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Telecommunications and Radio Engineering

ISSN Print: 0040-2508
ISSN Online: 1943-6009

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Telecommunications and Radio Engineering

DOI: 10.1615/TelecomRadEng.v70.i9.10
pages 749-758

FRESNEL FORMULAE FOR SCATTERING OPERATORS

I. V. Petrusenko
A. Usikov Institute of Radio Physics and Electronics, National Academy of Sciences of Ukraine
Yurii Konstantinovich Sirenko
L.N. Gumilyov Eurasian National University; A. Usikov Institute of Radio Physics and Electronics, National Academy of Sciences of Ukraine

ABSTRACT

For the scalar problem of mode diffraction on the abrupt waveguide discontinuity the Fresnel formulae for the reflection and transmission matrix operators are derived using the mode-marching technique. This generalized form of the matrix model is an immediate corollary of the proposed new statement of the problem. Making use of the energy conservation law in operator form, the correctness of the obtained Fresnel formulae for the scattering operators is proved analytically. Thus, the developed approach makes it possible to substantiate completely the widely used mode-matching technique for the class of diffraction problems under consideration.

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