A hybrid (finite difference-surface Green's function) method forcomputing transmission losses in an inhomogeneous atmosphere overirregular terrain

A standard parabolic equation (SPE) is used to approximate the Helmholtz equation for electromagnetic propagation in an inhomogeneous atmosphere. An implicit finite difference (IFD) scheme to solve the SPE is applied between the irregularly shaped ground and an altitude z =z_h, below which all inhomogeneities of the medium are assumed localized. The boundary condition at z=z _h is obtained by matching the IFD solution to a surface Green's function (SGF) solution within the uniform region above z =z_h. For ground slopes above about 1°, the IFD implementation of the impedance boundary condition at the ground is shown to maintain the validity of the approximation only for vertically polarized waves. Predictions using this hybrid finite difference (FD)-SGF method agree well with results obtained using other computational methods     

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.<>     

部分森林覆盖山区电波传播特性预测的快速算法

为提高部分森林覆盖山区电波传播特性预测的时效性,提出了一种基于宽角抛物方程(PE)的快速预测算法。采用PE通过分步傅里叶变换(SSFT)求解;在SSFT步进迭代过程中,根据传播路径上森林的等效介电常数、地形的起伏情况,动态选择PE的水平步长。通过对部分森林覆盖的不规则地形条件下的电波传播特性进行仿真,探讨了该方法的可行性和有效性。结果表明：相比于均匀大步长算法,该方法更准确;而相比于均匀小步长算法,该方法能够保证抛物方程的计算精确度,同时极大地提高计算效率。     

Accurate finite difference beam propagation method for complexintegrated optical structures

A simple and effective finite-difference beam propagation method in a z-varying nonuniform mesh is developed. The accuracy and computation time for this method are compared with a standard finite-difference method for both the 3-D and 2-D versions     

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     

A curvilinear coordinate-based split-step parabolic equation methodfor propagation predictions over terrain

Propagation of radiowaves over irregular terrain and in an inhomogeneous atmosphere is solved by the parabolic equation method using the split-step Fourier algorithm on a terrain-conformal mesh. A piecewise continuous coordinate system is generated by the specification of: (1) the terrain profile shape at discrete points and (2) an upper height. The resulting mesh is conformal to the terrain at the lower boundary and gradually flattens off at the maximum height. In addition to preserving the number of points on any vertical line between the terrain and the maximum height from one range step to another, the coordinate transformation used in the paper produces a correction term in the refractive index whose gradient diminishes with height. As a result, the sampling requirements over steep terrain are relaxed when compared to the Beilis-Tappert transformation. Formulation and results are given both for the horizontal and vertical polarizations     

三维地形匹配性能的一种快速估计方法

针对起伏较小三维地形的匹配系统,提出了一种匹配性能的快速估计方法。给出了匹配性能指标的定义,采用八联通区域的邻域完成了特征向量的多分辨率构造,使用多分辨率高斯马尔可夫随机场建立特征与匹配性能之间的关系。在特征提取的过程中,将基准图划分为若干个方块,提取的特征兼顾了邻域关系和多分辨率特性。给出了训练学习和推广的公式,使用最大后验准则,逐步推导出了性能指标估计值的解析解。最后,以实测数据为基础,通过实验验证了所提方法在运算效率和定位误差方面均有较好的性能。     

Tabulated interaction method for UHF terrain propagation problems

An integral equation (IE) solution to UHF terrain path-loss computation is described that dramatically reduces computation times (compared to both standard IE techniques and the fast far-field method) for typical propagation problems while maintaining the full-wave accuracy associated with IE solutions. Results are provided, which are in excellent agreement with published measured data     

A Fredholm integral equation method for propagation predictionsover small terrain irregularities

Two-dimensional propagation of vertical line source fields over lossy, irregular terrain is considered using the magnetic field integral equation. The terrain is characterized by its elevation profile and the local surface impedance, both of which may vary with distance. For treatment via the Fredholm integral equation, the domain under consideration is made finite by enclosing the terrain irregularity and the source within an arbitrary outer boundary. Absorbing boundary conditions are imposed on the outer boundary to reduce unwanted reflections from it. The integral equation is solved by the boundary element method with quadratic elements. Substantial comparison is made with specific canonical problems, with previously published results of other workers, and with measurements to validate the method     

An iterative finite difference beam propagation method for modelingsecond-order nonlinear effects in optical waveguides

An iterative finite difference beam propagation method based on the Crank-Nicholson scheme is presented to simulate continuous wave (CW) second-order nonlinear effects in optical waveguides with the depletion of the pump wave taken into account. This method is an extension of the linear finite difference beam propagation method and preserves the same order of accuracy. Comparisons with the previously published explicit finite difference beam propagation method and the rectangular approximation method are presented. Quasi-phase matched difference frequency generation in AlGaAs and quasi-phase-matched second harmonic generation in LiNbO₃ are considered in the evaluation, showing that one iteration for the IFD-BPM is sufficient for the simulation with good accuracy and without increasing much computation time     

Ground-wave propagation over irregular inhomogeneous terrain: Comparisons of calculations and measurements

A computer program that evaluates HF ground-wave attenuation over irregular inhomogeneous terrain has been developed based on a recently published integral equation. Calculated field strengths are compared with observed measurements for two actual paths. Both comparisons show encouraging agreement between calculations and measurement.     

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     

Low-truncation-error finite difference equations for photonicssimulation. I. Beam propagation

A methodology is presented that allows the derivation of low-truncation-error finite difference equations for photonics simulation. This methodology is applied to the case of wide-angle beam propagation in two dimensions, resulting in finite difference equations for both TE and TM polarization that are quasi-fourth-order accurate even in the presence of interfaces between dissimilar dielectrics. This accuracy is accomplished without an appreciable increase in numerical overhead and is concretely demonstrated for two test problems having known solutions. These finite difference equations facilitate an approach to the ideal of grid-independent computing and should allow the simulation of relevant photonics devices on personal computers     

Explicit finite difference beam propagation method: application to semiconductor rib waveguide Y-junction analysis

A novel explicit finite difference beam propagation method is developed and applied to the analysis of a strongly guiding semiconductor rib waveguide Y-junction. Its accuracy is confirmed by comparison with reported results. This method is much more efficient than the standard beam propagation method for the rib waveguide analysis.<>     

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.<>     

A fast time-domain finite element-boundary integral method forelectromagnetic analysis

A time-domain, finite element-boundary integral (FE-BI) method is presented for analyzing electromagnetic (EM) scattering from two-dimensional (2-D) inhomogeneous objects. The scheme's finite-element component expands transverse fields in terms of a pair of orthogonal vector basis functions and is coupled to its boundary integral component in such a way that the resultant finite element mass matrix is diagonal, and more importantly, the method delivers solutions that are free of spurious modes. The boundary integrals are computed using the multilevel plane-wave time-domain algorithm to enable the simulation of large-scale scattering phenomena. Numerical results demonstrate the capabilities and accuracy of the proposed hybrid scheme     

A noniterative approximate solution method for volume conductorproblems based on the finite difference method

A method was introduced to approximate the solution of the large set of simultaneous equations that result from the application of the finite-difference method to volume conductor problems. It is based on omitting small mesh connections that arise from star-mesh transforms in the finite difference network. The method has the potential to solve very large (n>10⁵) sets of equations. Preliminary results are presented     

A terrain parabolic equation model for propagation in thetroposphere

A method to model tropospheric radiowave propagation over land in the presence of range-dependent refractivity is presented. The terrain parabolic equation model (TPEM), is based on the split-step Fourier algorithm to solve the parabolic wave equation, which has been shown to be numerically efficient. Comparisons between TPEM, other terrain models (SEKE, GTD, FDPEM), and experimental data show predominantly excellent agreement. TPEM is also compared to results from an experiment in the Arizona desert in which range-dependent refractive conditions were measured. Although horizontal polarization is used in the implementation of the model, vertical polarization is also discussed     

Efficient interface conditions for the finite difference beampropagation method

It is shown that by adapting the refractive indexes in the vicinity of interfaces, the 2-D beam propagation method based on the finite-difference (FDBPM) scheme can be made much more effective. This holds especially for TM modes propagating in structures with high-index contrasts, such as surface polaritons. A short discussion is given on the applicability of the FDBPM