Explicit finite difference beam propagation method: application to semiconductor rib waveguide Y-junction analysis

A novel explicit finite difference beam propagation method is developed and applied to the analysis of a strongly guiding semiconductor rib waveguide Y-junction. Its accuracy is confirmed by comparison with reported results. This method is much more efficient than the standard beam propagation method for the rib waveguide analysis.<>     

Full-vectorial finite element beam propagation method withperfectly matched layers for anisotropic optical waveguides

Perfectly matched layer (PML) boundary conditions are incorporated into the full-vectorial beam propagation method (BPM) based on a finite element scheme for the three-dimensional (3-D) anisotropic optical waveguide analysis. In the present approach, edge elements based on linear-tangential and quadratic-normal vector basis functions are used for the transverse field components. To show the validity and usefulness of this approach, numerical examples are shown for Gaussian beam propagation in proton-exchanged LiNbO₃ optical waveguides. Numerical accuracy of the present PML boundary condition is investigated in detail by comparing the results with those of the conventional absorbing boundary condition (ABC)     

Three-dimensional method for simulation of multimode interferencecouplers

A three-dimensional (3-D) method for modeling multimode interference devices based on a finite element formulation is presented as an alternative to models having one-dimensional cross-sections only. The method is tested for couplers with two different strongly confined waveguides structures. The results show that full treatment of two-dimensional cross-section is of special importance for design and simulation of waveguide devices for which the effective index approximation is no longer valid. For deep rib waveguide geometries, excess loss greater than 15 dB can be obtained if the 3-D method is not used in the design of the couplers     

Method for analysing trapezoidal optical waveguides by anequivalent rectangular rib waveguide

The authors present a simple analysis, using first-order perturbation theory, to determine an equivalent rectangular rib optical waveguide that will model the propagation characteristics of a trapezoidal rib optical waveguide. The results obtained from this method show excellent agreement with the results from the more accurate finite element method     

New full-vectorial numerically efficient propagation algorithmbased on the finite element method

A new full-vectorial beam propagation algorithm based on the versatile finite element method, in order to accurately characterize three-dimensional (3-D) optical guided-wave devices, is presented. The computationally efficient formulation is based on the two transverse components of the magnetic field without destroying the sparsity of the matrix equation. The robust perfectly matched layer (PML) boundary condition is incorporated into the formulation so as to effectively absorb the unwanted radiation out of the computational domain. The efficiency and precision of the proposed full-vectorial propagation approach is demonstrated through the analysis of single optical waveguide, directional couplers, and electrooptic modulator     

Analysis of Z-invariant and Z-variantsemiconductor rib waveguides by explicit finite difference beampropagation method with nonuniform mesh configuration

An efficient and simple explicit finite difference beam propagation method (EFD-BPM) incorporating nonuniform mesh is described. The criteria for stability are developed, and it is shown that this algorithm is power conserving when the stability criteria are met. EFD-BPM is applied to the analysis of single and coupled semiconductor rib waveguides and its accuracy is confirmed by comparing the results with the reported results. Nonuniform mesh is found to improve the efficiency of the method significantly for the analysis of weakly guiding waveguide structures. Several coupled rib waveguide structures with curved input and output branching sections are analyzed using both three-dimensional EFD-BPM and two-dimensional finite difference BPM combined with effective index approximation     

Finite element beam propagation method for anisotropic opticalwaveguides

A finite element beam propagation method (BPM) for anisotropic optical waveguides is newly formulated. In order to treat a wide-angle beam propagation, a Pade approximant operator is employed and to avoid nonphysical reflection from computational window edges, a transparent boundary condition is extended to anisotropic materials. To show the validity and usefulness of this approach, the numerical results for an anisotropic planar waveguide and a magnetooptic channel waveguide are presented     

光束传播法中有效折射率参数的确定方法及比较

针对光束传播法(BPM)应用中有效折射率neff如何获得其准确值的问胚.本文给出了3种求解等效折射率的方法,从具有一定应用背景的多模脊形波导求解出发,利用3种方法分别求解了 9个模式的等效折射率,并且将结果进行分析比较,给出了各自的应用范围.     

Three-dimensional beam propagation analysis of nonlinear opticalfibers and optical logic gates

A three-dimensional (3-D) beam propagation method is described for the analysis of nonlinear optical fibers, where the finite element and finite difference methods are, respectively, utilized for discretizing the fiber cross section and the propagation direction. For efficient evaluation of wide-angle beam propagation Pade approximation is applied to the differential operator along the propagation direction. In order to improve the efficiency and accuracy of solutions, isoparametric elements and numerical integration formulae derived by Hammer et al. are introduced. The propagation characteristics of nonlinear optical fibers with linear core and nonlinear cladding are analyzed, and unique features of nonlinear guided-wave propagation are investigated. Furthermore, all-optical logic gates with practical, 3-D geometry consisting of optical fibers and a nonlinear film are proposed, and their operations of Boolean arithmetic are demonstrated     

A wide-angle finite element beam propagation method with perfectlymatched layers for nonlinear optical waveguides

A beam propagation method (BPM) based on the finite element method (FEM) is described for the analysis of both transverse electric (TE) and transverse magnetic (TM) waves propagating in nonlinear optical waveguides. A perfectly matched layer is introduced to avoid spurious reflections from computational window edges. For the wide-angle beam propagation analysis, the Pade approximation is introduced to the differential operator along the propagation direction. In order to improve numerical accuracy and efficiency, a finite element mesh and a reference refractive index are adaptively renewed at each propagation step, and to reduce computational effort for the nonlinear optical waveguide analysis, an iterative algorithm is also introduced. Waveguides with nonlinear self-focusing claddings are analyzed to investigate spatial soliton emission phenomena, and it is confirmed that soliton couplers can be easily constructed     

偏振不灵敏硅基二氧化硅阵列波导光栅设计

以深刻蚀和热氧化工艺为基础,提出了一种新的阵列波导光栅(AWG)制备技术.这一工艺可使AWG中的波导侧向留有一硅层.采用有限元法和有限差分束传播法分别计算了存在这一硅层时的波导应力分布和有效折射率.结果表明由于这一侧向硅层的存在,使AWG中波导在水平和垂直方向的应力趋于一致,AWG的偏振相关波长明显减小.     

Simulation of Tunable Power Multimode Interference Couplers with Deep Rib Structure

The muhimode interference （MMI） couplers, which operate at 1. 55 microns in deep rib InGaAsP/InP waveguide with large lateral confinement and tunable power splitting ratios, are of high interest in integrated optics. The gold contacts are applied on the top of waveguides where tuning is desired and the plasma effect will lead to negative refractive index change. The three-dimensional （3D） finite difference beam propagation method（FD-BPM） is used to model the tunable MMI couplers. The length of a 2 × 2 overlap-MMI is determined by FD-BPM, so the longitudinal position of tuning spots is obtained. The position of gold contacts with two types, the edge-pads or center-pad, are also determined. In our design, the length of MMI is 180 microns. If the width of pads is 50 microns and the refractive index is tuned from 0 to -0. 027, the power ratio is tuned from 50 ： 50 to the maximum 88.5 ： 11.4. For deep rib structure, the effective index（EI） method can not be used to simplify the 3D waveguide to plane waveguide because of its lower precision, and so the direct 3D FD-BPM simulation is necessary for the design of 3D MMI couplers.     

SOI波导弯曲损耗影响因素的分析

采用有效折射率方法EIM(effective index method)和二维束传播算法（2D-BPM）对SOI (silicon-on-insulator）波导弯曲损耗的几种影响因素进行了分析. 通过模拟发现弯曲损耗随弯曲半径的增大、波导宽度的增加及内外脊高比的减小而减小. 同时，改进波导结构，例如在弯曲波导外侧刻槽可以减小SOI脊形波导的弯曲损耗.     

Split-step finite difference analysis of rib waveguides

Presents a new rapid approach to the analysis of strongly guiding and longitudinally varying semiconductor rib waveguide structures. The technique, which is a synthesis of the beam propagation and finite difference methods is Hermitian, second-order accurate and intrinsically stable.<>     

多功能2×2 GaAs/GaAlAs多模干涉型光开关分析

提出了一种基于深刻蚀脊形光波导带模斑转换器的多功能2×2 GaAs/GaAlAs多模干涉型光开关,并用变量变换级数展开法及三维有限差分束传播法对其进行了模拟分析与优化设计.结果表明,通过控制多模波导中央的两段Schottky电极,器件可实现交叉态、直通态及3dB耦合器功能,并有较大的制作容差、较宽的工作带宽,只须一个多模波导,器件结构紧凑.采用深刻蚀脊形光波导能够满足多模干涉型器件的精确自镜像要求,并使输入/输出光波导在单模工作下有较大的横截面,较低的弯曲损耗及较小的耦合串扰.通道末端引入的模斑转换器可方便地与单模光纤连接耦合.     

一种三维有限差分光束传播法及其应用

利用交替追赶有限差分技术处理近轴标量波方程，建立了一种三维有限差分光束传播法。此方法收敛性好，可处理具有较复杂折射率分布的波导结构，并且在计算规则波导时传播方向的计算步长可取得较大。利用这种方法对电光诱导光波导器件和单模光纤的传输特性进行了分析。     

A finite-difference vector beam propagation method forthree-dimensional waveguide structures

A finite-difference vector beam propagation method (FD-VBPM) for three-dimensional waveguide structures is developed. The polarization dependence and coupling of the optical guided-waves in the 3-D structures can be modeled and simulated     

Simulation of three-dimensional optical waveguides by a full-vectorbeam propagation method

Simulations of optical guided waves in three-dimensional waveguide structures by a full vector beam propagation method are described. Two sets of coupled equations governing the propagation of the transverse electric and magnetic fields are derived systematically. Polarization dependence and coupling due to the vectorial nature of the electromagnetic fields are considered in the formulations. The governing equations are solved subsequently by finite-difference schemes. The vector BPM is first assessed for a step-index circular fiber by comparing the numerical results with the exact analytical solutions. The guided modes of a rib waveguide are then investigated in detail. Comparisons among the scalar, semi-vector and full-vector simulations of the rib waveguide are made. Finally polarization rotation of a periodically loaded rib waveguide operated fully based on the vector nature of the electromagnetic waves is modeled and simulated     

Exact polarised rib waveguide analysis

An exact Fourier operator transform method (F-OPT) is presented for finding the polarised mode propagation constants of a rib waveguide with any number of supporting layers and an arbitrary cladding. The implementation is of the order of one hundred times faster than the finite difference method for the same accuracy of the normalised propagation constant