Operator Fresnel Formulas in the Scattering Theory of Waveguide Modes

Part of the Springer Series on Atomic, Optical, and Plasma Physics book series (SSAOPP, volume 91)


A novel formulation of the problem of wave diffraction by abrupt and volume discontinuities in a waveguide is presented in this chapter. In the context of this formulation, the authors succeeded in solving a number of the long-discussed problems concerning mathematical properties of matrix models of the mode-matching technique. In particular, they rigorously justified the possibility to use the truncation technique, unconditionally converging in the norm of a space of infinite sequences, for numerical implementation of the developed matrix models. The operator-matrix analysis of the mode-matching technique has shown that the proposed approach leads to the operator Fresnel formulas, which generalize properly the well-known Fresnel formulas to the scattering operators.


Matrix Operator Waveguide Mode Projection Approximation Reflection Operator Pontryagin Space 
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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.University of Customs and FinanceDnipropetrovskUkraine
  2. 2.National Academy of SciencesO.Ya. Usikov Institute for Radiophysics and ElectronicsKharkivUkraine
  3. 3.L.N. Gumilyov Eurasian National UniversityAstanaRepublic of Kazakhstan

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