The finite-difference time-domain (FDTD) method is arguably the most popular numerical method for the solution of problems in electromagnetics. Although the FDTD method has existed for nearly 30 years, its popularity continues to grow as computing costs continue to decline. Furthermore, extensions and enhancements to the method are continually being published, which further broaden its appeal. Because of the tremendous amount of FDTD-related research activity, tracking the FDTD literature can be a daunting task. We present a selective survey of FDTD publications. This survey presents some of the significant works that made the FDTD method so popular, and tracks its development up to the present-day state-of-the-art in several areas. An "on-line" BibT/sub E/X database, which contains bibliographic information about many FDTD publications, is also presented. >

A selective survey of the finite-difference time-domain literature

An extension of the finite difference time domain is applied to solve the Schrodinger equation. A systematic analysis of stability and convergence of this technique is carried out in this article. The numerical scheme used to solve the Schrodinger equation differs from the scheme found in electromagnetics. Also, the unit cell employed to model quantum devices is different from the Yee cell used by the electrical engineering community. A bound for the time step is derived to ensure stability. Several numerical experiments in quantum structures demonstrate the accuracy of a second order, comparable to the analysis of electromagnetic devices with the Yee cell.

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Analysis of the finite difference time domain technique to solve the Schrödinger equation for quantum devices

A single-layer corporate-feed slot array antenna is presented. The single-layer structure is realized by adopting hollow rectangular coaxial lines for the corporate-feed circuit and placing the feeding circuit and the radiating elements in the same layer. Based on this, a 16 × 16-element slot array for the 60-GHz band is designed and fabricated by diffusion bonding of laminated thin copper plates. A 32.3 dBi gain and 72.2% antenna efficiency are confirmed at the design frequency of 61.5 GHz in the measurements. The 1-dB down gain bandwidth is 8.8%. The conductor loss of the antenna is estimated to be 0.85 dB at 61.5 GHz.

Single-Layer Corporate-Feed Slot Array in the 60-GHz Band Using Hollow Rectangular Coaxial Lines

The scaled boundary finite element method (SBFEM) is developed for the solution of waveguide eigenvalue problems, which combines the advantages of the finite element method and the boundary element method. A new variational principle formulation to derive the SBFEM equations for waveguide is developed. An equation of the dynamic stiffness matrix for waveguide representing the relationship between the ‘flux’ and the longitudinal field components at the discretised boundary is established. A continued fraction solution in terms of eigenvalue is obtained. By using the continued fraction solution and introducing auxiliary variables, the flux–longitudinal field relationship is formulated as a system of linear equations in eigenvalue then a generalised eigenvalue equation is obtained. The eigenvalues of rectangular, L-shaped, vaned rectangular and quadruple corner-cut ridged square waveguides are calculated and compared with analytical solution and other numerical methods. The results show that the present method yields excellent results, high precision and less computational time and rapid convergence is observed.

Scaled boundary finite element approach for waveguide eigenvalue problem

A hollow rectangular coaxial line is designed for the 60-GHz band and fabricated by diffusion bonding of laminated thin metal plates. A low transmission loss of 0.036 dB/cm is confirmed at 60 GHz by measurement in a designed rectangular coaxial line. The suspended inner conductor is supported by a thin plate. A longitudinal slot excited by the metal support and its linear array are presented. The proposed structures are verified by comparing the measured results with the designed ones. The 1.5% bandwidth of the linear array for reflection below $-{\hbox{14 dB}}$ is obtained by the measurement.

A Hollow Rectangular Coaxial Line for Slot Array Applications Fabricated by Diffusion Bonding of Laminated Thin Metal Plates

The paper describes the application of the finite-difference method in the time domain for obtaining the cutoff frequencies of TE and TM modes in waveguides of arbitrary cross-section. Maxwell's equations are discretised in a two-dimensional space. The application of the discrete Fourier transform also provides the spatial distribution of the modes in the cross-section of the waveguide. The method is validated against rectangular and a circular waveguides, each with a known cutoff spectrum. Finally, the method is applied to determine cutoff wavelengths and modal field distributions in a square coaxial waveguide.

E.A. Navarro

Papers

Study of TE and TM modes in waveguides of arbitrary cross-section using an FD-TD formulation