Review of numerical and approximate methods for the modal analysis of general optical dielectric waveguides

AbstactAbstact This paper reviews numerical and approximate methods for the modal analysis of general optical dielectric waveguides with emphasis on recent developments. Six groups of methods are reviewed, covering (1) the finite-element method, (2) the finite-difference method, (3) the integral-equation method, (4) methods based on series expansion, (5) approximate methods based on separation of variables, and (6) methods that do not fit into the above groups, ranging from the specialized ones for analysing restricted classes of waveguides to the most general ones for analysing inhomogeneous, arbitrarily-shaped, anisotropic waveguides. Some suggestions with regard to the selection of methods for particular applications are given.     

小尺寸低折射率差硅基二氧化硅阵列波导光栅

随着AWG型器件在光通信系统中的大规模应用,对低成本AWG芯片的需求越来越多。在各种降成本方案中,减小AWG芯片的尺寸是最有效的方法之一。本文介绍了一种新型小尺寸低折射率差硅基二氧化硅阵列波导光栅（AWG）的设计。在该AWG中,输入波导/输出波导与平板波导连接的部分制作成两侧为空气槽的高折射率差波导,所以在与输出平板波导连接处的相邻输出波导间距较小,这样可以在设计上缩短平板波导的长度、减少阵列波导的数量,实现较小的AWG芯片尺寸。该AWG的其它部分,如输入/输出波导与光纤耦合的部分、阵列波导光栅等均采用常规的低折射率波导工艺,所以就同时具有与常规的低折射率波导AWG相同的优点：如低耦合损耗、较好的串扰以及光学特性等。根据这个原理,设计了一种40通道100 GHz频率间隔的低折射率差硅基二氧化硅AWG,其芯片尺寸只有23.88 mm?10.5 mm,是传统相同材料制作的AWG尺寸的1/6。     

小尺寸低折射率差硅基二氧化硅阵列波导光栅

随着阵列波导光栅(Arrayed Waveguide Grating,AWG)型器件在光通信系统中的大规模应用,对低成本AWG芯片的需求越来越多.在各种降成本方案中,减小AWG芯片的尺寸是最有效的方法之一.本文介绍了一种新型小尺寸低折射率差硅基二氧化硅AWG的设计.在该AWG中,输入波导/输出波导与平板波导连接的部分制...     

Dielectric waveguide model for guided surface polaritons

Although surface polariton modes supported by finite-width interfaces can guide electromagnetic energy in three dimensions, we demonstrate for the first time to our knowledge that such modes can be modeled by the solutions of two-dimensional dielectric slab waveguides. An approximate model is derived by a ray-optics interpretation that is consistent with previous investigations of the Fresnel relations for surface polariton reflection. This model is compared with modal solutions for metal stripe waveguides obtained by full vectorial magnetic-field finite-difference methods. The field-symmetric modes of such waveguides are shown to be in agreement with the normalized dispersion relationship for analogous TE modes of dielectric slab waveguides. Lateral confinement is investigated by comparison of power-density profiles, and implications for the diffraction limit of guided polariton modes are discussed.     

Design and modeling of microwave photonic devices

Different types of finite element methods (FEMs) for microwave and optical waveguides are reviewed and are utilized for modeling of a traveling-wave (TW) optical modulator, as one of the typical microwave photonic devices. Using the quasi-TEM and the full-wave vector FEM solvers for microwave waveguides and the scalar FEM solver for optical waveguides, the behaviour of a TW Z-cut Ti:LiNbO3 Mach–Zehnder optical modulator with a ridge structure is investigated.     

Determination of the attenuation of planar waveguides by means of detecting scattered light

Due to the variety of waveguides in planar structures, the measurements of attenuation are characterized by a considerable variety of applied methods, developed for given type of waveguides. The method of measuring scattered light is, therefore, of much importance in the case of waveguides with a rather high attenuation, because it is an exceptionally fast and simple method, which is doubtlessly the effect of the development of numerical detection systems. The paper presents the process of measurements basing on scattered light, combined with an analysis of its application, as well exemplary results concerning the planar structures of waveguides achieved by means of ion exchange on soda-lime glass.     

梯形截面多量子阱脊形波导模式特性

本文根据多量子阱双折射率的性质,运用有效折射率法和WKB法对具有梯形截面多量子阱脊形波导的模式特性作了分析,导出了E_mn^x模和E_mn^y模的本征值方程.     

Circular arc plasmonic waveguide couplers between two-dimensional dielectric slab waveguides and plasmonic waveguides

We investigate the properties of arc plasmonic waveguide coupler between two-dimensional dielectric slab waveguides and plasmonic waveguides with two-dimensional finite difference time domain methods. The simulation results show that transmission efficiency between high index dielectric slab waveguides with width 300 nm and silver-air-silver waveguides with width 40 nm connected by the coupler can reach to 90.4% at optical communication wavelength. And, by optimizing the shapes near the ends of the coupler, the transmission efficiency can be improved to 98.4%.     

用极坐标下的广角光束传播法计算分析弯曲波导

采用了极坐标下的广角BPM(Beam Propagation Method)对弯曲波导进行了计算模拟,并与极坐标下近轴BPM方法进行了比较,取得很好的结果.     

Fabrication and Determination of Refractive Index Profile of the Planar Waveguides by Wedge Technique

Several planar waveguides have been fabricated. The waveguides have been polished for determination of their refractiveindex profiles (RIP) by wedge method. The RIP determined by inserting the sample in a Mach-Zehnder interferometer andapplying fringe analysis methods.     

Coordinate stretching for finite difference optical waveguide mode solvers

Numerical methods are necessary to calculate propagating modes in optical waveguides. The finite difference method is widely used because it is applicable to waveguides with arbitrary refractive index profiles and it is easy to implement. To improve the efficiency and to reduce the size of the resulting large sparse matrix, the finite difference method is often used with a variable grid size strategy. This is related to the technique of coordinate stretching. In this paper, we develop a technique for optimizing the coordinate stretching function based on discrete reflection coefficients. We demonstrate our method using a scalar model which is valid for weakly-guided optical waveguides.     

Surface plasmon polariton waveguides with subwavelength confinement

Surface plasmon polaritons(SPPs) are evanescent waves propagating along metal-dielectric interfaces, which provide an effective way to realize optical wave guiding with subwavelength confinement. Metallic nanostructures supporting SPPs,that is, plasmonic waveguides, are considered as required components to construct nanophotonic devices and circuits with a high degree of miniaturization and integration. In this paper, various types of plasmonic waveguides operating in the visible, infrared, and terahertz regions are reviewed, and the status of the research on their fundamentals, fabrications,and applications is provided as well. First, we discuss the mechanisms of SPPs beyond the diffraction limit, and their launching methods. Then, the characteristics of SPPs on various plasmonic waveguides are reviewed, including top-down and bottom-up fabricated types. Considering applications, certain prototypes of plasmonic devices and circuits constructed by plasmonic waveguides for bio/chemo sensing, router, and light modulation are demonstrated. Finally, a summary and future outlook of plasmonic waveguides are given.     

在LiNbO3∶Fe晶体中写入与存储圆形和环形波导

在光生伏打、自散焦光折变介质LiNbO₃∶Fe晶体中写入并存储了圆形与环形波导，并观察到了环形波导之间的相互作用.这种写入波导的方法和技术具有良好的应用前景. 关键词：     

Modal analysis of rib waveguide through finite element and mode matching methods

Two mode solvers based on the finite element and the mode matching methods are compared by way of analyzing rib waveguides. Differences between the normalized propagation constants provided by the two methods are always less than 10^–4 which is at least about one order of magnitude smaller than previously reported values. Results for lossy waveguides and field comparison are also presented.     

有增益及损耗的平板波导导模的精确微扰分析

给出求含有增益层与损耗层的突变与渐变折射率剖面多层平板波导导模的微扰与解析计算公式。举例讨论了导模模式的增益（或损耗）与结构参数和偏振的关系，本文方法较求解复本征值的打靶法等简便且节省机时，对于（半导体激光器与半导体激光放大器等）实际遇到的波导结构能给出精确数值结果，并可用以分析材料的增益系数或损耗对ＴＥ和ＴＭ模式及其增益的影响等问题。     

Complex modes and instability of full-vectorial beam propagation methods

Full-vectorial beam propagation methods (FVBPMs) are widely used to model light waves propagating in high-index-contrast optical waveguides. We show that the paraxial FVBPM and wide-angle FVBPMs based on diagonal Padé approximants are analytically unstable for waveguides with complex modes. The instability cannot be removed by enlarging the computational domain, increasing the numerical resolution, or using perfectly matched layers, because the complex modes are highly confined around the waveguide core.     

(Al)GaAs/AlGaAs周期光波导中的等幅基模

本文应用周期介质光波导的模场分布函数和特征方程分析了(Al)GaAs/AlGaAs周期光波导中结构参量及介质折射率对模场分布形状的影响,研究了波导中形成等幅基模的条件,讨论了相应参量的优化选择。     

Analysis of curved bends in arbitrary optical devices using cylindrical coordinates

An extension of the beam propagation algorithm based on the method of lines (MoL–BPM) is proposed and substantiated for analysis of curved bends–constituent parts of complicated optical devices, connecting waveguides with different orientation. Cylindrical coordinates are introduced. The formulas are compatible with those in Cartesian coordinates for analysis of straight waveguides. So, in combination concatenations of curved bends and straight waveguides can be examined in a uniform way. For the purpose of analysis in cylindrical coordinates a suitable set of wave equations without any approximation and valid for a general hybrid case is derived. To prove the accuracy of the MoL–BPM in cylindrical coordinates applying the derived formulas, the curvature loss of a rib waveguide was computed and compared with other methods showing very good agreement. As an application of the method two straight waveguides are connected by a curved bend and the power flow is determined.     

耦合波导管本征值的讨论

本文对文献提出一些不同的见解,对联系边界条件有另外的提法,在处理方法上亦有不同。本文认为耦合槽可以分为浅槽和深槽两种形式,首先对槽口的电场作了近似估计,然后用格林张量函数求出矩形和圆形波导耦合时的电磁场,再用边界条件得出本征方程;对于本征方程,认为可以用两个电路的导纳相等来理解。本文亦对耦合波导管的传输常数和原有波导管传输常数加以讨论,最后再对某些应用上的问题加以简单的讨论。     

降低AWG插入损耗和串扰设计新方法

在AWG器件的设计中引入了抛物线型的楔形波导结构,根据过渡区理论优化了引入的抛物线型楔形结构的形状和尺寸.采用抛物线型楔形结构代替直线型楔形结构,AWG的插入损耗降低了2 dB左右.在优化参数时使输出/输入波导间距与阵列波导间距取不同的值,并使输出/输入波导间距适当增大,而阵列波导间距取较小值,这样使得串扰降至－30 dB以下且插入损耗保持在低水平.运用光束传播方法给出器件的输出光谱并证实了理论上预想的结果.