Full-vector finite-element beam propagation method for three-dimensional nonlinear optical waveguides

A full-vector finite-element beam propagation method (VFE-BPM) in terms of all the components of slowly varying electric fields is described for the analysis of three-dimensional (3-D) nonlinear optical waveguides. Electric fields obtained with this approach can be directly utilized for evaluating nonlinear refractive index distributions. To eliminate nonphysical, spurious solutions, hybrid edge/nodal elements are introduced. Furthermore, to avoid spurious reflections from the computational window edges, anisotropic perfectly matched layer boundary conditions are implemented, and to reduce computational effort for the nonlinear optical waveguide analysis, an iterative algorithm is also introduced. The effectiveness of the present approach is verified by way of numerical examples: nonlinear directional couplers, spatial soliton emission phenomena, and soliton couplers.     

A Simple Numerical Method for Studying the Propagation Characteristics of Single-Mode Graded-Index Planar Optical Waveguides

A simple numerical method based on the Runge-Kutta method is presented to compute the propagation constant, the modal field, and the cutoff wavelength corresponding to the fundamental TE/sub 0/ and TM/sub 0/ modes of a planar optical waveguide with an arbitrary refractive index profile. The method is much simpler and requires less computational effort than the earlier reported numerical methods. We have also used the technique for an estimation of the effect of the /spl nabla/epsilon term in TM modes.     

Finite element beam propagation method for three-dimensionaloptical waveguide structures

A beam propagation method (BPM) based on the finite element method (FEM) is described for longitudinally varying three-dimensional (3-D) optical waveguides. In order to avoid nonphysical reflections from the computational window edges, the transparent boundary condition is introduced. The present algorithm using the Pade approximation is, to our knowledge, the first wide-angle finite element beam propagation method for 3-D waveguide structures. To show the validity and usefulness of this approach, numerical results are shown for Gaussian-beam excitation of a straight rib waveguide and guided-mode propagation in a Y-branching rib waveguide     

Full-wave analysis of guiding structures using a 2-D array of 3-DTLM nodes

A TLM approach to the full-wave analysis of guided wave structures is introduced. Instead of real pulses as in the conventional TLM method, complex pulses are used. Therefore a nonreciprocal phase shift in the z-direction can be introduced and used to connect the z arms in a 3-D node directly. As a result, the 3-D array of 3-D nodes, normally required in the TLM method to calculate the propagation and attenuation constant, is reduced to only one mesh unit in the z direction (a 2-D array of 3-D nodes). The propagation constant is determined by choosing a value and then calculating the frequency at which this value is valid from the Fourier transform of the impulse response. Losses are found by computing the exponential decay of time harmonic solutions at the eigenfrequencies of the structure     

Three-dimensional finite difference beam propagation algorithms forphotonic devices

Finite difference beam propagation techniques are developed for photonic devices with step-index distributions and arbitrarily large index differences. One technique, the eigenvector expansion method allows large propagation steps along uniform waveguide sections. The second technique, a propagation matrix series expansion method, is particularly suitable for three-dimensional wave propagation simulations. It can easily handle 10⁵ discretization points on personal computers or workstations. The first method employs absorbing boundary conditions while the second utilizes transparent boundary conditions at the edges of the computational windows. The accuracy and applicability of these techniques is demonstrated for several 2-D and 3-D test structures     

Fundamental modes of a nonsymmetric planar metamaterial waveguide

The properties of fundamental (lower) guided wave modes propagating in a nonsymmetric planar metamaterial waveguide are considered. A graphical approach is applied for the analysis of their dispersion characteristics oriented toward the determination of the waveguide’s parameters ensuring the propagation of these waves in the waveguide. It is shown that, a nonsymmetric waveguide, as a symmetric one, can support both forward and backward wave modes.     

Beam propagation analysis for tapered waveguides: taking account ofthe curved phase-front effect in paraxial approximation

A novel equivalent waveguide theory based on the conformal mapping method is employed to investigate the tapered waveguide with curved phase fronts. By using the theory, the curved phase fronts of a tapered waveguide would be transformed into the planar ones of its equivalent straight-liked structure. Therefore, the paraxial beam propagation method can be used to analyze the equivalent structures of tapered waveguides (even for wide-angle tapers). Two kinds of popular tapered waveguides, including the cross-sectional dimension tapering and the constant V-number tapering, are used to analyze by our combination of conformal mapping method and beam propagation method (BPM)     

有耗介质导波结构的高次杂交四边形边缘元分析

本文提出了一种高次杂交四边形边缘元方法。讨论了这种高次杂交边缘元的有限元空间构造，给出了其形函数的显形表达式。这种方法不仅消除了伪解而且能直接求解传播常数，从而无需迭代便能分析有耗介质导波结构的传输特性。对矩形导和条形介质填充波导本征模传播常数的计算表明这种高次杂交边缘元的计算精度比低次杂交边缘元要高出一个量级。     

Full vectorial finite-element-based imaginary distance beampropagation solution of complex modes in optical waveguides

In this paper, we address accurate computation of complex propagation constants and field distributions of different modes, in general, lossless and lossy optical dielectric waveguides. Using the vector finite-element formulation of the beam propagation method combined with the imaginary distance propagation technique, sequence of both the guided and leaky modes can be accurately calculated. To show the versatility and numerical precision of the proposed technique, we compute the modes of three different three-dimensional (3-D) waveguide structures and compare the results against those of other, different, vector formulations. Further, we present the design of a higher order mode filtering device, based on a 3-D leaky mode optical waveguide     

基于厄米-高斯函数法研究1维光子晶体波导

为了对折射率型1维光子晶体缺陷波导中的光传输进行有效数值模拟,采用此类型波导的厄米-高斯函数展开方法进行了研究。首先给出了计算方法的详细理论推导,然后利用该方法计算了偏振态不同、结构参量不同的情况下波导本征模式的色散关系、模场空间分布、能量控制因子及等效折射率。结果表明,1维光子晶体缺陷波导与阶跃平面光波导主要差别在于高阶模式,且可通过调节1维光子晶体的结构参量来有效调控高阶模式的传输。     

A linear-operator formalism for the analysis of inhomogeneousbiisotropic planar waveguides

Using the theory of linear operators, guided electromagnetic wave propagation in inhomogeneous (nonreciprocal) biisotropic planar structures is analyzed in terms of a 2×2 matrix differential operator. Based on the concept of adjoint waveguide, a new biorthogonality relation for the guided hybrid modes is derived. For the special case of reciprocal biisotropic media or chiral media, the linear-operator formalism leads to a self-adjoint problem. As an application example, a general analysis of the radiation modes of a grounded chiroslabguide is also presented     

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     

A very short planar silica spot-size converter using a nonperiodicsegmented waveguide

To reduce the coupling loss of a fiber-to-ridge waveguide connection, a planar silica spot-size converter for a wavelength of 1.55 μm is implemented in the form of a nonperiodic segmented waveguide structure with irregular tapering. A simple single-step lithography process is sufficient for the fabrication of the planar structures. An evolutionary algorithm has been successfully applied for the optimization. The simulated results obtained with a three-dimensional (3-D) finite difference beam propagation method (FD-BPM) program are compared with measurements of implemented couplers, showing very good agreement. A waveguide-to-fiber coupling efficiency improvement exceeding 2 dB per converter is shown. Structures obtained with this approach are very short (~140 μm) and simple to integrate on the same wafer with other planar structures such as phased arrays or ring resonator structures     

Frequency-selective transmission by a leaky parallel-plate-like waveguide

The phenomena of high frequency-selective transmission of a plane wave by a dielectric two-dimensional (2-D) periodic waveguide, comprising a uniform dielectric layer sandwiched by two finite thickness 2-D periodic structures served as the waveguide wall is described. This structure is termed a leaky parallel-plate-like waveguide because the waveguide walls are not perfect reflection mirrors. The scattering characteristics and dispersion relation, including the phase and attenuation constants, of the 2-D periodic waveguide are thoroughly analyzed with the modal transmission-line method and Floquet theory. The extraordinary open stopbands caused by the contra-flow coupling between a leaky parallel-plate-like waveguide and the leaky waves, which are generated by 2-D periodic structures (waveguide walls), are displayed in the form of the Brillouin diagram. The phase-match condition is used to verify the resonant coupling between the incident plane wave and the leaky parallel-plate-like waveguide modes. Specifically, the transmission peak frequencies are accurately predicted.     

Numerical analysis of near-infrared wave propagationcharacteristics in dielectric-coated parallel planar microstructuralwaveguides

In this paper, the properties of electromagnetic (EM) wave propagation in layered planar microstructural waveguides are investigated. Analytical and numerical results are presented on the propagation of a 1-μm EM wave in a parallel planar waveguide. Its walls are made of Au or Si, coated with a thin layer of SiO₂ and separated by a fluid. The propagation characteristics of even and odd TE and TM modes are described as a function of the coating thickness. It is shown that the propagation of TE modes exhibits a sudden shift in power flow distribution from the fluid to the coating when the coating thickness exceeds a critical value. This property may be exploited for micromachined sensor applications. TM modes do not exhibit this behaviour     

基于矢量波函数空间算子理论的波导系统有限元分析

该文介绍了一种能够消除非物理模的波导系统的有限元分析方法,从矢量波函数空间的偏微分算子理论出发,推导出具有简洁而自洽数学形式的完备的电磁波基本方程组,将电场矢量用两个标量函数表示,并用有限元法对这两个标量函数进行数值求解,从而得到了波导系统的有关参数,文中以加载膜片波导和E面矩形波导阶梯为例说明了这一分析及计算过程。     

A mode-preserving perfectly matched layer for optical waveguides

For numerical simulation of wave propagation in optical waveguides, we develop a mode-preserving boundary condition for the popular perfectly matched layer, which truncates the unbounded transverse plane. The method is particularly useful for single-mode longitudinally varying wave-guiding structures and it is easy to use for step-index planar waveguides. With this boundary condition, accurate numerical solutions can be obtained in a much smaller computational window. Numerical results based on the beam propagation method for a tapered waveguide are used to demonstrate the capacity of this boundary condition.     

Modal analysis of a planar waveguide with gain and losses

In this study, we analyze the waveguiding properties of a planar waveguide amplifier in which losses and gain can be present simultaneously. It is found that the subsequent modes comprise both loss and gain modes. Also, the dependence of the gain on the state of polarization turns out to be significant for realistic dielectric structures. For strong losses or gain, the standard transfer matrix approach may become numerically unstable, therefore, a scattering matrices formalism is employed. A semiconductor-like gain profile enables us to study the gain as a function of ω for realistic laser amplifier structures     

Improvements of the two-dimensional FDTD method for the simulationof normal- and superconducting planar waveguides using time seriesanalysis

Time-domain simulation results of two-dimensional (2-D) planar waveguide finite-difference time-domain (FDTD) analysis are normally analyzed using Fourier transform. The introduced method of time series analysis to extract propagation and attenuation constants reduces the desired computation time drastically. Additionally, a nonequidistant discretization together with an adequate excitation technique is used to reduce the number of spatial grid points. Therefore, it is possible to simulate normal- and superconducting planar waveguide structures with very thin conductors and small dimensions, as they are used in MMIC technology. The simulation results are compared with measurements and show good agreement