用分步傅里叶方法,对一维强非局域光晶格结构中空间孤子的脉动传播进行数值研究.分析了孤子的初始光束能量、非局域程度、光晶格调制强度、光晶格周期以及线性折射率的纵向调制率与空间孤子的脉动传播周期之间的关系,并对影响脉动传播的内在物理机制进行了讨论.同时,还研究了在线性折射率纵向调制情况下强非局域光晶格结构中空间孤子传输的开关行为. 关键词： 非局域非线性薛定谔方程 光晶格 空间孤子 光开关     

Modulation instability in a medium with a nonlocal nonlinearity

The general conditions of appearance of the modulation instability of spatially homogeneous regimes in media with a nonlocal response of nonlinearity are determined. By using, as an example, the nonlocality in the form of the truncated Lennard-Jones potential, which is characteristic of interatomic interaction in Bose-Einstein condensates, the region of stability is found and the character of structures arising upon the loss of stability is discussed.     

有界非局域非线性介质中空间光孤子传输的研究

对有界非局域非线性介质边界对孤子传输的影响进行了研究.基于非局域非线性薛定谔方程以及热传导的泊松方程,采用格林函数法求出了强非局域介质铅玻璃的响应函数和临界功率;从光线方程出发得到了偏离材料中心入射的光束中心振荡轨迹以及周期的解析解.通过数值模拟证明了该结果在不靠近样品边界的范围内都是准确的. 关键词： 空间光孤子 铅玻璃 非局域非线性     

Fabrication of gradient refractive index ball lenses

The theoretical model of the Maxwell fish eye sphere lens has long been regarded as an absolute optical instrument without practical application since it was proposed. But the study on the theory of Maxwell fish eye micro-spherical lens shows that at certain condition it has fine image formation ability and coupling efficiency. Based on the Fick's diffusion equations, the distribution function of refractive index of gradient refractive index (GRIN) ball lenses is derived. Lithium-containing silicate glass is fabricated and GRIN ball lenses whose diameters are from 0.3 to 3.0 mm are made by ion exchange and the sagging method in sodium nitrate. Radial refractive index profiles of these GRIN ball lens are measured by interferometer. Results show that the distribution of the index of refraction is a parabolic curve and in concordance with the computational consequence and its Δn is 0.0002.     

Slow light in a dielectric slab waveguide with a negative refractive index photonic crystal substrate

Slow light effect in a dielectric slab waveguide with a negative refractive index photonic crystal substrate is numerically investigated. The guided modes are confined in the core layer by total internal reflection. Dispersion and wave propagating properties are explored in details. The result demonstrates that light speed can approach zero at two adjacent frequencies, which is also verified by finite-difference time-domain (FDTD) simulation. Calculated Q-factors both exceed several thousand. The structure has the potential to be used as high-Q open cavity for dual-wavelength lasers or traveling wave amplifiers.     

向列相液晶中强非局域空间光孤子传输的理论研究

对向列相液晶中非局域空间孤子的传输进行了理论研究.基于非线性液晶孤子传输方程，采用Gauss形式的试探解，不仅得到了空间孤子的解析解,而且还在临界功率附近得到了呼吸子的解析解.通过数值模拟证明我们的结果比Conti和Assanto等人的结果更合理.同时，对液晶中的非局域孤子模型和Snyder等提出的强非局域孤子模型进行了全面的比较. 关键词： 向列相液晶 空间孤子 非局域非线性 呼吸子     

Solitons in optical lattices with nonlocal nonlinearity

The propagation of spatial solitons is systematically investigated in nonlocal nonlinear media with an imprinted transverse periodic modulation of the refractive index. Based on the variational principle and the infinitesimal approximation of Maclaurin series expansion, we obtain an analytical solution of such nonlocal spatial solitons and an interesting result that the critical power for such solitons propagation is smaller than that in uniform nonlocal self-focusing media. It is found that there exist thresholds in modulation period and lattice depth for such solitons. A stable spatial soliton propagation is maintained with proper adjustment of the modulation period and the lattice depth.     

温度对气体折射率的非线性影响

对测量群折射率的迈克耳孙白光干涉技术进行了改进,采用光栅线位移传感器提高反射扫描镜的位移精度. 实验确定了空气折射率对温度的非线性曲线拟合方程,其拟合因子的精度达到10-5℃-1.