A. V. Druzhinin

HIGH-FREQUENCY ELECTRODYNAMICS AND MECHANICS OF ANISOTROPIC MEDIA

The paper presents a new mathematical approach generally relating anisotropic electrodynamic characteristics to optical constants. A mathematical language is a hypercomplex algebra describing a spinor space. The problem of the Faraday magneto-optic effect – circular birefringence and dichroism – is solved within the framework of this formalism. The issue of using this formalism in problems of solid mechanics is discussed.

Acknowledgments: The research was performed under the state assignment from the Russian Ministry of Edu-cation and Science, theme Function, No. AAAA-A19-119012990095-0. It was partially financially supported by the RFBR, grant No. 20-02-00541.

References:

1. Ketkovich A.A., Strokov V.A. et al, V.V. Klyuev, ed. Pribory dlya nerazrrushayushchego kontrolya materialov i izdeliy, kn. 1 [Instruments for Nondestructive Testing of Materials and Products: handbook, book 1].  Moscow, Mashinostroenie Publ., 1986, pp. 48-115. (In Russian).
2. Vladimirov A.P. Dinamicheskaya spekl-interferometriya deformiruyemykh tel. [Dynamic Speckle Interferometry of Bodies under Deformation]. Ekaterinburg, UrO RAN Publ., 2004, 241 p. (In Russian).
3. Vladimirov A.P., Kamantsev I.S., Drukarenko N.A., Trishin V. N., Akashev L. A. & Druzhinin A. V. Assessing Fatigue Damage in Organic Glass Using Optical Methods. Opt. Spectrosc., 2019, 127, pp. 943–953. DOI:  10.1134/S0030400X19110286.
4. Akhmanov S.A., Nikitin S.Yu. Physical Optics. Moscow, MGU Publ., 2004, 656 p. (In Russian).
5. Gorshkov M.M. Ellipsometry. Moscow, Sov. Radio Publ., 1974, 200 p. (In Russian).
6. Fedorov F.I. Optika anizotropnykh sred [Optics of Anisotropic Media]. Minsk, Izd. Akad. Nauk BSSR, 1958.
7. Knyazev Yu.V., Maevskii V.M. Anisotropy of optical absorption in an yttrium single crystal. Optics and Spectroscopy, 1984, vol. 57, iss. 2, pp.153–157.
8. Druzhinin A.V., Lobov I.D., Maevsky V.M. Observation of the odd effect of light intensity variation as the light passes through an equatorially magnetized ferromagnetic film. Pisma v ZhTF, 1981, vol. 7, No. 18, pp. 1100–1102. (In Russian).
9. Druzhinin A.V., Vladimirov A.P. Tsvetkova E.V. Theoretical bases of magnetooptical refractometry for transparent media. Diagnostics, Resource and Mechanics of materials and structures, 2018, iss. 6, pp. 83–89. DOI: 10.17804/2410-9908.2018.6.083-089. URL: https://dream-journal.org/DREAM_Issue_6_2018_Druzhinin_A.V._et_al._083_089.pdf
10. Gerrard A., Burch J.M. Vvedenie v matrichnuyu optiku [Introduction to matrix methods in optics, Rus. transl.]. Moscow, Mir Publ., 1978, 343 p. (In Russian).
11. Rumer Yu.B. Spinornyy analiz [Spinor analysis]. Leningrad, ONTI NKTP SSSR, 1936, 105 p.
12. Druzhinin A.V., Druzhinina T.V. Electrodynamic criterion of solid stability. Vestnik UGTU–UPI, 2006, No. 11 (82), pp. 63–65.
13. Kantor I.L. and Solodovnikov A.S. Giperkompleksnye chisla [Hypercomplex Numbers]. Moscow, Nauka Publ., 1973.
14. Pontryagin L.S. Obobshcheniya chisel [Generalization of numbers]. Moscow, Nauka Publ., 1986.

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