Modulation instability in silicon optical waveguide considering linear loss

Taking into account the linear loss of silicon-on-insulator (SOI) waveguide, modulation instability (MI) induced by combined effects of self-phase modulation and waveguide dispersions is investigated. The impacts of various parameters to gain spectra of MI are analyzed theoretically, and direct numerical simulation of nonlinear Schroedinger equation is performed as well. Results show that strong MI takes place even in the existence of low light power. The linear loss of waveguide obviously impacts gain spectra of MI, even within ultra-short propagation distance. The peak gain frequency and bandwidth of gain spectra decrease to 41.683% and 41.6879% of their maximum at propagation distance z = 5 mm, respectively.     

Modulation instability in metamaterials with fourth-order linear dispersion,second-order nonlinear dispersion,and three kinds of saturable nonlinearites

The linearized nonlinear propagation equation and its coefficients, gain spectrum of modulation instability (MI) in metamaterials (MMs) with fourth-order linear dispersion, second-order nonlinear dispersion, and three kinds of saturable nonlinearites, are analytically deduced by utilizing the linear stability analysis and Drude electromagnetic model. Then variations of gain spectra of MI with the normalized angular frequencies and the optical power densities are calculated in real units. In the negative refractive region, two kinds of gain spectra are discovered. The first (second) one is close to (far from) the zero perturbation frequencies and it corresponds to the lower (higher) normalized angular frequencies. Moreover, the second one has higher cutoff frequency, which is obviously beneficial to generation of high-repetition-rate pulse trains. While in the positive refractive region, only the first kind of gain spectra is found. With increase of the optical power densities, the peak gains and the spectral widths of MI increase before decrease, but they vary the most rapidly (slowly) for the exponential (conventional) saturable nonlinearities. The MI characteristics and their corresponding applications can be adjusted by several methods.     

饱和非线性正折射异向介质中的调制不稳定性

直接从异向介质中包含饱和非线性、自陡峭和二阶非线性色散效应的非线性扩展传输方程出发,采用线性稳定性分析法,导出了调制不稳定性的色散关系、不稳定条件、无量纲的临界扰动频率和增益谱。计算和讨论了异向介质正折射区无量纲的增益谱随归一化角频率和入射功率密度的变化关系。结果表明,在异向介质正折射区,随归一化角频率和入射功率密度的不同,增益谱将会出现扰动频率大于零、扰动频率大于某个非零临界值、扰动频率大于零而小于某个非零临界值3种形式。在归一化角频率较小时,调制不稳定性可能出现阈值入射功率密度;且在较小的入射功率密度时,调制不稳定性只能出现在大于某个临界频率时。     

Modulational instability of optically induced nematicon propagation

We report the modulational instability （MI） analysis for the modulation equations governing the propagation of coherent polarized light through a nematic liquid crystal （NLC） slab, in the limit of low light intensity and local material response. The linear stability analysis of the nonlinear plane wave solutions is performed by considering both the wave vectors （k,l） of the basic states and wave vectors （K,L） of the perturbations as free parameters. We compute the MI gain, and the MI gain peak is reduced and the stable bandwidth is widened with the increase of the strength of the applied electric field. Further, we invoke the extended homogeneous balance method and Exp-function method aided with symbolic computation and obtain a series of periodic solitonic humps of nematicon profiles admitting the propagation of laser light in the NLC medium.     

Analytical Study on Propagation Dynamics of Optical Beam in Parity-Time Symmetric Optical Couplers

We present exact analytical solutions to parity-time(P T) symmetric optical system describing light transport in P T-symmetric optical couplers. We show that light intensity oscillates periodically between two waveguides for unbroken P T-symmetric phase, whereas light always leaves the system from the waveguide experiencing gain when light is initially input at either waveguide experiencing gain or waveguide experiencing loss for broken P T-symmetric phase. These analytical results agree with the recent experimental observation reported by Ru¨ter et al. [Nat. Phys.6(2010) 192]. Besides, we present a scheme for manipulating P T symmetry by applying a periodic modulation. Our results provide an efficient way to control light propagation in periodically modulated P T-symmetric system by tuning the modulation amplitude and frequency.     

光子晶体波导中的孤子传输及其延迟特性研究

研究了正方晶格和三角晶格空气背景硅介质柱光子晶体线缺陷波导导模左带隙边缘处的亮孤子脉冲传播特性及其慢光延迟特性. 采用平面波展开法仿真分析了波导相邻两行介质柱大小r₁和r₂以及波导宽度D对孤子脉冲传输所需峰值功率P₀和延迟时间T_s的影响,总结了其变化规律. 通过调整波导结构得到了正方晶格和三角晶格优化波导结构,优化后,正方晶格结构波导P₀减小了81.17%,T_s增加了66.32%;三角晶格结构波导P₀减小了73.7%,T_s增加了67.63%,实现了孤子传输性能的大幅度优化. 关键词： 光子晶体波导 光孤子 峰值功率 延迟时间     

亮孤子在宇称时间对称波导中的传输和控制

基于光波在宇称-时间(PT)对称波导中传输的理论模型, 数值研究了亮孤子在呈高斯分布的PT对称克尔非线性平板波导中的传输和控制. PT对称波导, 要求波导的折射率分布呈偶对称, 而增益/损耗分布呈奇对称. 结果表明: 当波导的折射率分布强度为正时, PT对称波导的中心折射率最大, 即使没有自聚焦克尔非线性效应, PT对称波导也可以束缚光波, 形成波浪形光束且长距离传输; 当折射率分布强度为负时, PT对称波导的中心折射率最小, 光波的传输方向发生偏移. 而增益/损耗分布可控制光波的偏移方向: 增益/损耗分布强度为正, 光波向左偏移; 强度为负, 光波向右偏移; 强度为零时, 光波被分为两束. 且当折射率分布强度为负时, 可以很好地抑制相邻亮孤子间的相互作用. 该研究结果可为未来PT对称波导在全光控制方面的应用提供一定的理论依据.     

抽运光与信号光的光强重叠因子和掺铒玻璃波导放大器的增益特性

在掺铒玻璃波导放大器（EDWA）的三能级速率-传输方程中,考虑两次离子交换工艺中波导掩模窗口宽度w不同所导致的抽运光、信号光模场与光强分布的不同,讨论不同w对EDWA增益特性的影响,得到光强分布的数值解.引入描述波导中抽运光和信号光的归一化光强重叠因子,对EDWA的传统近似解提出修正,得到了修正解,使其更加接近光强分布的数值解.模拟结果表明,在条波导长度为4 cm、抽运光波长为980 nm、功率为80 mW、信号光波长为1534 nm、功率为-10 dBm条件下,不同w所导致EDWA的增益差别可达297 dB.修正解的结果比传统近似解更加接近光强分布的数值解.修正解对于EDWA的理论研究、器件设计具有指导作用. 关键词： 集成光学 掺铒玻璃波导放大器 重叠积分因子 增益     

Spatiotemporal optical solitons in planar waveguide with periodically modulated cubic-quintic nonlinearity

The propagation and stability of spatiotemporal optical solitons (or optical bullets) in a planar waveguide with periodically modulated cubic-quintic nonlinearity is studied numerically as a function of the amplitudes of modulation (A _m ), the frequency of modulation (ω _m ) and the propagation distance z. The optical spatiotemporal solitons are the result of the balance between the nonlinear parameters, of dispersion (dispersion length, L _D ) and diffraction (diffraction length, L _d ) with temporal and spatial auto-focusing behavior respectively. With the objective of ensure the stability and preventing the collapse or the spreading of pulses, in this study we explore the cubic-quintic nonlinearity with the optical fields coupled by XPM and take into account several values for the non linear parameter α and for amplitudes (A _m ) and frequency (ω _m ) of modulation as a function of the propagation distance z and we cause the collisions of two pulses (envelope of the optical field) to ensure that the optical pulse are solitons. After numerical analysis of parameter settings selected four conditions and for all we get stable solitons and this paper shown that, for a fixed amplitude and frequency of modulation we have stable spatiotemporal solitons.     

开放的V型三能级系统中原子注入和退出速率对位相相关的无反转激光增益和强度空间演化的调制作用

利用数值计算结果, 研究了具有自发辐射诱导相干的开放V 型三能级原子系统中的传播效应. 研究表明: 改变探测场和驱动场之间的相对位相对无反转激光(LWI)增益和 强度随传播距离的变化即空间演化具有重要的影响; 而原子的注入速率比(S)和退出速率(r₀)的改变将对位相相关的LWI增益和强度的空间演化产生明显的调制作用. 在S(r₀)的一定取值范围内, S(r₀)的值越大, LWI增益和强度越大且强度达到极大值需要的传播距离越长; 相应封闭系统中LWI增益和强度的最大值及能产生增益的传播距离都小于开放系统. Doppler效应对LWI增益和强度的空间演化也具有明显的影响, 存在Doppler效应时得到的LWI增益和强度明显小于无Doppler效应时的值.     

Soliton propagation optimization and dynamic modulation in photonic crystal waveguide with polystyrene background

Bright optical soliton propagation properties near the left band edge of photonic crystal waveguide (PCW) are numerically investigated. Compared with the normal PCW with air background, by employing polystyrene as PCW background and adjusting the structure parameters simultaneously, the required soliton peak power sharply decreases from 8.63 × 10⁶ W/m to 9.98 × 10² W/m. The influence of optical loss on soliton propagation is numerically investigated. The dynamic modulation of the soliton propagation in PCW is realized, and a modulation range of 459 nm wavelength for the soliton transmission has been achieved. Simulation results show that the transmission wavelength, required soliton peak power and delay time decrease almost linearly as the external modulated voltage increases; the modulation sensitivities are 8.316 nm/V, 3.416 W/m/V and 16.6 ps/V, respectively.     

Scattering losses from planar waveguides with material inhomogeneity

Abstract

We consider the propagation of guided waves in a planar waveguide that has a finite-length segment of inhomogeneous media. Except for the inhomogeneous segment, which varies in length from 0 to 160λ, the waveguide is piecewise homogeneous everywhere. The inhomogeneity is modelled by two-dimensional random permittivity fluctuations that are numerically generated from an assumed Gaussian correlation function.

In 2D, the Maxwell equations are solved in the frequency domain for both TE and TM polarization by using modal expansion methods, perfectly matched absorbing boundary layers and the R -matrix transfer matrix algorithm. The guided waves are excited by a Gaussian beam incident on the waveguide aperture. For various waveguide design parameters, numerical results are given for waveguide power loss per unit length of waveguide inhomogeneity. The power loss curves are calculated as the average from numerous realizations of the random permittivity and the coefficient of variation is also given.     

高斯变迹布拉格光纤光栅中的调制不稳定性

利用激光脉冲在光纤光栅中传播时所遵守的相干耦合非线性薛定谔方程,研究了激光脉冲在高斯变迹布拉格光纤光栅中传输时，在反常色散区和正常色散区所产生的调制不稳定性.结果表明在反常色散区和正常色散区都能产生调制不稳定性；在反常色散区，当输入功率达到一定数值时，产生明显的有规律的增益谱；在正常色散区，在产生调制不稳定性功率区域，调制不稳定性存在并从给定值一直持续到无穷；并且，在反常色散区和在正常色散区，增益谱都受到高斯变迹函数的制约. 关键词： 高斯变迹 布拉格光栅 调制不稳定性 增益     

Inhibition of light tunneling in chirped and longitudinally modulated semi-infinite waveguide arrays

The inhibition of light tunneling in chirped and longitudinally modulated semi-infinite waveguide arrays where the refractive index is linearly modulated in the transverse direction and harmonically modulated along the light propagation direction is considered. We report on the effect of the refractive index transverse amplitude modulation rate, longitudinal modulation frequency and depth on tunneling inhibition in both linear and nonlinear regimes. We show that in the linear regime an optimal value for the transverse amplitude modulation rate of refractive index exists and can determine the optimal longitudinal modulation frequency or depth leading to a maximum of distance-averaged power fraction. In the nonlinear regime the tunneling inhibition dynamics is affected dramatically by the transverse amplitude modulation rate and the associated electric field amplitude of the input beam.     

Effects of pumped styles on power conversion efficiency and gain characteristics of phosphate glass Er3+–Yb3+-co-doped waveguide amplifiers

In order to analyze the power conversion efficiency (PCE) and the gain characteristics of the phosphate glass Er³⁺–Yb³⁺-co-doped waveguide amplifier (EYCDWA), formulas are derived from the rate equations and the light propagation equations under the uniform dopant and the steady-state conditions. In the derivation of these formulas, we have neglected the amplified spontaneous emission (ASE) and have introduced the initial energy transfer efficiency. By using these formulas, the effects of the pump power, signal power and waveguide length on the PCE and the gain characteristics of the EYCDWA are analyzed, and some useful results are obtained in three kinds of pumped styles, i.e. the forward-, backward- and bidirectional pumped styles.     

紫外表面等离激元在基于氧化锌纳米线的半导体-绝缘介质-金属结构中的输运特性研究

研究了紫外表面等离激元在半导体纳米线-绝缘介质-金属构成的波导结构中的输运问题,借助有限元方法,对这种波导所支持导模的电磁能分布、有效折射率、传播长度和有效模场面积随电磁参数和几何结构参数的依赖关系进行了分析.计算结果表明:以氧化锌纳米线作为增益介质,绝缘材料选择折射率小的空气,金属选择铝能够实现对输出光场的亚波长约束,有效模场面积达到λ2/100,同时保持低的传输损耗和高场强限制能力;有望用作纳米光源,使得相关的生物探测器件和医疗诊断设备实现更高的灵敏度和更小的体积.     

Asymmetric first-order Bragg interactions in an active dielectric waveguide

The asymmetric first-order Bragg interactions in an active planar dielectric waveguide are investigated for the case of even TE modes. Either the index or the gain is assumed to have a sinusoidal variation in the propagation direction. By a singular perturbation procedure using multiple space scales, the coupled-mode equations governing the nature of the Bragg interactions are systematically deduced and the characteristics of this instability are examined. For the gain-modulated waveguide having an average loss, there are two threshold values for the modulation index of the gain, one for absolute instability and the other for traveling wave amplification, and these threshold values are deduced. Representative numerical results are presented to illustrate the characteristics of the Bragg interactions.     

Hybrid vertical directional coupling between a long range surface plasmon polariton waveguide and a dielectric waveguide

To investigate light coupling between a long range surface plasmon polariton (LRSPP) waveguide and a conventional integrated optical component, a hybrid vertical directional coupler consisting of a LRSPP waveguides and a dielectric waveguide is investigated and fabricated. In the proposed coupler the dielectric waveguide and LRSPP waveguide are vertically configured for dense integration and strong coupling. The characteristics of the even and odd super-modes of the coupler are also analyzed to design the device. The fabricated device exhibits damped sinusoidal behavior along the coupling length due to propagation loss of the LRSPP waveguide. The maximum power transfer of 86% from the LRSPP waveguide to the dielectric waveguide is achieved at the coupling length of 600 μm. The measured characteristics of the device are in relatively good agreement with a theoretical analysis.     

强双折射光纤中单一频率传输区域的调制不稳定性

利用光脉冲在光纤中传播时所遵守的相干非线性薛定谔耦合方程,研究了单一频率的线偏振光,且偏振方向沿两个双折射轴的分量强度相等时,在反常色散区和正常色散区所产生的调制不稳定性.结果表明在反常色散区和正常色散区,对应不同的功率区域输入脉冲有不同的增益谱,并且当输入脉冲功率一定时,双折射性质变化导致增益谱表现出明显的不同.     

脊加载曲折波导行波管注波互作用的线性理论研究

提出了一类新型毫米波大功率微波器件——脊加载曲折波导行波管,推导出了引入电子注后的"热"色散方程.通过数值求解此方程,研究了加脊尺寸和电子注参数对小信号增益影响.计算结果表明:通过适当的尺寸设计和工作参数的选择,此结构在Kα波段具有18.51%的3 dB增益带宽和1.15 dB/周期的增益;相比于常规曲折波导结构,脊加载结构在保证一定带宽的情况下,具有更高的增益和电子效率;为了进一步提高增益,可以适当增加脊宽度和高度,也可在一定范围内增加电子注电流. 关键词： 毫米波 曲折波导 脊加载 小信号增益