A Compact 2-D Finite-Difference Frequency-Domain Method for Dispersion Characteristics Analysis of Trapezoidal-Ridge Waveguides

A compact two-dimension (2-D) finite-difference frequency-domain (FDFD) method is used to analyze the dispersion characteristics of single and double trapezoidal-ridge waveguides. The general 2-D FDFD formulation under orthogonal curvilinear coordinate system is derived from the difference form of Maxwell’s equations, and modified difference formulas at the trapezoidal-ridge section are built. After implementing the boundary conditions, the 2-D FDFD formulation is concluded as an eigen equation and then constructed by a highly sparse matrix. By solving the matrix-eigen equation, the dispersion characteristics of the ridged waveguides can be obtained. Computed results are in good agreements with the previously published and simulated ones, which prove the correctness of the method.     

Computer Analysis of Dielectric Waveguides: A Finite-Difference Method

A method for computing the modes of dielectric guiding structures based on finite differences is described. The numerical computation program is efficient and can be applied to a wide range of problems. We report here solutions for circular and rectangular dielectric waveguides and compare our solutions with those obtained by other methods. Limitations in the commonly used approximate formulas developed by Marcatili are discussed.     

基于有限元法的脊波导特征值分析

本文将有限元法引入到双脊、单脊和不对称脊波导特征值的分析中,求解出了三种脊波导的特征值,并给出了截止频率和主模带宽曲线。     

Two-Dimensional Metallic Photonic Crystal with Point Defect Analysis Using Modified Finite-Difference Frequency-Domain Method

We have derived a modified finite-difference frequency-domain (FDFD) algorithm for two-dimensional (2-D) metallic photonic crystal (MPC) analysis. Using this method, the numerical results for the transverse-electric (TE) and transverse-magnetic (TM) modes in square and triangular lattices are in excellent agreements with those from other method. Then the correspondence of the band gaps between a unit cell and a supercell is demonstrated. Furthermore, by comparing the field distributions of the defect modes in a point defected MPC and a point defected dielectric photonic crystal (DPC), it is found that the defect MPC has a higher degree of localization, which means that MPC is preponderant for resonator and waveguide applications in millimeter wave and sub-millimeter wave bands.      

一般正交曲线坐标系中的降维时域有限差分法

相对于常规的时域有限差分法(FDTD),降维时域有限差分法(R-FDTD)减少了约1/3的存储量。本文推导得出了一般正交曲线坐标系(GOC)中的降维时域有限差分法的基本公式,给出了其计算步骤,为在一般正交曲线坐标系中应用降维时域有限差分法奠定了基础。数值实验证实了这一方法的有效性。     

A Decoupled Formulation of the Vector Wave Equation in Orthogonal Curvilinear Coordinates, with Application to Ferrite-Filled and Curved Waveguides of General Cross Section

The introduction of a double complex-number system and the combining of the transverse field components into a compact composite structure enable the wave equation to be expressed in a form in which certain mathematical combinations of field components appear as entities completely decoupled from each other. Hence the equations can be solved for these combinations and ultimately for the components themselves. The method appears limited to guides of constant cross section and of either 1) isotropic medium and curved axis, or 2) axially anisotropic nonreciprocal medium and straight axis.     

曲边介质波导的有限元分析

本文应用曲边有限元方法有效地计算了曲边质波导的色散特性，编制了相应的计算程序,应用本文方法计算得到的椭圆旬质波导和组合椭圆介质波导的主模和高次模的色散曲线与文献[2],[3]的结果相当吻合。     

弯曲光波导端面修饰的设计方法

光波导的弯曲损耗一直是集成光学中一个值得人们重视的问题,为有效地减小光波导弯曲损耗,弯曲光波导的设计成为集成光学波导设计中的一个重要内容.本文在弯曲光波导保形变换方法的基础上,应用几何光学分析方法给出了波导弯曲损耗产生的简洁的物理图像,从而深入地分析了弯曲损耗产生的根本原因,并由此提出了弯曲光波导端面修饰的设计方法.理论分析表明,与传统的弯曲的光波导设计相比,该种设计方法可以有效地减小导波的模式泄漏,从而减小波导弯曲损耗.尤其是在弯曲光波导曲率半径、材料折射率等参数被设定的情况下,该种设计方法成为一种有效的设计方法.     

High Order Vectorial Analysis of Waveguides With Curved Dielectric Interfaces

This letter introduces a novel full vectorial higher order finite difference method for the modal analysis of optical waveguides with smoothly curved dielectric interfaces. Based on a simple Cartesian grid, a new matched interface and boundary formulation is derived to enforce the interface conditions so that the staircasing error can be eliminated. Benchmark problems are employed to validate the proposed method. A fourth order convergence is numerically confirmed irrespective of the presence of the step-index interfaces.      

An Alternative Method to Analyze Field Distribution in Curved Dielectric Waveguides

A simple and effective method is proposed to analyze the field distribution of a curved dielectric waveguide with rectangular cross-section. Numerical results are compared with the measured values. It is shown that the present approach is effective and reliable.     

A Method for Diminishing Total Transmission Losses in Curved Dielectric Optical Waveguides

A practical method for diminishing total transmission losses in curved dielectric optical slab waveguides is proposed. Asymmetric structures are introduced into curved sections. It is found that there exists an optimum asymmetric structure for the curved section which makes the total transmission loss minimum. And it is also found that the characteristics of total transmission loss do not critically depend upon the asymmetry of waveguide structure, so that some displacement from the optimum structure does not increase the loss in an appreciable amount.     

分析曲边截面波导主模特性的新方法

本文提出了分析曲边截面波导主模特性的一个新方法。分析方法是基于网络级联技术和横向谐振法的结合。通过对几种曲边波导主模传播特性的数值例算,表明本文方法精度较高,且简单易行,特别适合于实际工程应用。     

微波混频器频域全非线性分析法

本文首先建立了微波混频器件的频域计算模型,以及相应的频域谱平衡迭代算法,然后对多频信号激励下的微波混频器进行了分析,以此研究了混频器的频率变换特性。     

Three-Dimensional Finite-Difference Method for the Analysis of Microwave-Device Embedding

The embedding of microwave devices is treated by applying the finite-difference method to three-dimensional shielded structures. A program package was developed to evaluate electromagnetic fields inside arbitrary transmission-line connecting structures and to compute the scattering matrix. The air bridge, the transition through a wall, and the bond wire are examined as interconnecting structures. Detailed results are given and discussed regarding the fundamental behavior of embedding.     

系统频域分析的等效激励法和传递函数法

本文讨论了应用于线性时不变LTI系统的频域分析的两种技术。通过使用傅立叶变换FT的因果时域微分性质,给出了计算非零初始条件下因果激励的LTI系统响应的频域等效激励法;同时通过使用FT的非因果时域微分性质,给出了计算非因果激励的LTI系统响应的传递函数法。频域等效激励法和传递函数法分别是时域分析中的等效激励法和卷积法的频域版本,与时域等效激励法等效于时域卷积法一样,频域等效激励法也等效于传递函数法。     

单纯形法在非线性光波导传播特性分析中的应用

简要介绍了优化理论中的单纯形方法,并且应用到求解介质非线性光波导的色散方程。文中计算了非线性光波导传输特性的2个实例,1）非对称3层平板波导,由线性衬底、克尔型芯区和线性包层（LNL）组成;2）对称3层平板波导,由克尔型包层、衬底及线性芯区组成（NLN）。数值结果表明,非线性光波导的色散方程很困难求解时,单纯形方法对于分析非线性光波导的传输特性简便而且有效。     

Equivalent Resonant Cavity Model of Arbitrary Periodic Guided-Wave Structures and Its Application to Finite-Difference Frequency-Domain Algorithm

An equivalent resonant cavity model is proposed and developed for efficiently and accurately extracting the complex propagation constant of any arbitrary bounded and unbounded periodic guided-wave structures, which is known as a difficult eigenvalue problem with respect to a deterministic or S-parameter-based field solver. In this study, this problem is formulated as a standard eigenvalue one, which is made possible by effectively translating the transmission distance-related attenuation part of complex propagation constant into a time-dependent damping factor. This allows the development of an equivalent resonant cavity model to substitute or replace the periodic guided-wave model, leading to a complex frequency simulation model. As a result, the simulation time and storage requirement are then reduced significantly with this complex frequency approach. A finite-difference frequency-domain algorithm combined with this model is used to demonstrate the concept, and the properties of arbitrary complex closed/open periodic guided-wave structures are rigorously investigated. The proposed algorithm has been validated by both simulations and experiments     

Transmission Characteristics of Curved Dielectric Waveguides with Arbitrarily Transverse Profiles

The transmission characteristics of curved dielectric waveguide are analyzed with a method, which combines the staircase approximation with the edge element analysis and mode matching procedure. In each stair the uniform waveguide is treated with edge element method. Then the transmission property of the whole curved guiding structure is calculated with multimode network methods. The effectiveness of the present method is justified by the results given in the literature. It is believed that this approach can be applied to a variety of curved dielectric waveguides with arbitrary transverse profiles.     

A Generalized Two-Dimensional Coupled-Mode Analysis of Curved and Chirped Periodic Structures in Open Dielectric Waveguides

A generalized two-dimensional coupled mode analysis of curved and chirped quasi-periodic structures in planar dielectric waveguides has been formulated. This analysis can be used to design curved and chirped quasi-periodic stuctures for obtaining phase matched interaction between two specific guided-wave beams. Alternatively, it can be used to calculate the amplitude and the phase of the diffracted guided-wave beam for a given quasi-periodic structure and for a specific incident beam, including the effect of the phase mismatch. The numerical example of linear chirped grating lenses with F= 10, f= 20 mm, Lambda/sub min/ = 2mu m, Lambda/sub max/ = 4.1mu m, and grating grooved length= 65mu m is presented.     

色散金属的时域有限差分方法

表面等离子体激元具有使光场局域化和局域电磁场增强等特性,在纳米光子学和微观检测等诸多领域显示出广泛的应用潜力.时域有限差分（FDTD）数值计算方法能仿真激光与亚波长金属微结构相互作用的表面等离子体效应.金属具有色散性质,其相对介电常数模型有Drude模型和Lorentzs模型及它们相结合的Drude-Lorentzs模型,能拟合金属在可见光和近红外部分或全部波段的色散特性.FDTD数值计算要采用增加辅助变量和相应的辅助差分方程的方法使FDTD迭代计算稳定.