用基于磁场的改进型有限差分法分析光波导的全矢量本征模

提出一种改进的有限差分法,用以求解全矢量磁场波方程,分析光波导承载的全矢量本征模.离散交叉项时,采用与波导结构无关的六点差分格式,考虑磁场分量的导数在芯包分界处的不连续性,比传统四点差分格式有更高的计算精度.分析阶跃型光纤、矩形和脊形光波导的全矢量本征模问题,给出全矢量基模的磁场分布及其归一化传播常数,揭示全矢量本征模的混合特性,所得结果与解析法、高精度模横向谐振法的结果吻合,验证了方法的收敛性与计算精度.     

基于3D-VTGM-SBPM平行定向耦合器模拟研究

提出基于变量变换伽辽金法的三维半矢量束传播法(3D-VTGM-SBPM),可直接应用于三维光波导器件的光波传输模拟.采用适当的变量变换,将三维半矢量BPM基本方程归结为一阶常微分方程组,避免了非物理反射且能反映模场的偏振特性,成功的分析了基于脊形光波导的平行定向耦合器的光波传输特性.     

无源光器件的传播模场分析

以波导结构的单向耦合器为例，将复坐标变量完全匹配层应用于光器件的模场分析，采用有限差分方法构造出模场的本征方程，通过数值求解得到器件的传播模场和等效折射率。结果表明等效折射率随间距变化而变化，间距越大，等效折射率越趋向于单根光波导的值，为准确分析无源光器件内部模场分布打下了基础。     

聚合物脊形光波导TM模色散特性的偏振修正

有机聚合物脊形光波导的色散特性对聚合物光子学器件性能具有重要影响.本文利用标量变分理论计算脊形光波导的有效折射率,其用到的近似光场分布运用变分有效折射率法获得.考虑折射率分布的横向变化,基于导模满足的矢量波动方程,利用微扰法对标量变分理论所得有效折射率进行偏振修正,求得精度更高的色散特性.对聚合物多模脊形光波导基模和高阶模的色散特性进行分析,研究了波导结构参数对色散特性的影响,分析了单模波导TM、TE基模的偏振色散特性.研究结果表明,运用本征方程分析TM模的色散特性误差大,必须加以修正;而对于TE模,其误差相对较小.     

基于全矢量模式匹配法的三维弯曲波导本征模式计算

采用精确、严格的全矢量模式匹配法，计算了三维脊型弯曲波导和条形弯曲波导的本征模式，分析了模式折射率和辐射损耗随弯曲半径的变化关系.计算结果与已报道的有限差分法的结果符合很好.对文献中已报道但没有深入分析的现象给出了合理的解释.半径为50和12 μm的条形波导的计算结果表明：当波导的弯曲半径减小时，发生在分界面处的TE-TM模耦合会显著增强，这将导致弯曲波导中的模式不再是传统意义上的准TE模和准TM模，而是混合模.随着半径的减小，混合模的横向分量之间的差异会减小，当两个横向分量达到近似相等的强度时，波导的偏振相关性将会大大减小. 关键词： 导波光学 全矢量模式匹配法 微环谐振腔 光波导理论     

星形光波导耦合器的耦合特性分析

根据TE0模光波导的本征场分布、瑞利索末菲标量衍射积分公式和激励源与光波导耦合的匹配效率公式,给出光波导端面衍射和耦合的归一化发射系数和接收系数计算公式,推导出光波导端面非接触耦合的耦合效率计算公式。光波导模场分布采用高斯函数近似表达,给出简洁的计算光波导端面非接触耦合的耦合效率函数表达式。最后,基于星形光波导耦合器结构参量的特点,将累加运算采用积分运算近似表达,给出星形光波导耦合器接收光波导总的接收效率与耦合器基本参量的关系,阐明了星形光波导耦合器的耦合特性。     

InGaAs/InAlAs多量子阱脊形波导及定向耦合器光波特性准矢量分析

提出了一种基于级数展开的三维准矢量束传播法(SE-QV-BPM)用以分析由InGaAs/InAlAs多量子阱构成的脊形光波导及定向耦合器.结果表明，刻蚀深度相同时，TM模比TE模在水平方向限制强，且TM模的模场在波导角上出现畸变；波导间距相同时，定向耦合器TM波的耦合长度大于TE波的耦合长度，对偏振态敏感.分析获得了浅/深刻脊形光波导承载的准矢量TE/TM基模、定向耦合器承载的TE/TM偶/奇模的模场分布及其有效折射率，模拟了光场在定向耦合器中的传输演变情况.另外，SE-QV-BPM导出矩阵小，计算效率高 关键词： 级数展开 准矢量束传播法 多量子阱 InGaAs/InAlAs     

空间交叉波导耦合特性分析

由两根在空间呈X型放置的光波导组成的空间交叉波导结构是构成垂直耦合光分束器、垂直耦合光滤波器、垂直耦合光开关和垂直耦合上/下复用器等三维集成光学器件的基本结构单元.提出用一种等效模场匹配法分析空间交叉波导耦合特性,将矩形波导的场分布看成是对圆对称光纤场分布的微扰,解决了对角区场分布的表达,从而计算空间交叉波导的耦合长度,并用三维全矢量光束传输法验证了分析结果.将两种方法所得的空间交叉波导耦合长度加以比较,最大误差为1.2%,平均误差为0.9%.结果表明该等效模场匹配法具有精度高、运算速度快等优点,为基于空间交叉波导的三维集成光学器件的设计和分析提供理论基础.     

左手介质椭圆光波导基模传播特性

在椭圆柱坐标系中,采用分离变量方法,得出了左手介质椭圆光波导本征方程的近似解,通过数值计算,分析了椭圆波导偏心率、左手介质的电容率、磁导率对椭圆光波导基模传播特性的影响,并将左介质光波导与右手介质光波导基模特性进行对比,得出左手介质光波导的基模特性与右手介质光波导基模特性差别不大的结论.     

矩形光波导E_(00)~y模衍射特性分析

基于Marcatili近似理论,给出了一种矩形光波导Ey00模模场的近似表达,根据平面波角谱理论,推导出了矩形光波导Ey00模衍射场的空间频谱表达式,探讨了其x轴方向上的空间频谱分布特性,分析了矩形光波导Ey00模在x,y轴方向上的光传输因子M2,并采用方形桶桶中功率对矩形波导Ey00模空间频率半宽度进行数值分析,得到了由方形桶桶中功率定义的矩形光波导Ey00模空间频率半宽度随归一化频率变化的关系曲线。     

Full-vectorial analysis of optical waveguides by the finite difference method based on polynomial interpolation

Based on the polynomial interpolation, a new finite difference (FD) method in solving the full-vectorial guided-modes for step-index optical waveguides is proposed. The discontinuities of the normal components of the electric field across abrupt dielectric interfaces are considered in the absence of the limitations of scalar and semivectorial approximation, and the present FD scheme can be applied to both uniform and non-uniform mesh grids. The modal propagation constants and field distributions for buried rectangular waveguides and optical rib waveguides are presented. The hybrid nature of the vectorial modes is demonstrated and the singular behaviours of the minor field components in the corners are observed. Moreover, solutions are in good agreement with those published early, which tests the validity of the present approach.     

Planar waveguide analysis by the spectral index method. I: Rib and uniformly buried waveguides

The scope of the spectral index method for solving general planar waveguiding problems is analysed by first showing how simple it is to set up a closed-form transcendental equation whose solution is very accurate; the solution is so fast that the method can be used as a subroutine, making it possible to solve many two-dimensional problems fully, even for coupled rib waveguides, without using effective index approximations. The method is then extended to the uniformly buried waveguide of rectangular cross-section, and the corresponding coupler, thereby unifying the effective index, transverse resonance and spectral index methods for the first time, and giving an asymptotic expression for the coupling length without using overlap integrals. Finally, sample numerical results and optical field profiles are given for the rib waveguide and rib waveguide coupler.     

梯形截面脊波导的特性分析

提出了用有效折射率法结合转移矩阵理论对梯形截面脊波导进行数值分析的新方法。对梯形截面脊波导中模式传播常数和模式间耦合系数的分析表明,梯形截面脊波导与稍宽的矩形截面脊波导行为相同。这一结论有利于简化梯形截面脊波导的设计,提高实际器件的精度。     

Solutions of the full- and quasi-vector wave equations based on H-field for optical waveguides by using mapped Galerkin method

The mapped Galerkin method in solving the full-vector and quasi-vector wave equations in terms of transverse magnetic fields (H-formulation) for optical waveguides with step-index profiles is described. By transforming the whole x-y space onto a unit square and using two-dimensional Fourier series expansion, the modal distributions and propagation constants for optical waveguides are obtained in the absence of boundary truncation. Results for step-index circular fiber, buried rectangular waveguide, and optical rib waveguide are presented. Solutions are good agreed with exact solutions and numerical results by using vector nonlinear iterative method, Fourier operator transform method, and vector beam propagation method.     

Numerical calculations of modes of optical waveguides with two-dimensional refractive index profiles by a field correction method

Abstact We describe a numerical method devised to calculate the lower-order modes of optical waveguides with two-dimensional transverse index profiles. This method is based on finite-difference approximation of the scalar wave equation and the minimization of the error in the field shape of a mode. The field correction method can be applied to waveguides with large index steps and generates the mode's scalar propagation constant and its field. To test the field correction method, it is applied to a three-layer optical fibre and the results are compared with exact solutions. The error in the calculations of the modal effective indices is found to be of the order of 10^-6. Example mode calculations are given for fused couplers and rib waveguides.     

A Modified full-vectorial finite-difference beam propagation method based on H-fields for optical waveguides with step-index profiles

A modified full-vectorial finite-difference beam propagation method based on H-fields in solving the guided-modes for optical waveguides with step-index profiles is described. The propagation is split into two substeps. In the first substep, the field propagates in the absence of the cross-coupling terms, and then they are evaluated and double used in the second substep. An improved six-point finite-difference scheme is constructed to approximate the cross-coupling terms along the transverse directions. By using the imaginary-distance procedure, the field patterns and the normalized propagation constants of the fundamental modes for a buried rectangular waveguide and rib waveguide are presented, and the hybrid nature of the full-vectorial guided-modes is demonstrated. Solutions are in good agreement with the benchmark results from film mode matching method, which tests the validity and utility of the present method.     

离散谱折射率法分析深刻蚀、单模GaAs/GaAlAs脊形光波导

本文采用离散谱折射率法对深蚀刻、GaAs/GaAlAs多层脊形光波导模式特性进行了具体分析和设计,获得了较大截面、低损耗的单模脊形光波导.利用这种横向具有最大折射率差的深蚀刻脊形光波导不但可以提高多模干涉(MMI)型器件的性能,而且在设计和制作弯曲波导、分支结构时,具有结构紧凑、易于集成等优点.     

Numerical analysis of a rib optical waveguide with trapezoidal cross section

Dispersion relations and field distributions in rib optical waveguides with several sizes of trapezoidal cross sections are investigated by using a new highly accurate numerical method, which is based on the Rayleigh principle and on the least-squares method.     

用平面映射边界条件的伽辽金法分析耦合脊形光波导

用平面射映边界条件的伽辽金法分析耦合脊形光波导的结果表明，耦合脊形光波导的耦合能力随脊高增加而减小，随波导间距增加呈指数衰减。给出了耦合脊形光波导所承载的偶、奇模电场分布，其结果与采用其它方法得出的结果吻合得较好，可以优化波导光电子器件的结构参数。另外，平面映射边界条件避免了非物理反射，待求矩阵小，计算效率高。     

Modelling of rib waveguide bends for sensor applications

Wave propagation through curved bends in integrated optical waveguides is governed by the evanescent field and the radiation loss of the eigenmodes. Since these parameters are influenced by the refractive index of the surrounding medium, circular bends in rib waveguides have been successfully employed as chemical sensors for liquids and gases. In this paper the electromagnetic field, the refractive index and the radiation loss of the eigenmodes are precisely determined by a fully vectorial approach based on the method of lines. An axial discretization and Bessel functions of complex order are employed for the rigorous computation of the evanescent field. The intensity distributions of the first modes in a rib waveguide are presented. The influence of the rib height on the sensitivity of the modal index to the refractive index of the surrounding medium is investigated. The results are useful for the optimization of the sensor design.