Kamenosuke Yasuura

Numerical analysis of a thin-film waveguide by mode-matching method

A new numerical analysis is proposed to investigate accurately the propagation characteristics of a dielectric thin-film waveguide, and its algorithm is presented. In this method, the Rayleigh principle previously used in conventional mode-matching techniques is extended to the Fourier transform of the wave field in the boundary-value problem for an unbounded object. Successful numerical results for dispersion relations and field distributions in a rib waveguide are obtained in detail, accompanied by their error estimations. The propagation characteristics, including field distributions in an optical rib waveguide, are investigated precisely for several geometries, and it is confirmed that the mode-matching method is accurate and effective for numerical analysis, not only with bounded objects, but also with unbounded objects such as thin-film waveguides in integrated optics.

Numerical algorithm based on the mode-matching method with a singular-smoothing procedure for analyzing edge-type scattering problems

An effective numerical method for analyzing edge-type scattering problems is presented with its analytical foundations. The general theory is applied to an arbitrarily shaped two-dimensional scatterer with an edge point, convergence of the approximate solutions is proven, and an algorithm for numerical computation is derived. The algorithm is employed for the resolution of the problem of a rectangular cylinder. Numerical data on the speed of the convergence show the validity and the efficiency of this method. Some examples for far-field patterns and back scattering cross sections as functions of the wavenumber are given.

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.

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 on Isotropic Elastic Waveguides by Mode-Matching Method - I. Analytical Foundations and General Algorithms

A new method for computer-aided calculation, the mode- motching merhod, based on the Rayleigh expansion theorem, is pro- posed in order to analyze the boundary condition problem of elastic fields, and its analytical foundations and general algorithms are dis- cussed. The alastic fields are represented by scalar potential functions which are solutions of Helmholtz equations and expanded by the well- known separated solutions. Introducing the formal Green functions, the integral representations of the potentials are derived. The Rayleigh expansion theorem assures the existence of the infinite sequence of the truncated modal expansions which uniformly converges to the true field in arbitrarily shaped cross section. Through this theorem and the integral representations, the procedure of the mode-matching method is described simply so that the truncated modal expansions are made to fit for the boundary conditions in the least squares sense. Conse- quently this new method may ensure more precise analyses not only on the dispersion characteristics, but also on the field distributions of the particle velocity or the stress by small amount of computational efforts, than the other numerical methods reported so far. The general algo- rithm for the mode-matching method is described in the cases of forced and free vibrations of the homogeneous isotropic elastic waveguide with arbitrarily shaped cross section.

Diffraction Gratings in Japan

A brief introduction to the history of grating research in Japan is presented. The current studies on the design, production, and electromagnetic theories of diffraction gratings are surveyed, covering various design methods, ruling engines, mechanically ruled stigmatic concave gratings, blazed plane holographic gratings, and the numerical method (called either the mode-matching method or the point-matching method) for analysing the physical properties of gratings.