Analysis of an Improved Split-Step Algorithm for Simulating Optical Transmission Systems

The standard Split-Step algorithm for calculating the signal transmission through optical fibres is significantly accelerated without relevant loss of accuracy by applying IIR filters as well as Fourier transformations for the linear operator. Depending on the system topology, high speed-up factors can be achieved by switching back and forth between time and frequency domain algorithms for the linear operator. Two different IIR filters are applied for calculating linear and parabolic dispersion. The efficiency of this algorithm in combination with an innovative step-size allocation method is evaluated.     

Profiling Voids Embedded in a Slab by a Non-Linear Model

In this paper, by applying a non linear model for the electromagnetic inverse scattering, a technique for the dielectric profiling of a planarly layered medium is investigated and applied to void localization and diagnostics inside a homogeneous lossless slab (one-dimensional geometry). Data are collected under plane wave multifrequency normal incidence. Suitable finite dimensional representations for the unknown functions are introduced and their influence on the model is discussed. The resulting functional equation is solved by the method of weighted residuals and the solution algorithm amounts to minimizing a non quadratic function, where particular attention is devoted to reduce the occurrence of local minima. Finally, the inversion algorithm is validated by applications to both simulated and experimental data.     

Simulation of Ultrashort Laser Pulse Propagation in Silica Fibre by FDTD+

The finite-difference time-domain algorithm is extended to solving the Maxwell's equations with nonlinear terms which include all exact Sellmeier-fitting values in this paper. The results obtained by the presented method are in good agreement with those from experiments, and this method is even better than solving the generalized nonlinear Schrödinger equation by split-step Fourier method. The spectral phase of propagated pulses is also obtained by the presented method, which is important for investigation of single-cycle optical pulse generation via phase compensation of the nonlinear-chirped in silica fibers.     

Reliable CAD Analyses of CMOS Radio Frequency and Microwave Circuits Using Smoothed Gate Capacitance Models

The problems with convergence caused by both voltage- and charge-controlled models of MOSFET gate capacitances are often a limiting factor of the computer aided design tools. In the paper, an idea of the exponential smoothing of model discontinuities is proposed. The method is demonstrated on smoothing the gate capacitance discontinuity at zero drain-source voltage. An advanced integration algorithm convenient for the computer aided design of radio frequency and microwave CMOS circuits suppressing possible physically incorrect results of the traditional methods is also described. The updated model and algorithm are checked by analyzing a sophisticated CMOS flip-flop circuit.     

Numerical simulation of nonuniformly time-sampled pulse propagation in nonlinear fiber

Numerical simulation of pulse propagation in nonlinear optical fiber based on nonlinear Schrodinger equation plays a significant role in the design, analysis, and optimization of optical communication systems. Unconditionally stable operator-splitting techniques such as the split-step Fourier method or the split-step wavelet method have been successfully used for numerical simulation of uniformly time-sampled pulses along nonlinear optical fibers. Even though uniform time sampling is widely used in optical communication systems simulation, nonuniform time sampling is better or even desired for certain applications. For example, a sampling strategy that uses denser sampling points in regions where the signal changes rapidly and sparse sampling in regions where the signal change is gradual would result in a better replica of the signal. In this paper, we report a novel method that extends the standard operator-splitting techniques to handle nonuniformly sampled optical pulse profiles in the time domain. The proposed method relies on using cubic (or higher order) B-splines as a basis set for representing optical pulses in the time domain. We show that resulting operator matrices are banded and sparse due to the compact support of B-splines. Moreover, we use an algorithm based on Krylov subspace to exploit the sparsity of matrices for calculating matrix exponential operators. We present a comprehensive set of analytical and numerical simulation results to demonstrate the validity and accuracy of the proposed method.     

初始啁啾对光子晶体光纤中飞秒脉冲压缩的影响

运用分步傅里叶方法数值模拟了飞秒高斯脉冲在光子晶体光纤中的传输,计算分析了初始啁啾对脉冲压缩效应的影响.结果表明,初始啁啾有利于增强压缩效果,提高脉冲压缩质量和峰值功率,但使得最佳光纤长度减小.选取合适的光纤长度,可有望对各种波长的脉冲进行压缩.     

An Immitance Based Tool for Modelling Passive One-Port Devices by Means of Darlington Equivalents

An immitance-based method is presented to model measured orcomputed data, obtained from a “passive one-port physical device” by means of its Darlington equivalent. In other words, the given data ismodelled as a lossless two port terminated in a unit resistor. The basis of the new modelling tool rests on the numerical decomposition of the given immitance data into its Foster and minimum parts. Therefore, the proposed technique does not require any choice for the circuit topology to build the model. Rather, the optimum circuit topology that characterises thegiven data is the natural consequence of the modelling process proposed in this paper. A main algorithm is presented to construct the model from the given data. It is expected that the proposed modelling tool will findpractical applications in the behaviour characterisation, simulation, and design of high speed/high frequency analog/digital mobile communication sub-systems manufactured on VLSI chips. An antenna-modelling example is included to systematically exhibit the implementation of the modelling technique.     

皮秒脉冲在光子晶体光纤中的压缩效应

为了研究初始啁啾和初始输入功率对脉冲压缩的影响,运用对称分步傅里叶方法数值模拟了皮秒高斯脉冲在光子晶体光纤中的传输过程.增大初始啁啾和输入功率可以得到更大的压缩因子,同时最佳光纤长度减小,它们之间基本成线性关系.并且在初始啁啾值和初始功率比较小时,在最佳光纤长度处,品质因子和压缩因子不是同时达到最大值.结果表明,若选取适当的光纤长度和初始峰值功率,可以实现啁啾脉冲在光子晶体光纤中的有效压缩.     

Flexible Digital Receiver Architecture with Optimized Components

Future wireless communication systems require increased flexibility, lower power consumption, smaller size and decreasing costs for the terminals and therewith for the components. By replacing analogue by digital signal processing the degree of integration and the flexibility of a terminal with respect to multi-mode capability can be improved.In a highly integrated implementation the most critical components are the A/D-converter and the digital filter stages due to high speed and low power requirements. In this contribution a novel concept for a flexible, digital receiver with highly optimized components will be presented. The concept is based on down-conversion of the broadband receive signal to a low intermediate frequency. The main modules of the receiver are a properly designed ΔΣ-modulator for A/D-conversion, and novel digital filtering stages. It will be demonstrated, that the use of cascaded low-order wave digital lattice filters results in a number of advantages and makes a very efficient realization in VLSI-technology feasible.     

五阶非线性对光纤中高斯型脉冲传输特性的影响

从含修正项的非线性薛定谔方程出发,采用变分法,导出了五阶非线性情况下光纤中高斯型脉冲参数随传输距离的演化方程组,求出了振幅与脉宽、频率与啁啾、脉宽与啁啾之间的三个解析约束关系,得出了脉宽随传输距离演化的解析解,讨论了五阶非线性对光纤中高斯型脉冲传输特性的影响.并且描绘了五阶非线性系数和啁啾对脉宽的影响、啁啾与初始啁啾对脉宽的影响、脉宽随传输距离以及五阶非线性系数、脉宽随传输距离以及初始啁啾四种情况下的三维图形.     

采样对数值模拟光纤中光脉冲传输演化的影响

光脉冲在光纤中传输时,光纤的非线性效应和色散将会使其变形。在考虑了以上两种影响因素后,给出了利用分步傅立叶变换法正确模拟光脉冲在光纤中传输的采样间隔选取依据,模拟了在不同采样间隔下光纤输出端的光脉冲形状和频谱,由此讨论了采样间隔对数值模拟光纤中光脉冲传输演化的影响。数值模拟结果验证了采样间隔选取依据的正确性。     

Modelling of 2-D Real Rational Reactance Functions. A Parameter-Based Approach

Lossless (reactive) one-ports are of great importance in the field of linear network theory. This statement also applies for the two-dimensional (2-D) case, where the design of corresponding impedance or admittance functions is a much more challenging task. In this paper a model for 2-D real rational reactance functions is introduced which is a rational function in p₁ and p₂ where the coefficients are functions of parameters. The following features make it best suited for the computer based design of lossless one-ports, namely no dependencies between the real valued parameters, coverage of the whole class of 2-D real rational reactance functions, and the coefficients are polynomials in the parameters. The synthesis of 2-D lossless networks and skew symmetric matrices form the basis of our considerations.     

离散效应对光子晶体光纤中飞秒脉冲压缩影响

为了研究离散效应对光子晶体光纤中飞秒信号脉冲压缩的影响,采用分步傅里叶方法数值求解耦合的非线性薛定谔方程,模拟了双飞秒脉冲在光子晶体光纤中的非线性传输过程;计算和分析了离散效应和非同步耦合对信号脉冲压缩的影响。结果表明,当抽运脉冲在反常色散区进行抽运,而信号脉冲在正常色散区入射时,在群速度色散、3阶色散,自相位调制及交叉相位调制联合作用下,信号脉冲在传输过程中不仅被压缩且存在最佳光纤长度;离散效应导致信号脉冲压缩因子减小,所需最佳光纤长度增加以及压缩后的脉冲频谱呈现不对称,采用非同步耦合有利于改善信号脉冲的压缩质量。     

自傅立叶光孤子的相互作用特性

用分步傅立叶变换方法数值求解非线性薛定谔方程,研究了一阶自傅立叶光孤子信号在光纤传输中的相互作用特性。证明了算法内部不存在理论误差。数值模拟结果表明：（1）一阶自傅立叶孤子对中的相互作用表现不同于一阶标准孤子对,它类似于二阶或准二阶孤子之间的相互作用特性。两孤子经历一段周期性的相互吸引后,出现强烈的相互排斥;（2）孤子相互作用特性不足以用孤子的阶去区分或分类,在同一阶的孤子中,不同的脉宽对孤子的相互作用有显著不同的影响;（3）微弱的三阶色散效应有利于抑制一阶自傅立叶孤子间的相互作用。     

光纤传输模型的计算机仿真研究

光纤的物理模型一般采用非线性薛定谔方程的描述,论文介绍用分步傅立叶方法采用计算机模拟实现光纤传输物理模型,并用该计算机模型进行交叉相位调制效应的模拟。     

任意波形超短光脉冲合成器研究

综述了超短光脉冲产生方式;详细阐述了几种典型的产生超短光脉冲的方法,分析了其特点.介绍了一种新型的任意波形光脉冲合成技术,通过对光谱的每个谱线分别进行独立地操控来制作光脉冲的傅立叶合成器,能够产生任意波形的超短光脉冲.     

三阶色散对光纤中高斯型脉冲传输特性的影响

从含修正项的非线性薛定谔方程出发,采用变分法,导出了在三阶色散情况下光学高斯型脉冲参数随传输距离的演化方程组;在此基础上,求出了振幅与脉宽、频率与啁啾、脉宽与啁啾之间的三个重要约束关系;并进一步得出了脉宽随传输距离演化的解析解;讨论了三阶色散对光纤中高斯型脉冲传输特性的影响.     

五阶非线性光纤中光扰动所致超短脉冲串的产生

从光纤中包含五阶非线性效应的扩展非线性薛定谔方程出发,采用分步傅里叶算法,数值模拟了连续光波的幅度受到正弦光扰动的调制后在光纤中演化分裂成超短脉冲串的过程,探讨了五阶非线性效应和正弦调制周期对脉冲串形成和演化特点以及相应频谱的影响.结果表明,与三阶非线性相比,正五阶非线性使形成超短脉冲串的最佳光纤长度缩短,形成的单个脉冲宽度更窄、峰值功率更高,负五阶非线性则相反.正弦调制周期将影响脉冲串的重复率和最佳光纤距离.随传输距离的增加,单个脉冲可能分裂成两个甚至三个分脉冲,在主脉冲之间还可能出现一定数量的峰值功率弱的次脉冲.就频谱特性而言,正(负)五阶非线性可增多(减小)光波频率成分、加宽(窄化)频谱;视主脉冲有无分裂以及次脉冲的存在与否,频谱的形状也会不同.     

Continuous and Discrete Wavelet Transform Analysis of Nonlinear Pulse Propagation in Single Mode Fibers

The use of the continuous wavelet transform and the discrete wavelet transform in analyzing the propagation of optical pulses in nonlinear dispersive fibers is discussed. The analysis is based on the split-step wavelet algorithm which reaches reasonable accuracy as compared to the well-known split-step Fourier method.