The bidirectional mode expansion method for two-dimensional waveguides: the TM case

The mode expansion propagation method is a modelling technique for a large variety of waveguide components. Until now only the case with TE modes has been reported; we give details on the mode expansion propagation method for TM modes. Instead of one type of overlap integral in the TE case, a TM analysis requires two kinds of overlap integrals. The inclusion of radiation modes in this method is discussed. The modifications in the algorithm to include waveguides with gain or loss structures are also considered.As an example, the method was used for analysing a grating-assisted codirectional coupler. In particular, the radiation loss is calculated and compared with calculations when TE modes, instead of TM modes, propagate through the codirectional coupler. The radiation losses are found to be much higher for TM modes.     

Numerical algorithm for waveguide and leaky modes determination in multilayer optical waveguides

A new algorithm for waveguide and leaky modes spectrum calculation in multilayer planar waveguides is proposed. The method is of high computational efficiency due to the preliminary search for propagation constants approximation. Numerical efficiency of this algorithm is demonstrated for several waveguide structures. Waveguide and leaky modes propagation constants calculated for these structures using proposed method are in good agreement with previously published results.     

Modes of open layered anisotropic waveguides: a numerical method with exponential convergence

A spectral-element type approach to determine the propagation characteristics of the bound modes of an open planar layered anisotropic waveguide is proposed. The main feature is the expansion of the electromagnetic field in each internal layer on different sets of Legendre polynomials. In the two embedding halfspaces, sets of weighted Laguerre polynomials are used. In this way, the method converges with exponential rate with increasing number of basis functions. No transcendental equation has to be solved and even modes that may exhibit coinciding or very close propagation constants are computed with great accuracy. A detailed analysis of the convergence properties of the algorithm is carried out and a way to estimate and control the error on the propagation constants is discussed.     

Fast convergence and higher-order mode calculation of optical waveguides: perturbation method with finite difference algorithm

We present an efficient algorithm for determining mode eigenvalues as well as field distributions of optical waveguides with two-dimensional transverse refractive index profile. The algorithm is devised with the analytical perturbation correction method combined with the finite difference approximation of Helmoltz's equation. The technique is simple and does not involve solving any eigenvalue equation or matrix formalism. The algorithm reduces abruptly the computation time required for the field convergence to mode, and can calculate any higher-order modes without the need of any pre-conditioning the field w.r.t. waveguide geometry, or calculation of previous order modes and/orthogonalization. The analysis can yield precisely both scalar and polarized modes. By applying it to waveguide problems whose solutions are otherwise known, the efficacy of the method has been established.     

Three-dimensional vectorial analysis of waveguide structures with the method of lines

The method of lines (MoL) a special eigenmode algorithm has been proven as an efficient tool for the analysis of waveguide structures in optics and microwaves. The electric and magnetic fields in the cross-section and their derivatives with respect to the cross-section coordinates are discretized with finite differences (FD) while analytic expressions are used in the direction of propagation. The numerical effort for analyzing three-dimensional structures with a two-dimensional discretization can be very high, particularly if vectorial characteristics have to be taken into account. In this paper we introduce a reduction of the eigenmode system to keep the effort moderate. Only a certain number of eigenmodes is determined with the Arnoldi algorithm. We will show then how the electric field distribution of the eigenmodes can be computed from the magnetic field and vice versa. To match the fields at the interfaces we introduce left eigenvectors which are the inverse of the field distributions. The formulas were applied to the analysis of a polarization converter consisting of a periodical perturbation of a waveguide structure. A rotation angle greater than 80° was determined.     

有限磁场中等离子体圆柱波导的传播特性

分析了有耗介质中等离子体圆柱波导在有限外加磁场中的传播特性.重点讨论了波导传播常数随等离子体参数、介质参数和外加磁场的变化.分析结果表明，有限强磁场中的等离子体波导的传播特性比无外磁场或外加磁场为无穷大时具有更强的控制能力. 关键词：     

Computation of higher-order waveguide modes by imaginary-distance beam propagation method

Abstact Yevick and Hermansson presented an efficient numerical method for calculating fundamental modes of optical waveguides. We extend their technique to higher-order eigenmodes. Using a finite-difference beam propagation method, we obtain propagation constants and field profiles for the three lowest-order TE modes in an asymmetric rib waveguide.     

有损金属圆波导中电磁波传输特性的研究

基于电磁模式的色散方程，研究了有损金属圆波导中电磁模式的传输问题.在考虑了损耗层厚度影响的情况下，得到了各模式传输常数的近似解析表达式，此式适用于截止频率附近.通过解析表达式和波导模式色散方程，对衰减常数和相位常数进行了大量数值计算，得到了它们随损耗层厚度、频率以及损耗层电导率的变化规律，两种方法所获得的结果有较好的一致性.研究表明，损耗强度和损耗层厚度的变化会改变波导中电磁模式的色散和简并特性，对于改善高功率回旋行波放大器中注波互作用带宽和模式竞争非常有益. 关键词： 有损圆波导 相位常数 衰减常数 色散方程     

Low-loss surface modes and lossy hybrid modes in metamaterial waveguides

We show that waveguides with a dielectric core and a lossy metamaterial cladding (metamaterial-dielectric guides) can support hybrid ordinary-surface modes previously only known for metal-dielectric waveguides. These hybrid modes are potentially useful for frequency filtering applications as sharp changes in field attenuation occur at tailorable frequencies. Our results also show that the surface modes of a metamaterial-dielectric waveguide with comparable electric and magnetic losses can be less lossy than the surface modes of an analogous metal-dielectric waveguide with electric losses alone. Through a characterization of both slab and cylindrical metamaterial-dielectric guides, we find that the surface modes of the cylindrical guides show promise as candidates for all-optical control of low-intensity pulses.     

基于损耗介质加载波导的回旋行波管放大器的互作用分析

损耗介质波导对提高回旋行波管放大器的稳定性等性能具有积极的作用.本文基于损耗介质波导中工作模式的场表达式,推导出电子回旋脉塞互作用线性理论.通过系统的数值计算发现损耗介质波导与光滑金属圆波导中的工作模式从场型分布和色散关系上都具有一一对应关系;通过Laplace变换,利用互作用线性理论计算工作模式的起振场型和阈值,并研究互作用系统磁场、电流和介质层对放大特性的影响.这些研究成果对促进损耗介质在回旋行波管放大器中的运用和高稳定性回旋行波管放大器的发展具有积极的作用.     

利用超格子模型对布拉格光纤的研究

为了研究布拉格光纤的模式特征和传输特性,提出了超格子模型,利用傅里叶级数表示光纤横向折射率分布,利用平面波展开法分析布拉格光纤的能带结构,基于厄米-主斯函数的局域正交函数展开法,从全矢量耦合波动方程出发,得到关于模式传播常量和电场展开系数的本征方程,从而分析布拉格光纤的模式特征。以高折射率芯布拉格光纤为例,实现了该算法,得到基模与二次模的横向电场分布、基模色散曲线和模式双折射。基模的模式双折射可用于衡量算法的精度,结果表明该算法精度较高。超格子模型不仅可以用于研究高折射率芯布拉格光纤,而且同样可以研究低折射率区域导光的布拉格光纤。     

Numerical modelling of TE and TM modes in lossy nonlinear optical waveguides

The intensity-dependent characteristics of nonlinear TE and TM waves in a thin film bounded by lossy nonlinear media are analysed by the finite-element method. In this approach, the power-dependent complex propagation constants and local complex electromagnetic field distributions of lossy nonlinear TE and TM waves are obtained directly from the given lossy nonlinear waveguides, without any approximations. Numerical results for these modes in a lossy nonlinear waveguiding system with different absorption coefficients are given. It is shown that the complex dispersion relations, for both TE and TM modes, are strongly power dependent.     

Full-vectorial finite-difference beam propagation method based on the modified alternating direction implicit method

A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on $H$ fields. The cross-coupling terms are neglected in the first sub-step, but evaluated and doubly used in the second sub-step. The order of two sub-steps is reversed for each transverse magnetic field component so that the cross-coupling terms are always expressed in implicit form, thus the calculation is very efficient and stable. Moreover, an improved six-point finite-difference scheme with high accuracy independent of specific structures of waveguide is also constructed to approximate the cross-coupling terms along the transverse directions. The imaginary-distance procedure is used to assess the validity and utility of the present method. The field patterns and the normalized propagation constants of the fundamental mode for a buried rectangular waveguide and a rib waveguide are presented. Solutions are in excellent agreement with the benchmark results from the modal transverse resonance method.     

用有效折射率法和有限元法分析多量子阱条形光波导

本文提出了一种快速和精确分析多量子阱(MQW)条形光波导的新算法。它基于有效折射率法和有限元法的结合。首先,由等效的平面波导替换多量子阱条形结构,用有效折射率法从原来问题得到平面波导的折射率分布;然后,用有限元法计算等效结构中E_(mn)~x模和E_(mn)~y模的传播常数和场强分布。文中给出了任意阱数和不同宽度多量子阱的对称结构和不对称结构的结果。     

Bidirectional beam propagation method based on the method of lines for the analysis of photonic band gap structures

The bidirectional beam propagation method based on the method of lines is proposed as an innovative and efficient algorithm to investigate the optical properties of photonic band gap (PBG) structures. A few examples illustrate the application of this technique to the modeling of passive, lossy and active one-dimensional and index confined PBG structures. The algorithm results are validated by comparison with those obtained via the transfer matrix method, the mode-matching method and the finite difference time domain method. With respect to these methods, the present algorithm exhibits accurate results with reduced computer resources.     

Direct computation of higher-order propagation modes using the imaginary-distance beam propagation method

In this paper we present an extension to the standard method of eigenmode-extraction using the imaginary-distance beam propagation method. We show that it is possible to directly extract higher-order propagation modes of arbitrary shaped waveguide structures by propagating the field along the imaginary axis when the parameters are chosen in an appropriate manner. This method requires an assumption of the propagation constant of the eigenmode. In many cases this value can be determined using fast approximate techniques like the effective index method. Additionally, the approximate mode shape may be introduced as a starting condition and can further accelerate the extraction of the eigenmode. The overall number of propagation steps needed to extract multiple eigenmodes is then significantly smaller than in the case when extracting the modes sequentially with the former method.     

有损耗波导中非线性TE波的数值模拟

本文发展了一种以有限元技术为基础的数值方法,用它分析有损耗波导中的非线性TE模。在这种方法中,非线性有损耗波导中TE波与功率有关的复传播常数和局城电场分布,可从这种波导直接得到,没有任何近似。作为这种方法的应用,计算了非线性有损耗波导系统中TE0模的功率色散关系和电场分布。     

Investigation of the guided modes in anisotropic diffused slab waveguide with embedded metal layer

Abstract

The optical characteristics of the TE and TM guided modes of a multilayer anisotropic two-dimensional waveguide are investigated by using the field component transformation matrix, and also taking into account the substrate intrinsic dispersion. The embedded thin metal layer effects on the propagation constant for both lossless approximated and exact solutions are presented. The lossless approach is accurate enough for the TE waves, but it is not for the TM ones, which exhibit changes of about 10^?6 for the equivalent index. The TM modes also present attenuation constant changes between the lossy and weakly-lossy solutions of the order of 9 dB/cm. Several complex field component mappings are drawn, and the surface plasma waves are also examined.     

Spatial structure of the coherence parameter of the sound field in an irregular arctic waveguide

Results of numerical simulation of the total and coherent sound fields and the coherence parameter for a multimode acoustic signal excited by a monochromatic sound source and propagating in an irregular arctic waveguide are presented. Expressions used as the basis for the algorithm of the sound field calculation by the method of coupled normal modes are given. Both regular and stochastic sound scattering by horizontal inhomogeneities of the bottom, water medium, and ice cover are taken into account. It is found that, in the course of sound propagation in an arctic waveguide, an anomalous variation of the energy coherence parameter of the sound field as a function of distance is observed. This variation manifests itself in the form of local peaks of the field coherence parameter. This fact should be taken into account in both the measurements of the ice cover characteristics by acoustic methods and the evaluation of the efficiency of the operation of receiving arrays.