Zhixiang Huang

Survey on Symplectic Finite-Difference Time-Domain Schemes for Maxwell's Equations

To discretize Maxwells equations, a variety of high-order symplectic finite-difference time-domain schemes, which use th-order symplectic integration time stepping and th-order staggered space differencing, are surveyed. First, the order conditions for the symplectic integrators are derived. Second, the comparisons of numerical stability, dispersion, and energy-conservation are provided between the high-order symplectic schemes and other high-order time approaches. Finally, these symplectic schemes are studied by using different space and time strategies. According to our survey, high-order time schemes for matching high-order space schemes are required for optimum electromagnetic simulation. Numerical experiments have been conducted on radiation of electric dipole and wideband S-parameter extraction of dielectric-filled waveguide. The results demonstrate that the high-order symplectic scheme can obtain satisfying numerical solutions under high Courant-Friedrichs-Levy number and coarse grid conditions.

Application of the symplectic finite-difference time-domain scheme to electromagnetic simulation

An explicit fourth-order finite-difference time-domain (FDTD) scheme using the symplectic integrator is applied to electromagnetic simulation. A feasible numerical implementation of the symplectic FDTD (SFDTD) scheme is specified. In particular, new strategies for the air-dielectric interface treatment and the near-to-far-field (NFF) transformation are presented. By using the SFDTD scheme, both the radiation and the scattering of three-dimensional objects are computed. Furthermore, the energy-conserving characteristic hold for the SFDTD scheme is verified under long-term simulation. Numerical results suggest that the SFDTD scheme is more efficient than the traditional FDTD method and other high-order methods, and can save computational resources.

High-order unified symplectic FDTD scheme for the metamaterials

Abstract A high-order unified symplectic finite-difference time-domain (US-FDTD) method, which is energy conserved, for modeling the metamaterials is proposed. The lossless Drude dispersive model is taken into account in US-FDTD scheme, and the detailed formulations of the proposed US-FDTD method are also provided. The high-order split perfectly matched layers (SPML) are used as the absorbing boundary conditions (ABCs) to terminate the computational domain. The analysis of Courant stability and numerical dispersion demonstrate that US-FDTD scheme is more efficient than the traditional time domain numerical methods. Focusing and refocusing of the electromagnetic wave in target detection is validated using the normal incident Gaussian beam with a matched slab. Oblique incidence results associated with the inverse Snell effect and the phase compensation effect of the composite slab further demonstrated the efficiency of the method. Numerical results for a more realistic structure are also included. All the results agree well with the theoretical prediction. The method proposed here can be directly put into using as a time-domain full-wave simulation tool for applications in metamaterials.

Waveguide simulation using the high-order symplectic finite-difference time-domain scheme

Abstract—The high-order symplectic finite-difference time-domain scheme is applied to modeling and simulation of waveguide structures. First, the perfect electric conductor boundary is treated by the image theory. Second, to excite all possible modes, an efficient source excitation method is proposed. Third, the modified perfectly matched layer is extended to its high-order form for absorbing the evanescent waves. Finally, a high-order scattering parameter extraction technique is developed. The cases of waveguide resonator, waveguide discontinuities, and periodic waveguide structure demonstrate that the high-order symplectic finite-difference time-domain scheme can obtain better numerical results than the traditional finite-difference timedomain method and save computer resources.

A New Conformal FDTD(2,4) Scheme for Modeling Three-Dimensional Curved Perfectly Conducting Objects

A new high-order conformal FDTD(2,4) scheme is proposed to solve the electromagnetic scattering from 3-D curved perfectly conducting objects. For electric field components, the update equations do not need to be modified. For magnetic field components, the inner loop is treated with the locally conformal technique, and the outer loop is unmodified. Numerical results demonstrate that the high-order conformal scheme can obtain better numerical precision under coarse grid condition compared with the low-order conformal method and the high-order staircasing approach, which in turn saves CPU time and memory.

Scattering of a Gaussian Beam by a Conducting Spheroidal Particle With Non-Confocal Dielectric Coating

A semi-analytic solution to the Gaussian beam scattering by a conducting spheroidal particle with non-confocal dielectric coating is obtained within the framework of the generalized Lorenz-Mie theory (GLMT). By virtue of a transformation between spheroidal and spherical vector wave functions, a theoretical procedure is developed to deal with the non-confocal boundary conditions. Numerical results of the normalized differential scattering cross section are evaluated for coated spheroidal particles.

High-order symplectic FDTD scheme for solving a time-dependent Schrödinger equation

Abstract Using the three-order symplectic integrators and fourth-order collocated spatial differences, a high-order symplectic finite-difference time-domain (SFDTD) scheme is proposed to solve the time-dependent Schrodinger equation. First, the high-order symplectic framework for discretizing a Schrodinger equation is described. Then the numerical stability and dispersion analyses are provided for the FDTD(2, 2), higher-order FDTD(2, 4) and SFDTD(3, 4) schemes. Next, to implement the Dirichlet boundary condition encountered in the quantum eigenvalue problem, the image theory and one-sided difference technique are manipulated particularly for high-order collocated differences. Finally, a detailed numerical study on 1D and 2D quantum eigenvalue problems is carried out. The simulation results of quantum wells and harmonic oscillators strongly confirm the advantages of the SFDTD scheme over the traditional FDTD method and other high-order approaches. The explicit SFDTD scheme, which is high-order-accurate and energy-conserving, is well suited for a long-term simulation and can save computer resources with large time step and coarse spatial grids.

Design of a new type of broadband antenna with indoor distribution

Based on the principle of discone antenna, a new type of broadband omnidirectional antenna is presented. According to antenna loading technology, introducing the cone surface profile of the broken line structure and short-circuit load of ways which use three short-circuit branches improve the low-frequency electrical characteristics of the antenna and the bandwidth. A very good miniaturization is achieved which reduces the total size. The physical antenna is produced. The calculated and measured VSWR patterns seem to be in good agreement with each other. The VSWR is less than 1.5 at 800MHz-2600MHz. H plane has an ominidirectional radiation pattern. As to small size and low cost, it will have good market prospects.

Scattering of on-axis Gaussian beam by a uniaxial anisotropic object

Based on the extended boundary condition method, a semi-analytical solution to the scattering of an on-axis Gaussian beam by an arbitrarily shaped uniaxial anisotropic object is constructed. For the on-axis incident Gaussian beam, scattered fields as well as internal fields are expanded in terms of appropriate spherical vector wave functions, and the unknown expansion coefficients of the scattered fields are determined by using Schelkunoffs equivalence theorem and continuous boundary conditions. Numerical results of the normalized differential scattering cross section are presented, and the scattering characteristics are discussed concisely.

Scattering by a Multilayered Infinite Cylinder Arbitrarily Illuminated With a Shaped Beam

A method of calculating the scattered electromagnetic fields of a multilayered infinite cylinder, for arbitrary incidence of a shaped beam, is presented. A complete set of coefficients, which describes the electromagnetic fields within the different regions of a multilayered infinite cylinder, is determined by solving a system of linear equations derived from the boundary conditions. As an example, for a tightly focused Gaussian beam propagating perpendicularly to the cylinder axis of a two-layered and three-layered infinite cylinder, the three-dimensional (3D) nature of the scattering problem, greatly different from the case of an incident plane wave, is described in detail, and numerical results of the normalized differential scattering cross section are evaluated.