Introduction to Yasuura’s Method of Modal Expansion with Application to Grating Problems

  • Akira MatsushimaEmail author
  • Toyonori Matsuda
  • Yoichi Okuno
Part of the Springer Series on Atomic, Optical, and Plasma Physics book series (SSAOPP, volume 99)


In this chapter we introduce the theory of the Yasuura’s method based on modal expansion and explain the methods of numerical computation in detail for several grating problems. After a sample problem we discuss the methods for solving two types of problems that require additional knowledge and steps, that is, scattering by a dielectric cylinder and diffraction by a grating. Some numerical results are shown to give an evidence of an experimental rule for the number of linear equations in formulating the least-squares problem that determines the modal coefficients. After confirming the rule we show a couple of examples of practical interest, i.e., scattering by a relatively deep metal grating, plasmon surface waves on a metal grating placed in conical mounting, scattering by a metal surface modulated in two directions, and scattering by periodically located dielectric spheres. To provide supplementary explanations of particular problems, four appendices are given; H-wave scattering from a cylinder, the normal equation and related topics, conical diffraction by a dielectric grating, and comparison of modal functions and the algorithm of the smoothing procedures.



The authors thank Mr. BenWen Chen and Mr. Rui Gong, Centre for Optical and Electromagnetic Research, South China Academy of Advanced Optoelectronics, South China Normal University for preparing the figures in Sect. 8.3.1 including numerical computations.

One of the authors (A.M.) wish to express his thanks to Japan Society for Promotion of Science (JSPS) for partial support to the work in Sects. 8.3.2 and 8.3.5 under Grant Number JP15K06023 (KAKENHI).

Another one of the authors (Y.O.) is grateful to Prof. S. He, COER-SCNU, COER-ZJU, and JORSEP-KTH for his continuous help and encouragement.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Akira Matsushima
    • 1
    Email author
  • Toyonori Matsuda
    • 2
  • Yoichi Okuno
    • 3
  1. 1.Kumamoto UniversityKumamotoJapan
  2. 2.National Institute of Technology, Kumamoto CollegeKumamotoJapan
  3. 3.South China Normal UniversityGuangzhouChina

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