A full-vectorial beam propagation method for anisotropic waveguides

An extension of the full-vectorial beam propagation method to anisotropic media is presented. Optical waveguides made of anisotropic materials can be modeled and simulated. The polarization dependence and coupling due to both the material and the geometric effects are considered     

A finite element method using ring element with rectangular cross-section to numerically analyze the circular symmetric electromagnetic field

In the numerical analysis of electromagnetic field with circular symmetry, the method of analysis by ring element with rectangular cross-section has more advantages than others. The element characteristic equations (element describing matrices) for this kind of elements in relation to Laplace’s, Poisson’s and Helmholtz’s equations are derived. Using this element, the field structure of cylindrical capacitor, the capacitance and quality factor at the end of loaded coaxial cavity are successfully analyzed.     

Improved full-vectorial beam propagation method with high accuracy for arbitrary optical waveguides

An improved finite-difference (FD) full-vectorial beam propagation method is introduced for arbitrary optical waveguides with a dramatic improvement in accuracy. This method is developed based on the generalized Douglas scheme and a novel FD formula for the cross-coupling terms which, expressed in explicit form, is independent of specific types of waveguides. The present method is demonstrated for a strongly guiding rib waveguide.     

有限元光束传输法分析锥形线性波导

文章介绍了有限元光束传输法(FE BPM)和完美匹配层法的结合,并用该法分析了不同折射率比和仰角的锥形线性波导,说明了这种方法的有效性和实用性.     

A finite element beam propagation method for strongly guiding andlongitudinally varying optical waveguides

A unified finite element beam propagation method is described for both TE and TM waves propagating in strongly guiding and longitudinally varying optical waveguides with magnetooptic materials. In order to avoid nonphysical reflections from the computational window edges, the transparent boundary condition is introduced for both polarizations. In order to show the validity and usefulness of this approach, numerical examples are presented for a directional coupler composed of two parallel identical waveguides, an S-bend, a Y-branching optical isolator, and a 4-ports optical circulator. The present algorithm is, to our knowledge, the first beam propagation method for modeling nonreciprocal magnetooptic components     

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)     

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 collocation-Galerkin finite element model of cardiac actionpotential propagation

A new computational method was developed for modeling the effects of the geometric complexity, nonuniform muscle fiber orientation, and material inhomogeneity of the ventricular wall on cardiac impulse propagation. The method was used to solve a modification to the FitzHugh-Nagumo system of equations. The geometry, local muscle fiber orientation, and material parameters of the domain were defined using linear Lagrange or cubic Hermite finite element interpolation. Spatial variations of time-dependent excitation and recovery variables were approximated using cubic Hermite finite element interpolation, and the governing finite element equations were assembled using the collocation method. To overcome the deficiencies of conventional collocation methods on irregular domains, Galerkin equations for the no-flux boundary conditions were used instead of collocation equations for the boundary degrees-of-freedom. The resulting system was evolved using an adaptive Runge-Kutta method. Converged two-dimensional simulations of normal propagation showed that this method requires less CPU time than a traditional finite difference discretization. The model also reproduced several other physiologic phenomena known to be important in arrhythmogenesis including: Wenckebach periodicity, slowed propagation and unidirectional block due to wavefront curvature, reentry around a fixed obstacle, and spiral wave reentry. In a new result, the authors observed wavespeed variations and block due to nonuniform muscle fiber orientation. The findings suggest that the finite element method is suitable for studying normal and pathological cardiac activation and has significant advantages over existing techniques     

An efficient GPU acceleration format for finite element analysis

This paper proposes a new Graphics Processing Unit （GPU）-accelerated storage format to speed up Sparse Matrix Vector Products （SMVPs） for Finite Element Method （FEM） analysis of electromagnetic problems. A new format called Modified Compile Time Optimization （MCTO） format is used to reduce much execution time and design for hastening the iterative solution of FEM equations especially when rows have uneven lengths. The MCTO-applied FEM is about 10 times faster than conventional FEM on a CPU, and faster than other row-major ordering formats on a GPU. Numerical results show that the proposed GPU-accelerated storage format turns out to be an excellent accelerator.     

Explicit finite difference vectorial beam propagation method

A vectorial beam propagation method (VBPM) is formulated and implemented using the explicit finite difference (EFD) scheme. The accuracy of semivectorial EFD-BPM, where the polarisation coupling is ignored but polarisation dependence is included, is found to be as good as that of full-vectorial EFD-BPM.<>     

An efficient scalar finite element formulation for nonlinearoptical channel waveguides

A self-consistent numerical approach based on the scalar finite element method is described for the analysis of both TE-like and TM-like nonlinear guided waves in optical channel waveguides. In order to improve the convergence and accuracy of solutions, isoparametric elements and numerical integration formulae derived by Hammer et al. are introduced. Numerical results are presented for nonlinear elliptical core optical fibers, and it is confirmed that in this approach, highly accurate solutions can be obtained with small scale computation. Furthermore, graded-index nonlinear optical channel waveguides are also analyzed, and the influence of refractive-index profiles on propagation characteristics of the nonlinear guided waves is investigated     

A modified finite element method for analysis of finite periodicstructures

A modified finite element method with new solving algorithm is proposed to analyze electromagnetic problems of finite periodic structures. Dielectric-loaded parallel-plate waveguides with rectangular and triangular dielectric gratings are tackled as an example of the present approach. Numerical results are checked by the self-convergence test and by comparing with those obtained by other methods. Finally, the dependence of the scattering parameters on the frequency, the period number, and the grating height is analyzed and compared     

An assessment of finite difference beam propagation method

A finite-difference beam propagation method (FD-BPM) is outlined and assessed in comparison with a conventional beam propagation method (FFT-BPM) which uses fast Fourier transformation. In the comparative study three straight waveguides with different index profiles that are frequently encountered in integrated optics are utilized. Using both methods normalized effective index values of the eigenmodes of these waveguides are calculated and compared with the exact values obtained from analytical expressions. As a further accuracy criterion, the power loss due to numerical errors when an eigenmode of a waveguide is excited is evaluated. Based on this comparison the accuracy, computational efficiency, and stability of the FD-BPM are assessed     

Finite element/finite difference propagation algorithm for integrated optical device

A propagation algorithm based on finite elements and a finite difference discretisation of the scalar wave equation is investigated as an alternative to the beam propagation method. The new approach overcomes the assumption of low contrast media in the BPM and allows the propagation of arbitrary input fields in strongly guiding structures.<>     

Optimization of planar devices by the finite element method

The finite-element method is an efficient and flexible way of computing the scattering parameters of N-port planar devices (microstrip, stripline, rectangular waveguide, etc.). In addition, it can provide, at little extra cost, the sensitivity of scattering parameters to changes in the shape of the device. such information can lead to a faster automatic optimization of the shape. This approach has been implemented with high-order, triangular finite elements and the Broyden-Fletcher-Goldfarb-Shanno optimization scheme. Sensitivities were computed for an empty parallel-plate waveguide and for a rectangular waveguide containing a dielectric slab. The agreement with analytical solutions was excellent. The method was used to determine the optimum shape of a microstrip 3-dB hybrid and was found to require far fewer analyses than a previous technique     

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     

Study of electromagnetic wave propagation through dielectric slab doped randomly with thin metallic wires using finite element method

A new numerical simulation method using the finite element methodology (FEM) is presented to study electromagnetic propagation through a dielectric material slab doped randomly with thin and short metallic wires. The FEM approach described in many standard text books and published papers, is appropriately modified to account for the presence of thin and short metallic wires. Using this modified FEM approach, the transmission and reflection characteristics of a material slab (homogeneous dielectric slab doped randomly with thin and short metallic wires) placed in an X-band rectangular waveguide are estimated. The estimated results are compared with the numerical results obtained using the CST microwave studio simulation tool.     

A note on hybrid finite element method for solving scatteringproblems

The hybrid finite-element formulation (HFEM) originated by P. Silvester and M.S. Hsieh (1971) is modified in such a way that it results in a sparse or uniformly banded matrix, rather than a partly full and partly sparse nonuniform matrix. The modification is accomplished by changing the sequence of matrix substitutions and substantially improves the computational efficiency and enhances the capability of the method, which is demonstrated by numerical examples. A comparison with other numerical techniques is presented     

基于有限元法LED散热强化研究

为了解决大功率LED散热问题,构建了包括LED固体部件及外部流体空间的三维数学模型。基于有限元法,应用k-ε模型模拟自然对流换热条件下LED模组散热情况。模拟结果表明,LED模组温度场分布不均,芯片结温较高;受芯片功率密度及位置布设的影响,中心翅片的散热效果差。通过改变散热器结构,设计了两种翅片组合形式,虽然换热面积有所减少,但由于中心翅片的对流换热得到强化,达到了降低结温的效果,提高了散热性能。