Conventional Mode-matching Method Research Articles

Novel analytical solutions without finding complex roots for oblique wave scattering by submerged porous/perforated structures

This study develops new analytical solutions to oblique wave scattering by submerged porous/perforated structures on the basis of linear potential theory. Two cases of a porous (rubble mound) breakwater and a horizontal perforated plate are considered. The new solutions have the novelty of using a contour integral technique to avoid finding the complex roots (wave numbers) of complex dispersion equations for water wave motion over porous/perforated structures. In the solution procedure, the linear equation systems for the expansion coefficients in velocity potentials are obtained by using the conventional mode-matching method. However, the matrix elements involving the complex wave numbers are recast by using the contour integral technique, and then the expansion coefficients are determined without knowing the explicit knowledge of complex wave numbers. As a result, the difficulties arising in solving the complex dispersion equations in the traditional solutions are avoided completely. The calculation results of the new solutions agree well with known results of analytical approaches with complex wave numbers, analytical solutions based on the velocity potential decomposition method, and numerical solutions based on the multi-domain boundary element method. This study gives a simple and elegant procedure to tackle water wave interactions with submerged porous/perforated structures, and the solutions can be used as a reliable alternative tool for fast engineering preliminary analysis.

RIGOROUS AND FAST CONVERGENT ANALYSIS OF A RECTANGULAR WAVEGUIDE COUPLER SLOTTED IN COMMON WALL

Abstract—Rigorous and fast convergent analysis of a coupler slotted in common wall between two dissimilar rectangular waveguides is described by a mode-matching method combined with Fourier transform technique and consideration of the singularity of electromagnetic field around edges. Comparing with a conventional mode-matching method, the present method has two advantages. One is that it can avoid the usage of the dyadic Green’s function, the other is that it can overcome the relative convergence problem. The consideration of the field singularity has greatly improved the convergence and the calculated accuracy of a solution. This analysis is rigorous and the computer cost is very low.

Generalized reaction and unrestricted variational formulation of cavity resonators. II. Nonorthogonal and free-boundary mode-matching method

For pt. I see ibid., vol. 50, no. 11, p. 2480-90 (2002). This paper addresses a systematic method whereby the conventional mode-matching method is generalized to the cases where the set of modes used for the field expansion within a cavity resonator are relaxed to be orthogonal or satisfy any specific boundary conditions. It is shown that this approach is based on the unrestricted variational formulation of a cavity resonator. Reciprocity theorem and generalized reaction are the mathematical foundations of this new formulation. We have shown that the conventional mode-matching method is a special case of this generalized formulation and indeed is variational in nature. More precisely, we have proven that, if the field distribution obtained based on the conventional mode-matching method is used as a trial one in some variational formulas, the resonant frequency will be the same as the one obtained by the mode-matching method.

Quasi-static analysis of coupled microstrip lines with asymmetrical finite metallization thickness

This paper describes the quasi-static analysis of coupled microstrip lines with asymmetrical finite metallization thickness. A generalized mode-matching method extended from the conventional mode-matching method has been used to analyze the inhomogeneous structure with arbitrary metallization thickness and is validated through comparison with those from other available results. This method cannot only provide a simple approach to the quasi-static analysis of the inhomogeneous structures with arbitrary metallization thickness, but can also be applied to analyze the effect of metal penetration depth into the substrate. The results show that the asymmetrical finite metallization thickness and metal penetration depth into the substrate can be newly added to the quasi-static design parameters of coupled microstrip lines.

Investigation of metal-penetrating depth in shielded microstrip line

In this letter, the propagation characteristics of metal-penetrating depth into the anisotropic substrate in a shielded microstrip line are investigated. A vertical directional mode-matching method (MMM), extended from the conventional mode-matching method, including an inhomogeneous eigenfunction for analyzing this structure has been used and applied to analyze the effect of metal penetration into the anisotropic substrate. The results show that the characteristic impedances and effective dielectric constants of a shielded microstrip line can be represented as a function of the metal-penetrating depth into the substrate. © 1998 John Wiley & Sons, Inc. Microwave Opt Technol Lett 19: 396–398, 1998.

Analysis of Complex Rectangular Dielectric Waveguides

In this paper, a rigorous method for the analysis of the propagation characteristics of various rectangular waveguides is proposed based on the recent development of the numerical mode matching method for multi-region, vertically stratified media. Unlike the conventional two-dimensional finite element method which is widely used for the analysis of dielectric waveguide problems, the numerical mode matching method proposed in this paper uses the propagation properties of the waves on the cross-section of the waveguides to convert the two-dimensional problem into a few one-dimensional problems. These one-dimensional problems are then solved with the one-dimensional finite element method, resulting in a great saving of the number of unknowns needed. A major difference between this method and the conventional mode matching method is that the eigenvalues and eigenmodes of the constituent layered media are found numerically by using a one-dimensional finite element method, which makes the method more versatile ...

Numerical method for calculating surface current density on a two-dimensional scatterer with smooth contour

A numerical method is presented for finding the surface current density on a two-dimensional smooth scatterer. This method is an improved version of a method which one of the authors presented as an adjoint method to the conventional mode-matching method (MMM) for finding the scattered field. After formulating the problem, we interpret the method being adjoint to the conventional mode-matching method and show that the method yields a sequence of approximate current densities converging to the true density in the mean squares sense. Next we propose the improved method and prove the fact that this method yields a sequence of approximate solutions which converges to the true density uniformly on the contour of the scatterer. We then state that the method is an adjoint one to the mode-matching method with a smoothing procedure (SP) which we proposed as a powerful numerical method for the scattered field. Numerical results of some sample calculation are attached to show the effectiveness of the new method.

Numerical analysis of diffraction from a grating by the mode-matching method with a smoothing procedure

A numerical technique based on the mode-matching method with a smoothing procedure is presented for analyzing the diffraction of electromagnetic waves by a grating. The general algorithm for the problem of an arbitrarily shaped periodic surface is described taking the case of H polarization. To show the validity of this algorithm, plane-wave diffraction by a triangular grating is analyzed, and the results are compared with those obtained by the conventional mode-matching method. It is demonstrated that the sequence of approximate solutions calculated by the algorithm presented in this paper converges to the true solution much faster than the sequence produced by the conventional mode-matching method. Some numerical examples on the efficiency are presented.