Masafumi Fujii

Multiresolution analysis similar to the FDTD method-derivation and application

A three-dimensional (3-D) multiresolution analysis procedure similar to the finite-difference time-domain (FDTD) method is derived using a complete set of three-dimensional orthonormal bases of Haar scaling and wavelet functions. The expansion of the electric and the magnetic fields in these basis functions leads to the time iterative difference approximation of Maxwells equations that is similar to the FDTD method. This technique effectively models realistic microwave passive components by virtue of its multiresolution property; the computational time is reduced approximately by half compared to the FDTD method. The proposed technique is validated by analyzing several 3-D rectangular resonators with inhomogeneous dielectric loading. It is also applied to the analyses of microwave passive devices with open boundaries such as microstrip low-pass filters and spiral inductors to extract their S-parameters and field distributions. The results of the proposed technique agree well with those of the traditional FDTD method.

A wavelet formulation of the finite-difference method: full-vector analysis of optical waveguide junctions

We have developed an efficient, large-stencil finite-difference scheme of the time-dependent Maxwells curl equations based on the wavelet-collocation formulation in the time-domain. The proposed scheme enables, for the first time within a limited computational resource, full-vector analysis of three-dimensional rib waveguides that are typically used in integrated planar optical devices. The formulation takes advantage of compactly-supported interpolating bases to expand and represent the electric and magnetic fields. Moreover, unlike the well-known beam propagation methods, the numerical scheme is based on the first-principle algorithm with no explicit approximation, and thus rigorous and versatile for various types of boundary conditions. We demonstrate the efficiency of the method by first analyzing a straight rib-waveguide and examining the convergence of the results. Then we investigate a Y-shaped junction structure that is electrically too large to analyze with the conventional finite-difference time-domain scheme.

Application of biorthogonal interpolating wavelets to the Galerkin scheme of time dependent Maxwell's equations

A family of biorthogonal interpolating wavelets has been applied to time-domain electromagnetic field modeling through the wavelet-Galerkin scheme. The scaling functions are the Deslauriers-Dubuc interpolating functions and the wavelets are the shifted and contracted version of the scaling functions. This set of bases yields a simple algorithm for the solution of Maxwells equations in time domain due to their interpolation properties. The derivation of the algorithm is presented in this paper, followed by a series of numerical verifications on some resonant structures.

Field-singularity correction in 2-D time-domain Haar-wavelet modeling of waveguide components

A time domain Haar-wavelet based modeling technique has been applied to 2-D waveguide problems including discontinuities. The principal original contribution of this paper is the correction of the field singularity at the edge of a conductor by quasi-static field approximation. Combination of quasi-static correction and wavelet modeling considerably improves the computational efficiency compared to conventional time domain analysis techniques.

Field singularity correction in 2-D time domain Haar wavelet modeling of waveguide components

A time domain Haar-wavelet based modeling technique has been applied to 2-D waveguide problems including discontinuities. The principal original contribution of this paper is the correction of the field singularity at the edge of a conductor by quasi-static field approximation. Combination of quasi-static correction and wavelet modeling considerably improves the computational efficiency compared to conventional time domain analysis techniques.

Accurate analysis of losses in waveguide structures by compact two-dimensional FDTD method combined with autoregressive signal analysis

An efficient two-dimensional finite-difference time-domain (2-D FDTD) method combined with an autoregressive (AR) signal analysis has been proposed for analyzing the propagation properties of microwave guiding structures. The method is especially suitable for analyzing lossy transmission lines; and in contrast with previous approaches, it is based on an algorithm of a real domain only. The algorithm is verified by comparing the numerical results with exact solutions for dielectric loaded rectangular waveguides. The conductor losses in a variety of microstrip lines and coplanar waveguides have been accurately estimated by solving the electromagnetic fields in the conductors directly.

Formulation of a Haar-wavelet-based multi-resolution analysis similar to the 3-D FDTD method

A 3-D multi-resolution analysis procedure similar to the FDTD method is derived using Haar-wavelets. The method is validated by analyzing several 3-D rectangular resonators with inhomogeneous dielectric loading. It is also applied to the analyses of microstrip low pass filters with open boundaries, and their S-parameters are extracted. The results are compared with those of the traditional FDTD method.

Interpolating wavelet Galerkin model of time dependent inhomogeneous electrically-large optical waveguide problems

Biorthogonal interpolating wavelets have been applied to inhomogeneous electromagnetic field modeling through the wavelet-Galerkin scheme, yielding a simple and versatile algorithm for the time dependent Maxwells equations. The resulting scheme significantly reduces the computational expenditure particularly in the modeling of electrically large optical waveguides while maintaining high accuracy.

FDTD modeling of switching noise in multi-layered digital circuits with CMOS inverters and passive lumped elements

Multi-layered digital circuits such as LSI packages, has been analyzed by using a Finite-Difference Time-Domain (FDTD) method. Linear lumped elements, resistors and capacitors, and nonlinear lumped elements, CMOS drivers, are included in the analyses. Various noises as well as digital pulse propagation in multi-layered circuits are effectively analyzed by this technique.