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Telecommunications and Radio Engineering
SJR: 0.202 SNIP: 0.2 CiteScore™: 0.23

ISSN 印刷: 0040-2508
ISSN オンライン: 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; University of Customs Affair and Finances, 8, Rogaleva St., Dnepropetrovsk 49000, Ukraine
Yurii Konstantinovich Sirenko
O.Ya. Usikov Institute for Radio Physics and Electronics, National Academy of Sciences of Ukraine, 12, Academician Proskura St., Kharkiv 61085, Ukraine; V.N. Karazin Kharkiv National University, 4 Svobody Sq., Kharkiv 61022, Ukraine; L.N. Gumilyov Eurasian National University, 2, Satpayev St., Astana 010008, Republic of Kazakhstan

要約

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.

参考

  1. Born, M. and Wolf, E., Principles of optics: Electromagnetic theory of propagation, interference and diffraction of light.

  2. Mittra, R. and Lee, S.W., Analytical techniques in the theory of guided waves.

  3. Shestopalov, V.P. and Shcherbak, V.V., Matrix operators in diffraction problems.

  4. Petrusenko, I.V., Analytic - numerical analysis of waveguide bends.

  5. Petrusenko, I.V., Basic properties of the generalized scattering matrix of waveguide transformers.

  6. Petrusenko, I.V. and Sirenko, Yu.K., Generalization of the power conservation law for scalar mode-diffraction problems.

  7. Petrusenko, I.V. and Sirenko, Yu.K., Abrupt discontinuities: the reflection operator is a contraction.

  8. Shestopalov, V.P., Kirilenko, A.A., and Masalov, S.A., Convolution-type matrix equations in the theory of diffraction.

  9. Weyl, H., The classical groups: Their invariants and representations.

  10. Richtmyer, R.D., Principles of advanced mathematical physics.


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