Analytical stability analysis of dark and bright self-guided wavesin layered self-defocusing nonlinear media

We present an analytical stability analysis on dark (black and gray) self-guided waves and the fundamental state of the bright self-guided waves with nonzero intensity background trapped in a thin self-defocusing nonlinear film bounded by an infinite self- defocusing medium of different nonlinearity. It is found that the gray self-guided wave and the fundamental state of the bright self-guided waves with nonzero intensity background are stable to both symmetric and asymmetric perturbations, whereas the black self-guided wave is stable to symmetric perturbation but unstable to asymmetric perturbation (in contrast to the corresponding one in a uniform self-defocusing medium). For the nonlinear waveguides with the linear refractive index n_c, in the cladding smaller than that n_f the film the instability of the black self-guided waves is shown to result from the presence of the complex growth rate, while the instability for that trapped in a hollow waveguide (n_cc>n_f) may arise from the presence of either real or complex growth rate, depending on the waveguide parameters     

Linear and Nonlinear Optical Pulse Propagation in Photonic Crystal Waveguides Near the Band Edge

In this paper, the propagation of optical pulses in photonic crystal waveguides (PCWs) near the edge of the guided band is numerically investigated. In the linear regime, it is shown that group velocity dispersion can significantly limit the maximum bit rate of the optical signal. On the other hand, better performance is obtained using soliton waves. Both bright and dark solitons can significantly increase the maximum bit rate that can be achieved in the nanosecond delay regime. The influence of higher order dispersion and optical loss is numerically investigated. The results indicate that near the band edge soliton propagation in PCWs can be stable, provided that the optical losses are kept low. This could open a path towards implementing compact nonlinear elements and delay lines in integrated form.      

非线性空间调制对两分量玻色-爱因斯坦凝聚孤子演化的影响

考虑具有谐振势的两分量玻色-爱因斯坦凝聚（BEC）中的亮孤子,采用数值模拟方法研究了非线性空间调制对线性耦合两分量BEC中的孤子演化的影响。结果表明,s-波散射长度的空间变化改变了孤子的密度包络;在合适的初始条件下,可以存在稳定的孤子态;孤子的演化依赖于非线性空间调制系数的符号和大小。     

Some study on dark and bright optical solitons in a real system with periodically distributed dispersion and nonlinearity

We study the dynamics of short optical pulses in a real system with periodically distributed dispersion and the nonlinearity is governed by the higher order nonlinear Schrödinger equation (HNLSE) with linear and nonlinear gain (loss). Under specific parametric circumstances, where the dark and bright solitary waves are combined, a set of entirely new types of solitary waves with nonlinear chirp have emerged. For a properly intense optical pulse in the combined solitary waves, the binding of the bright and dark solitary waves is very strong. It is seen that by numerical simulation, these pooled types of solitary-like solutions show a high degree of stability while propagating over an extremely long distance in the considering system, even in the presence of a high degree of perturbation of the amplitude and white noise. All constraint relations on the physical parameters are explicitly shown to be related to the development and to the dynamical study of the chirped solitary like solution in the considering medium.     

Self-switching in hollow waveguides with a Kerrlike nonlinearpermittivity

The dispersion relations, stability, and excitation of the stationary nonlinear transverse electric (TE) waves guided by a nonlinear hollow waveguide are examined numerically. This waveguide consists of a self-focusing nonlinear film bounded by two identical linear claddings of the higher refractive index. Since a minimum power for guidance of the stationary waves always exists, the nonlinear hollow waveguide acts as a lower threshold device. A stability analysis using the beam propagation method shows that all the stationary TE_n modes, including the asymmetric TE₀ mode, are stable on the positively sloped branch (dP/dβ>0) of the nonlinear dispersion curve. The lower threshold device using the nonlinear hollow waveguide exhibits very sharp power-switching characteristics, and the required device length is fairly short     

Stability analysis of nonlinear TE polarized waves inmultiple-quantum-well waveguides

A stability analysis of TE polarized nonlinear guided waves in multiple-quantum-well waveguides is presented. In particular, a scalar finite element approach has been used in order to numerically investigate symmetrical as well as asymmetrical field distributions and their properties. For high input power, the analysis reveals the stable and the unstable nature of asymmetrical and symmetrical multiple quantum well waveguide solutions. Similar features to single linear film bounded by nonlinear media are pointed out. The limits of the homogeneous slab approximation are discussed     

TM-polarized nonlinear guided waves in multilayer systems

The ability of various multilayer systems to support TM-polarized nonlinear guided waves is studied. A flexible numerical technique which includes the proper consideration of the nonlinear crossing conditions is used to calculate the field profiles and derive the dispersion relations. The fundamentals of the model are described, and the algorithm is applied to several nonlinear film configurations. For the sake of comparison with the finite-element method, a single linear film, embedded between two nonlinear materials, is treated. A three-film unit cell, consisting of a high-index linear film, sandwiched between two low-index nonlinear, ones is considered. This is the elementary unit cell of a composite geometry, a ten-unit-cell superlattice, which is then studied. It is found that unlike TE-polarized nonlinear guided waves in multilayer systems, the TM waves reveal a distinct power maximum. The inclusion of saturation effects in the analysis is straightforward     

Asymmetric dark modes in symmetric nonlinear waveguides

We show that symmetric nonlinear waveguides can support the asymmetric dark modes. The existence of a novel class of bright nonlinear guided wave with nonzero-intensity background is also demonstrated     

Guided Waves in Inhomogeneous Focusing Media Part III: Wall Effects, Losses, and the Transition from Fast to Slow Waves

This paper is concerned with the determination of field patterns, propagation constants, and losses for axially propagating modes guided by an enclosed circular cylindrical, radially inhomogeneous dielectric of the type discussed in Parts I and II. The homogeneous outer medium (/spl gamma/ /spl ges/ /a) is assumed to have a large relative permittivity /spl epsiv//sub 2/, and the analysis includes the perfect conductor case /spl epsiv//sub 2/ /spl rarr/ /spl infin/. The transition to trapped waves as the binding effect increases is demonstrated. Propagation constants in the case with loss are determined using a perturbation technique.     

New nonlinear magnetostatic surface waves in a ferromagnetic (YIG)

The general propagation characteristics of magnetostatic surface waves guided by a single interface of a semi-infinite nonlinear dielectric cover and a ferromagnetic substrate (YIG) have been derived. The nonlinear dielectric cover has intensity dependent refractive indices. The magnetostatic approximation is considered and retardation is ignored in describing the electromagnetic fields in the structure. The used magnetostatic approximation is leading to new waves and might be called nonlinear magnetostatic surface waves. The propagation of these waves is non-reciprocal in contrast to the linear magnetostaic surface waves, which had been only found in the negative direction of propagation.     

An efficient scalar finite element formulation for nonlinearoptical channel waveguides

A self-consistent numerical approach based on the scalar finite element method is described for the analysis of both TE-like and TM-like nonlinear guided waves in optical channel waveguides. In order to improve the convergence and accuracy of solutions, isoparametric elements and numerical integration formulae derived by Hammer et al. are introduced. Numerical results are presented for nonlinear elliptical core optical fibers, and it is confirmed that in this approach, highly accurate solutions can be obtained with small scale computation. Furthermore, graded-index nonlinear optical channel waveguides are also analyzed, and the influence of refractive-index profiles on propagation characteristics of the nonlinear guided waves is investigated     

A Perturbation Method for Complex Root Finding of Nonlinear Electromagnetic Waves

Aspects of the perturbation method are presented and implemented on the analytic function of the complex variable for the propagation of nonlinear electromagnetic surface guided by a thin film. The behavior of nonlinear TE waves guided by asymmetrical dielectric thin film, bounded by a generalizes nonlinear substrate with a permittivity of the form ? ～ | E |^δ is analyzed. The complex roots, which correspond to the propagation and attenuation coefficient are obtained and discussed.     

区域多任务安全隐患排除的机器人调度策略

针对灰狼优化算法易陷入局部最优且单一算法不易解决障碍物空间多机器人隐患搜排的调度问题,提出了一种分步引导式多机器人安全隐患协同排除调度策略。首先引入非线性收敛因子调整策略和静态加权平均权重策略改进灰狼优化算法以避免算法陷入局部最优;随后通过改进的灰狼优化算法先后两次求解遍历顺序,引导机器人规划搜索路径与排除隐患点路径;最后在领航者-跟随者模型的基础上多机器人编队与队形变换避障,逐一到达隐患点位置实现多机器人的调度策略。通过国际通用6个基准函数进行测试,改进的灰狼优化算法在收敛速度、搜索精度及稳定性上均有明显提高,验证了区域多任务安全隐患排除的分步引导式多机器人协同调度策略的有效性。     

Application of Davidenko's Method to a Lossy Nonlinear Waveguide

Davidenko's method is implemented for determining the complex propagation constants (Modal index and attenuation coefficient) of nonlinear TE waves guided by an asymmetrical lossy nonlinear dielectric wave-guide. The waveguide structure has a generalized nonlinear substrate with a permittivity of the form ? ～ | E |^δand an absorbing cover making the propagation constant to be complex. Davidenko's method shows to be a fast and accurate analysis in finding the complex propagation constants. The effects of initial condition parameter on the propagation characteristics are investigated, analyzed and discussed.     

Finite-element solution of nonlinear TM waves inmultiple-quantum-well waveguides

Intensity-dependent characteristics for TM-polarized optical waves guided by multiple-quantum-well (MQW) waveguides with arbitrary nonlinear media are numerically analyzed by the finite element method. In this approach, self-consistent solutions are obtained through a simple iterative procedure. The power-dependent dispersion relations and magnetic-field (H_x) as well as two electric-field ( E_y and E_z) profiles for nonlinear TM waves in MQW waveguides with three different nonlinear mechanisms are presented. It is shown that, for the waveguides with molecular orientational mechanism, a distinct power limiting action for nonlinear TM modes exists     

Nonlinear guided waves in multilayer systems

A nonlinear matrix formalism that allows the calculation of the optical field within a nonlinear multilayer system is presented. Taking advantage of this technique, the field profiles are calculated and the dispersion relation of nonlinear guided waves in such configurations is derived. The numerical results reveal that several field profiles occur, each attached to a certain unit cell of the multilayer system. The various field profiles apply to the corresponding branches of rich structured nonlinear dispersion curves. A comparison of the results of those yielded by an effective medium model is carried out. Appreciable differences are found and are discussed in detail     

Finite-element formalism for nonlinear slab-guided waves

A unified computer-aided numerical approach, based on the finite-element method, is developed for analyzing optical waves guided by dielectric slab waveguiding structures with arbitrary nonlinear media. In the formulations, both TE and TM polarizations are considered. For the TM case, the biaxial nature of nonlinear refractive index is considered without any approximation. Numerical results are presented for nonlinear TE and TM waves propagating in symmetric slab waveguides. The dependence of dispersion relations on the refractive-index profile of the film is examined     

Coupling Between Guided Surface Waves, Lateral Waves, and the Radiation Fields by Rough Surfaces--Full-Wave Solutions

In this paper explicit expressions are presented for the guided surface waves and lateral waves that are excited when radiation fields are incident upon rough surfaces. Similarly, expressions are presented for the radiation fields scattered by rough surfaces that are excited by surface waves and lateral waves. In addition, coupling between the surface waves and the lateral waves due to surface irregularities is considered in detail. The solutions, which are based on a full-wave approach to the problem, are subject to the exact boundary conditions at the irregular interface. These are shown to be consistent with the reciprocity relationship in electromagnetic theory. The validity of the approximate impedance boundary condition is examined and consideration is given to excitation at the grazing incidence, the Brewster angle, and to waves incident at the critical angle for total internal reflection. Optimum conditions are determined for coupling between the radiation fields, the surface waves, and the Iateral waves incident upon irregular boundaries. Thus this work is applicable to problems of radio wave propagation near an irregular interface between two media and excitation of guided waves by irregular dielectric structures.     

TM waves in nonlinear saturable thin films: a multilayered approach

The dispersion of guided TM (transverse magnetic)-polarized waves in a thin nonlinear saturable film bounded by linear media is investigated. The film is assumed to be isotropic with both of the electric field components contributing to its dielectric function. The variation of the wave effective index with the guided power and also with the surface magnetic field intensity is obtained. Different mechanisms giving rise to the nonlinearity of the film are shown to result only in small quantitative differences in the dispersion behavior. A recursive scheme for solving the nonlinear wave equation within the film is fully described. The scheme relates to the saturable dielectric function used and its based on the stratification of the film region into a large number of linear sublayers     

对称非线性薄膜波导TE模的色散特性

用均匀（重整化）微扰方法分析Ｋｅｒｒ型非线性薄膜两侧为折射率相等的包层与衬底情形ＴＥ模的传播特性，传播常数用表征非线性的功率密度极值作为参数来表示。在微扰法失效情况下，用数值积分法求解。本文方法简便，节省机时，对典型实例的计算结果与精确数值计算结果十分符合。