FWM generation in higher order fiber dispersion managedtransmission line

Describes, in terms of fiber parameters, four-wave-mixing generation in a higher order fiber dispersion managed transmission line in which positive and negative dispersion fibers are used to manage both second- and third-order fiber dispersion. An analysis shows that the full-width at half-maximum interaction in dense wavelength-division-multiplexing systems can be reduced by properly setting the channel spacing to suit the dispersion allocation in the transmission line     

Electrical spectrum measurements of dispersion in higher order mode fibers

We present a novel technique for measuring the chromatic dispersion of the higher order mode of an optical fiber. The measurement technique is simple, accurate, and capable of measuring the dispersion of kilometer lengths of fiber without the need for mode converters. The dispersion of the LP/sub 02/ mode is measured for several different fibers, and accuracies of better than 1%, compared with a measurement with the modulation phase shift method, are achieved.     

Development of higher order FDTD schemes with controllable dispersion error

A new methodology that facilitates the control of the inherent dispersion error in the case of higher order finite-difference time-domain (FDTD) schemes is presented in this paper. The basic idea is to define suitable algebraic expressions that reflect numerical inaccuracies reliably. Then, finite-difference operators are determined via the minimization of the error estimators at selected frequencies. In order to apply this procedure, an error expansion in terms of cylindrical harmonic functions is performed, which also enables accuracy enhancement for all propagation angles. The design process produces a set of two-dimensional (2-D) FDTD algorithms with optimized frequency response. Contrary to conventional methodologies, the proposed techniques adjust their reliability range according to the requirements of the examined problem and can be, therefore, more efficient in computationally demanding simulations.     

Numerical solution of higher order mode cutoff frequencies inasymmetric TEM cells by Galerkin method

The authors describe a Galerkin method (GM), which determines efficiently the basis functions satisfying the edge conditions and the size of the elements on the Neumann boundaries in this paper. The calculated higher order mode cutoff frequencies in both symmetric and asymmetric TEM cells by the GM are presented. The authors could then solve the technical debate for TE₁₂-, TE₀₃-, TM ₁₁-, and TM₁₂-mode cutoff frequencies in the symmetric TEM cell. It is also shown that the measured resonant frequencies of a designed asymmetric TEM cell agree well with the predicted data by the GM     

Pulse broadening due to higher order dispersion and itstransmission limit

If we are to significantly increase the transmission speed of optical networks, the impact of higher order dispersion must be clarified. This paper gives general expressions that describe pulse broadening due to even and odd higher order dispersion in a single-mode fiber. The intrinsic impulsive responses for even order dispersion (beyond the second order) are characterized by symmetrical waveforms with long trailing skirts, whereas the responses for odd orders show asymmetrical strongly oscillating waveforms. The transmission limits are also analytically obtained for each higher nth order that induces intersymbol interference. Transmission lengths are limited by the factor of 1/B₀ⁿ where B₀ is the bit rate and n is the dispersion order     

Convergence-optimized, higher order vector finite elements formicrowave simulations

We introduce a general class of higher order parameter-dependent Whitney elements, unlike previous approaches that resulted in specific element definitions. All elements of this kind provide the same solution, but their convergence properties may be significantly different. The most essential fact, though, is the introduction of an optimization procedure, which reveals the existence of an optimal, with respect to convergence, element. The produced second order elements are tested in both two-dimensional (2-D) and three-dimensional (3-D) microwave simulations     

A higher order (2,4) scheme for reducing dispersion in FDTDalgorithm

A finite-difference time-domain (FDTD) scheme with second-order accuracy in time and fourth-order in space is discussed for the solution of Maxwell's equations in the time domain. Compared with the standard Yee (1966) FDTD algorithm, the higher order scheme reduces the numerical dispersion and anisotropy and has improved stability. Dispersion analysis indicates that the frequency band in which the higher order scheme yields an accurate solution is widened on the same grid, this means a larger space increment can be chosen for the same excitation. Numerical results show the applications of the scheme in modeling wide-band electromagnetic phenomena on a coarse grid     

A higher order FDTD method in Integral formulation

We present a fourth-order (4, 4) finite-difference time-domain (FDTD)-like algorithm based on the integral form of Maxwell's equations. The algorithm, which is called the integro-difference time-domain (IDTD) method, achieves its fourth-order accuracy in space and time by taking into account the spatial and temporal variations of electromagnetic fields within each computational cell. In the algorithm, the electromagnetic fields within each cell are represented by space and time integrals (or integral averages) of the fields, i.e., the electric and magnetic fluxes (D,B) are represented by the surface-integral average, and the electric and magnetic fields (E,H) by the line and time integral average. In order to relate the integral average fields in the staggered update equations, we have obtained constitutive relations for these fields. It is shown that the IDTD update equations combined with the constitutive relations are fourth-order accurate both in space and time. The fourth-order correction terms are represented by the modified coefficients in the update equations; the numerical structure remains the same as the conventional second-order update equations and more importantly does not require the storage of field variables at the previous time steps to obtain the fourth-order accuracy in time. Furthermore, the Courant-Friedrichs-Lewy (CFL) stability criteria of this fourth-order algorithm turns out to be identical to the stability limits of conventional second-order FDTD scheme based on differential formulation.     

Fully-differential current-mode higher order filters using all grounded passive elements

In this paper the realization of nth order (n ≥ 3) fully-differential current-mode filters using Current Differencing Current Conveyors (CDCC) has been presented which results in circuits employing all grounded passive elements. In contrast to earlier known realizations of fully-differential filters which invariably require more than one capacitors per pole, the proposed realization employs only one capacitor per pole. The cut-off frequency of the realized filter can be electronically tuned when all the grounded resistors associated with the integrators are implemented by identical CMOS grounded voltage-controlled-resistors (VCR) driven by a common control voltage. The methodology has been illustrated by realizing a fifth order Butterworth filter as a specific example whose workability has been verified using SPICE simulations in 0.18 µm TSMC technology. A reduced-component-version of the designed fifth order Butterworth filter has also been presented which also employs all grounded RC components but does not have electronic-tunability. Some representative simulation results have been included.     

A higher order electron wave propagation method

A finite-difference propagation scheme for simulating electron currents through arbitrary quantum structures is presented in this paper. It is shown that due to the strong interaction of external fields and electrons, the trajectories predicted using higher order propagation operators are a significant improvement over that of lower order schemes, especially in cases where the longitudinal electron momentum is not accurately known. A novel boundary condition based on the popular transparent boundary condition is used for minimizing unphysical reflections off the computation boundaries even in the presence of strong lateral electric fields. The application of this scheme is illustrated through a few examples     

碰撞等离子体的高阶FDTD算法

给出了电磁波在均匀、碰撞等离子体中传播的四阶时间和四阶空间FDTD算法.该算法比Yee氏FDTD算法每一个网格每一维增加一个存储单元,与常规的二阶等离子体FDTD算法相同.由于采用四阶时间和四阶空间近似,因此该算法能有效地减小数字色散误差,其频带宽度比二阶算法的频带宽度更宽.为了验证该高阶算法的正确性,对均匀、碰撞等离子体平板的电磁波反射系数进行了计算,并与解析结果、二阶FDTD计算结果进行了比较,证明了该算法的高效和精确.     

Modelling of industrial conveyorized applicators using higher order vector finite elements.

This paper presents a finite element time domain method for the solution of Maxwell's equations in microwave heating applicators using first and second order vector finite elements. Results are compared with experimental data and it has been shown that second order vector finite elements have many advantages over first order elements. Capitalising on the high accuracy and low computational cost attainable by higher order elements, an industrial conveyor belt system is numerically analyzed.     

Comparison of the dispersion properties of higher order FDTD schemes and equivalent-sized MRTD schemes

The dispersion errors of higher order finite-difference time-domain (HO-FDTD) algorithms are compared to those of multiresolution time-domain (MRTD) algorithms that have equivalent spatial stencil sizes. Both scaling-function-based MRTD (S-MRTD) and wavelet-function-based MRTD (W-MRTD) schemes are considered. In particular, the MRTD schemes considered include the Coifman scaling functions and the Cohen-Daubechies-Feauveau (CDF) biorthogonal scaling and wavelet functions. In general, the HO-FDTD schemes are more accurate than their MRTD counterparts.     

Errors due to spatial discretization and numerical precision in thefinite-element method

The effects of the spatial discretization and the numerical precision on a plane wave propagating through a finite-element mesh are investigated in this work. The spatial discretization results in dispersion in the amplitude and the phase of the wave and in a non-uniform rate of convergence within an element. The finite precision in the calculations used in a finite-element code results in degraded accuracy. These errors are investigated as a function of the node density, the order of the elements, and the precision of the calculations used in the finite element code. The errors for first- through eighth-order elements are investigated both analytically and numerically     

Numerical Simulation of BOR scattering and radiation using a higher order FEM

Numerical simulations of body-of-revolution geometries for scattering and radiation problems are presented. The formulation consists of a finite element-boundary integral (FE-BI) method which is based on a finite element method that uses higher order nodal-based scalar basis functions for the azimuthal field component and higher order edge-based vector basis functions for the transverse field. This formulation, when combined with a symmetric FE-BI hybridization scheme, yields a final system of equations that is more accurate than earlier first-order formulations. Numerical examples are given to demonstrate the accuracy and capabilities of the higher order solution.     

Numerical solution of higher order mode cut-off frequencies insymmetric TEM cells using finite element method [EMI measurementapplications]

The higher-order-mode cut-off frequencies in symmetric transverse electromagnetic cells are computed with the finite-element method. Transverse electric and transverse magnetic modes are considered. For symmetry, only one-quarter of the cross section is analyzed. Electric and magnetic walls are introduced in the cross section, which includes the effect of the gap between the center conductor and the sidewalls. This arrangement enhances the accuracy of the solution. The results obtained by this method are compared with those of other methods. Discrepancies observed in the results of other methods are explained. The present method is the more powerful one; with this method, mode identification can easily be made using an eigenvector solution     

有耗介质中时域精细积分方法的数值色散分析

分析了时间步长、空间步长、电导率和电磁波传播方向对时域精细积分(PITD)方法的数值损耗和数值色散的影响。结果表明:PITD的数值损耗大于电磁波的真实损耗,其数值波速可以大于电磁波的真实波速。PITD的数值损耗和数值色散都基本上不受时间步长的影响。随着空间步长的减小,PITD的数值损耗和数值色散的误差都逐步减小。当电导率较小时,PITD的数值损耗和数值色散的误差比时域有限差分(FDTD)方法的大。但当电导率较大时,PITD的数值波速却比FDTD的数值波速更加接近于电磁波的真实波速。PITD的数值损耗和数值色散的各向异性在三维情况下的值要大于其在二维情况下的值。数值算例表明:对良导体而言,PITD比FDTD拥有更高的计算精度和更快的计算速度。     

A special higher order finite-element method for scattering by deepcavities

A special higher order finite-element method is presented for the analysis of electromagnetic scattering from a large, deep, and arbitrarily shaped open cavity. This method exploits the unique features of the finite-element equations and, more importantly, the unique features of the problem of scattering by a large and deep cavity. It is designed in such a manner that it uses minimal memory, which is proportional to the maximum cross section of the cavity and independent of the depth of the cavity, and its computation time increases only linearly with the depth of the cavity. Furthermore, it computes the scattered fields for all angles of incidence without requiring significant additional time. The technique is implemented with higher order tetrahedral and mixed-order prism elements, both having curved sides to allow for accurate modeling of arbitrary geometries. Numerical results show that higher order elements yield a remarkably more accurate and efficient solution for scattering by three-dimensional (3-D) cavities. Of the two kinds of element, the mixed-order prism is optimal for the proposed special solver     

A hybrid finite element method for 3-D scattering using nodal andedge elements

A hybrid finite element method for three-dimensional scattering is presented and numerical examples shown. This approach, which couples finite element discretization with the method of moments, is particularly well suited for monostatic radar cross section calculations. The method is based on a scalar and vector potential formulation of Maxwell's equations, the use of nodal elements, and a highly efficient body of revolution implementation of the method of moments. Combined nodal and edge elements are employed to accurately model fields around corners and edges. A curvature-based sampling criterion is derived and shown to ensure accurate answers for highly curved scatterers. Numerical results and Cray computer timings are compared with published results for an edge element code using radiation boundary conditions     

Simultaneous suppression of third-order dispersion and sideband instability in single-channel optical fiber transmission by midway optical phase conjugation employing higher order dispersion management

In optical phase conjugation (OPC) systems, the third-order dispersion (TOD) of optical fibers and the nonlinear resonance at well-defined signal sideband frequencies called sideband instability (SI) mainly limit the transmission performance. We propose, for the first time, a scheme for simultaneous suppression of both TOD and SI in OPC systems using a periodic higher order dispersion-managed link consisting of standard single-mode fibers (SMFs) and reverse dispersion fibers (RDFs). Computer simulation results demonstrate the possibility of 200-Gb/s data transmission over 10 000 km in the higher order dispersion-managed OPC system, where the dispersion map is optimized by our system design strategies.