New integral equations for design of optical circuits

该项目的首席研究员田中和夫教授于1988-1989年在光波导不连续问题中发现了散射系数与导模系数之间新的数学关系。利用这一关系，我们得到了一种基于新的积分方程法（导模提取积分方程：GMEIE）的光电路设计新算法。介质光波导不连续问题可以看作是大尺寸介质物体的散射问题，这类问题可以用传统的边界元法（BEM）进行数值求解。边界元法求解积分方程的技术是现代数值技术中最正统的方法，有关边界元法的经验和知识是众所周知的。因此，这些经验和知识可以应用于光波导电路的设计。本项目取得了以下新成果：我们评估了基于GMEIE.2的新算法的各种数值计算特性。文中给出了对各种光波导不连续现象的分析实例，结果与严格解一致。此外，我们还将我们的方法应用于难以分析的问题，并获得了合理的结果。结果表明，该方法适用于光电路计算机辅助设计（CAD）的求解。结果表明，该方法适用于近场光学中量子电子波导电路和光学电路的设计。

Head investigator Prof.Kazuo Tanaka of this project has discoverd new mathematical relation between scattering coefficient and coefficient of guided-mode in the optical-waveguide discontinuity problems in 1988-1989. Using this relation, we obtained a new algorithm for design of optical circuits based on new integral equation method (guided-mode extracted integral equation : GMEIE). We can regard the dielectric optical-waveguide discontinuity problems as a scattering problems of large-sized dielectric objects and these kinds of problems can be solved numerically by the conventional boundary-element method(BEM). Techniques of solving integral equations by BEM is the most orthodox method in modern numerical techniques and a large mount of experiences and knowledge concerning BEM are well known. Therefore, these experiences and knowledge can be used in the design of optical waveguide circuits. We obtained following new results in, this project :1. We evaluated various properties of numerical calculation of the new algorithm based on GMEIE.2. We showed many examples of analysis of various kind of optical-waveguide discontinuities and also showed that our results agree with rigorous solution. Furthermore, we applied our method to problems which have been difficult to analyze and obtained reasonable results. We found that our new method is very suitable to solver of Computer aided design (CAD) of optical circuits.3. We showed that our method is applicable to the design of quantum-electron waveguide circuits and optical-circuits in near field optics (NFO).