New integral equations for design of optical circuits

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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).