Analysis of arbitrary index profile planar optical waveguides and multilayer nonlinear structures: a simple finite difference algorithm

we present here a simple numerical method to obtain the mode effective indices as well as field distributions of modes of any arbitrary profile planar optical waveguide. The method is based on the solutions of scalar and semivectorial Helmoltz’s equation by finite difference algorithm and devised with a field convergence technique. This approach is quite general and can be applied straightforwardly to calculate the guided as well as quasi- or leaky modes of any arbitrary planar structure without the need to solve any eigenvalue equation or any complex matrix formalism. Besides providing the ease of application, the algorithm is particularly useful for waveguides with any graded index profile or with irregular multilayered structure and multilayered waveguides with a localised arbitrary nonlinear film. The performance of our method is verified against typical problems with analytical solutions or having results known otherwise, and is shown to yield results with good accuracy.     

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.     

A new semi-analytical method for the analysis of tapered optical waveguides

Tapered waveguide are used in number of integrated optic devices such as directional couplers, modulators, switches mode converters, etc. Most of the methods analyzing tapered waveguide are numerical in nature. In this paper we present a simple, fast and accurate semi analytical method for z-varying waveguide. However, very few idealized structures can be analyzed directly. The present method consists of separating transverse and longitudinal variation in the wave equation, leading to a differential equation with z-varying coefficients for the field variation along z-axis. For the transverse variation local normal theory is applied. Now this equation is applied to specific taper geometries like linear down taper. Computational are done assuming typical values. We observe variation of power mode profile and mode width. Waveguide loss is also including in the analysis. Finally the analytical simulation results have been verified by the commercial Opti-BPM software.     

Optimized design of a new three branch optical waveguide

A new type of 1 × 3 Y-branch optical waveguide structure with a cone transitional section is introduced in this paper. The symmetrical branch ratio of the 1 × 3 Y branch optical waveguide is obtained by changing the width of this waveguide. The loss and the uniformity are obtained by using the finite difference beam propagation methods, and their values are 0.2 dB and 0.05 dB, respectively. Therefore, it provides some experimental basis for production of three branch optical waveguide.     

Scalar analysis of arbitrarily shaped optical waveguides by full guided mode expansion method and optimized sine method

This paper shows that the full guided mode expansion method and the optimized sine method, with a rather rigorous procedure of determing the dimensions of reference waveguides, provide simple, fast and accurate way for the scalar analysis of arbitrarily shaped optical waveguides. Use of a smaller matrix results in good agreement with previous works.     

有限宽平板波导中的克尔空间孤子及全光器件的设计

利用数值模拟的方法研究了倾斜入射的傍轴光束在有限宽非线性平板波导内的传输规律.研究发现,当不同波长相同束宽的光束各以临界功率倾斜入射波导时,如果倾斜角、入射点都一样,它们将沿大致相同的周期性的Z字形路径传输;如果光束功率进一步增大,相邻反射点之间的间距随传输距离有逐渐变大的趋势,Z字形路径不再有严格的周期性;当功率相当大时,光束将沿波导z方向传输,不再在波导的两个边界之间来回反射.利用倾斜入射光束在波导内的传输路径随功率而变的特点,设计了一个功率开关和一个光时分解复用器. 关键词： 空间光孤子 有限宽非线性平板波导 全光器件     

时域有限差分法的混凝土超声波损伤分析

混凝土质量的好坏直接影响到建筑物的安全性,选用方便实用的方法对其内部裂纹进行检测具有显著意义。该文首先借助时域有限差分法,建立了混凝土声场数学模型。之后对不同内部缺陷尺寸的混凝土模型进行了超声波数值模拟,分别从时域和频域对接收到的超声信号进行了分析。结果发现,当内部存在缺陷时,接收信号时域幅值明显变小,接收信号的幅值与缺陷尺寸大小呈指数关系,且接收信号传播时间与缺陷宽度呈线性关系。最后以初次到达信号的频域能量为特征指标,得出其与混凝土内部开裂缺陷尺寸呈指数关系。该方法为混凝土超声无损检测建立合适的数学模型提供了参考。     

Longitudinal mode competition in semiconductor lasers under optical feedback: Regime of short-external cavity

This paper introduces a theoretical study of longitudinal mode competition in semiconductor lasers subject to optical feedback. The study is based on a model of time-delay multimode rate equations taking into account both symmetric and asymmetric suppressions of modal gain. The model is numerically solved and applied to the case of a short-external cavity. Mode competition is characterized along the feedback-induced period-doubling route to chaos as well as under chaotic dynamics. Contributions of symmetric and asymmetric gain suppressions to both mode dynamics and modal operation under OFB are clarified. The results show that under chaotic dynamics, mode competition induces multimode hopping giving rise to asymmetric multimode output spectra. In regimes of continuous-wave operation, mode competition supports single-mode oscillation, and the side-mode suppression ratio improves with the increase of feedback. In the regime of strong feedback, the lasing mode moves to either long- or short-wavelength side in a seemingly random fashion, which is strongly related to asymmetric gain suppression.     

束变换环孔激光谐振腔的环束场传输差分计算

 通过使用新的坐标变量和光场的表达形式，推导了新坐标系下环束场传输的偏微分方程，给出了相应差分方程的截断误差和稳定性条件，使得环束场传输计算速度大幅提高；使用二阶精度的Crank-Nicolso差分方法对束变换环孔激光谐振腔的环束场传输进行了计算，并与W.D.Murphy和M.L.Bernabe所给M-B积分近似方法的计算结果进行了比较，证实了该方法无论计算速度和精度都优于M-B积分近似方法。     

基于MPI和OpenMP的三维弹性波方程混合并行有限差分算法*

三维弹性波方程有限差分模拟具有大计算量和大内存消耗的特点,在常规计算机上使用传统算法往往无法满足计算要求。该文以高性能计算机集群为平台,基于MPI和OpenMP混合编程技术,构建了一种新型三维弹性波方程并行有限差分算法。该算法基于MPI将总任务分配给多个进程,同时在每个进程中基于OpenMP将子任务分配给多个线程。各个进程具有独立的内存空间,各个线程共享所在进程的内存空间。充液井孔声场的数值模拟结果表明,与基于OpenMP的并行有限差分算法相比,基于MPI和OpenMP的混合并行有限差分算法可以利用计算机集群的多个节点进行并行计算,既极大地提高了计算速度,又有效地降低了单个节点的内存消耗。     

高精度有限差分法模拟Kelvin-Helmholtz不稳定性

 WENO有限差分格式有较高的分辨精度,适合复杂流场的计算,在国际上被广泛采用。本文利用WENO有限差分格式求解2维守恒型欧拉方程,实现了对无粘流体中Kelvin-Helmholtz不稳定性的数值模拟。速度剪切方向采用周期边界条件;扰动增长方向采用嵌边出流边界条件,一个不稳定波长分布64个网格。数值模拟给出的扰动幅值线性增长率与线性稳定性分析给出的结果很好符合,显示了该格式的有效性和精度。数值模拟给出了清晰的密度等值线,表明该方法还具有较好的界面变形捕捉能力。     

Consistency and variations in optical characteristics of four-layer polymeric waveguides

In the present work, four-layer polymeric waveguides have been fabricated and characterized by interchanging the film layer. Using polyvinyl alcohol (PVA) and styrene acrylonitrile (SAN) polymer it has been shown that polymers do not loose their own property in multilayer structure and better efficiency can be achieved in the form of low propagation losses and mode filtration. Due to high contrast of PVA and SAN films, a broad spectrum of refractive index in four-layer structure has been achieved.     

A stable and conservative method for locally adapting the design order of finite difference schemes

A procedure to locally change the order of accuracy of finite difference schemes is developed. The development is based on existing Summation-By-Parts operators and a weak interface treatment. The resulting scheme is proven to be accurate and stable.     

高精度有限差分法模拟Kelvin-Helmholtz不稳定性

WENO有限差分格式有较高的分辨精度,适合复杂流场的计算,在国际上被广泛采用。本文利用WENO有限差分格式求解2维守恒型欧拉方程,实现了对无粘流体中Kelvin-Helmholtz不稳定性的数值模拟。速度剪切方向采用周期边界条件;扰动增长方向采用嵌边出流边界条件,一个不稳定波长分布64个网格。数值模拟给出的扰动幅值线性增长率与线性稳定性分析给出的结果很好符合,显示了该格式的有效性和精度。数值模拟给出了清晰的密度等值线,表明该方法还具有较好的界面变形捕捉能力。     

Computation of effective propagation parameters in the optical domain with a finite difference time domain method

The study of optical scattering by heterogeneous media is a complex topic where homogenization is very helpful and rigorous methods are useful. Finite difference time domain (FDTD) method coupled with Monte Carlo process is used to compute the effective parameters of heterogeneous media. Effective parameters based on the coherent field propagation of a beam in the medium are determined in bidimensional geometry and for both polarizations. It is applied to media composed of small particles embedded in an host medium, for relevant ranges of particle sizes and optical constants for both binder and particles. The results are compared to the Maxwell–Garnett and Bruggeman mixing laws and the Foldy–Twersky and Keller perturbative approximations, leading to the assessment of their validity domain.     

Measurement of the optical transmission modes and losses of the poled guest–host polymer NAEC/PEK-c planar waveguides

The polyetherketone (PEK-c) guest–host polymer planar waveguides doped with (4′-nitro)-3-azo-9-ethyl-carbazole (NAEC) were prepared. The waveguide films were poled by corona-onset poling at elevated temperature (COPET), and the corona poling setup includes a grid voltage making the surface-charge distribution uniform. By using the prism-in coupling method, the dark-line spectrum given by the reflected intensity versus the angle of incidence have been obtained, and the optical transmission losses of mth modes have been measured for the poled polymer waveguides at λ=632.8 nm. The measurement result showed that the optical loss of the fundamental mode is less than 0.7 dB cm⁻¹ for the TE polarization.     

Design and analysis of coplanar waveguide optical modulator using finite element method

An analysis is given on the finite element method (FEM) for calculating the various parameters of optical modulators and a computer program is written to solve the finite element equation. Based on this method, a Mach-Zehnder type electro-optic modulator with coplanar waveguide (CPW) electrode is designed and fabricated. When compared with the Fourier series method, small differences on the 3-dB bandwidth, characteristic impedance and half-wave voltage, etc. are obtained.     

Propagation-mode near-field method for measuring optical waveguides of graded index profile: some considerations on TM-modes

A new set of formulae is developed for profiling refractive index of optical waveguides using the propagation-mode near-field method. Effects of graded-index profile on wave equations for TM-modes are taken into account. Anisotropic waveguides are also studied.     

Mode analysis of realistic optical waveguide structures and microstructured holey fibers by modal field evolution

In this article, we describe a useful technique for calculating modes of practical optical waveguides having two-dimensional arbitrary transverse refractive index profile. The method uses a finite difference platform for evaluating Helmholtz's equation in scalar and semivectorial forms through a field evolution algorithm. The method is straightforward, easy to handle and does not involve any complex analysis or matrix formulation. We tested the accuracy of our analysis approach by applying it on a large number of realistic waveguide problems having known results or results available in the literature. The formulation has facilitated us to study the modal properties, viz., field distribution, birefringence, dispersion and mode effective area, of a variety of practical two-dimensional structures namely, planar structure, coupler, semiconductor optical waveguides, optical fibers and arbitrary profile microstructured fibers which are uniquely important in photonics and guided-wave devices. The algorithm will therefore be very useful in designing and studying any arbitrary-structure waveguides, and to explore new geometry and properties.