Fedorov’s Covariant Methods in the Electromagnetic Field Theory

Creation, progress and trends of development
  • L. M. Barkovskii
  • G. N. Borzdov
Part of the NATO ASI Series book series (ASHT, volume 28)


Fedor Ivanovich Fedorov, the well-known theoretical and mathematical physicist, Professor of the Byelorussian State University (BSU), Academician and Member of the Presidium of Academy of Sciences of the Republic of Belarus and President of the Byelorussian Physical Society has died on October 13th, 1994 in Minsk, Belarus. He devoted more than 60 years of his life to scientific work, pedagogical and scientific organizational activities.


Dielectric Permittivity Magnetic Anisotropy Evolution Operator Anisotropic Medium Crystal Optic 
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  1. 1.
    Pockels, F. (1906) Lehrbuch der Kristalloptik, Teubner, Leipzig and Berlin.zbMATHGoogle Scholar
  2. 2.
    Szivessy, G. (1928) Kristalloptik, in Handbuch der Physik 20, Springer, Berlin.Google Scholar
  3. 3.
    Fedorov, F.I. (1955) On the polarization of electromagnetic waves, Dokl. Akad. Nauk SSSR 102, 69–71.MathSciNetzbMATHGoogle Scholar
  4. 4.
    Fedorov, F.I. (1965) Covariant description of properties of light beams, Zh. Prikl. Spektrosk. 2, 523–533.Google Scholar
  5. 5.
    Fedorov, F.I. (1966) On the beam transformation at the interaction of light with matter, Zh. Prikl. Spektrosk. 4 58–63.Google Scholar
  6. 6.
    Born, M. (1933) Optik, Springer, Berlin.CrossRefGoogle Scholar
  7. 7.
    Fedorov, F.I. (1955) On the theory of total reflection, Dokl. Akad. Nauk SSSR 105, 465–468.MathSciNetzbMATHGoogle Scholar
  8. 8.
    Fedorov, F.I. (1956) The inhomogeneous waves and total reflection, Trudy Inst. Fiz. Mat. Akad. Nauk BSSR No. 1, 11–31.Google Scholar
  9. 9.
    Fedorov, F.I. (1958) Optics of Anisotropic Media, Izd. Akad. Nauk BSSR, Minsk.Google Scholar
  10. 10.
    Fedorov, F.I. (1976) Theory of Gyrotropy, Nauka i Tekhnika, Minsk.Google Scholar
  11. 11.
    Fedorov, F.I. and Filippov, V.V. (1976) Reflection and Refraction of Light by Transparent Crystals, Nauka i Tekhnika, Minsk.Google Scholar
  12. 12.
    Tamir, T. (1972) Inhomogeneous wave types at planar structures: I. The lateral wave, Optik, 36, 209–269.Google Scholar
  13. 13.
    Krinchik, G.S. and Chetkin, M.V. (1961) Exchange interaction and magnetooptical effects in ferrite garnets, Zh. Eksperim. i Teor. Fiz. 41, 673–680.Google Scholar
  14. 14.
    Fedorov, F.I. (1956) “Transfer principle” and the general theory of optical properties of absorbing crystals, Opt. Spektrosk. 1, 807–808.Google Scholar
  15. 15.
    Fedorov, F.I. (1959) On the theory of optical activity of crystals. I, II, Opt. Spektrosk. 6, 85–93, 377–383.Google Scholar
  16. 16.
    Fedorov, F.I. (1972) The theory of optical activity of crystals, Usp. Fiz. Nauk 108, 762–764.CrossRefGoogle Scholar
  17. 17.
    Fedorov, F.I. (1973) On the optics of magnetic gyrotropic crystals, Vestsi Akad. Nauk BSSR, Ser. Fiz. Mat. Nauk No. 5, 70–79.Google Scholar
  18. 18.
    Fedorov, F.I. (1974) Plane waves in gyrotropic crystals, Vestsi Akad. Nauk BSSR, Ser. Fiz. Mat. Nauk No. 1, 48–54.Google Scholar
  19. 19.
    Ginzburg, V.L. (1972) Development of crystal optics with taking into account of spatial dispersion, Usp. Fiz. Nauk 108, 749–752.CrossRefGoogle Scholar
  20. 20.
    Agranovich, V.M. and Ginzburg, V.L. (1972) On the phenomenological electrodynamics of gyrotropic media, Zh. Eksperim. i Teor. Fiz. 63, 838–843.Google Scholar
  21. 21.
    Agranovich, V.M. and Yudson, V.I. (1973) On the phenomenological electrodynamics of gyrotropic media, Opt. Commun. 9, 58–60.CrossRefGoogle Scholar
  22. 22.
    Bokut, B.V., Serdyukov, A.N., and Fedorov, F.I. (1973) On the occasion of the article of V.M. Agranovich “On the phenomenological electrodynamics of gyrotropic media”, Zh. Prikl. Spektrosk. 19, 377–380.Google Scholar
  23. 23.
    Fedorov, F.I. (1968) Theory of Elastic Waves in Crystals, Plenum Press, New York.CrossRefGoogle Scholar
  24. 24.
    Fedorov, F.I. (1979) Lorentz Group, Nauka, Moscow.zbMATHGoogle Scholar
  25. 25.
    Voigt, W. (1902) Weiteres zur Aufklärung der Eigenschaften pleochroitischer Krystalle, Gött. Nachr. 5, 269–277.Google Scholar
  26. 26.
    Fedorov, F.I. and Petrov, N.S. (1963) Special case of inhomogeneous electromagnetic waves in transparent crystals, Opt. Spektrosk. 14, 256–261.Google Scholar
  27. 27.
    Petrov, N.S. and Fedorov, F.I. (1963) New type of plane electromagnetic waves in absorbing crystals, Opt. Spektrosk. 15, 792–796.Google Scholar
  28. 28.
    Fedorov, F.I., Petrov, N.S. and Filippov, V.V. (1985) Special waves in transparent biaxial crystals, Zh. Prikl. Spektrosk. 42, 844–849.Google Scholar
  29. 29.
    Barkovskii, L.M., Borzdov, G.N. and Fedorov, F.I. (1975) Impedance of a plane electromagnetic waves in optically active media, Dokl. Akad. Nauk BSSR 19, 305–308.Google Scholar
  30. 30.
    Barkovskii, L.M. and Borzdov, G.N. (1975) Tensor impedance and transformation of light beams by systems of anisotropic layers. I. Normal incidence, Opt. Spektrosk. 39, 150–154.Google Scholar
  31. 31.
    Barkovskii, L.M. (1975) One-dimensional wave equation of electrodynamics of in-homogeneous anisotropic media and an operator method for its solution, Zh. Prikl. Spektrosk. 23, 304–309.Google Scholar
  32. 32.
    Barkovskii, L.M. (1976) On the tensor of refractive indices in crystal optics, Kristalhgrafiya 21, 445–449.Google Scholar
  33. 33.
    Barkovskii, L.M. (1979) Spectral expansions of operators of refractive indices in crystals, Zh. Prikl. Spektrosk. 30, 115–123.Google Scholar
  34. 34.
    Fedorov, F.I., Barkovskii, L.M. and Borzdov, G.N. (1982) Tensor dispersive equations, Dokl. Akad. Nauk BSSR 26, 684–687.zbMATHGoogle Scholar
  35. 35.
    Barkovskii, L.M., Borzdov, G.N. and Fedorov, F.I. (1983) Operator phases and non harmonic optical fields in crystals, Zh. Prikl. Spektrosk. 39, 996–1000.Google Scholar
  36. 36.
    Barkovskii, L.M., Borzdov, G.N. and Lavrinenko, A.V. (1987) Fresnel’s reflection and transmission operators for stratified gyroanisotropic media, J. Phys. A20, 1095–1106.Google Scholar
  37. 37.
    Borzdov, G.N. (1990) Evolution operators of electromagnetic waves in crystals. I–III, Kristallografiya 35, 535–558.MathSciNetGoogle Scholar
  38. 38.
    Barkovskii, L.M. and Sharapaeva, V. (1996) Local and global involutive algebras in the problem of light propagation, Opt. Spektrosk. 80, 789–798.Google Scholar
  39. 39.
    Gourant, R. (1962) Partial Differential Equations, New York-London.Google Scholar
  40. 40.
    Barkovskii, L.M., Borzdov, G.N. and Fedorov, F.I. (1990) Evolution operators in the electrodynamics of spatially dispersive media, J. Mod. Opt. 37, 85–97.MathSciNetCrossRefGoogle Scholar
  41. 41.
    Borzdov, G.N. (1992) Lorentz-covariant surface impedance and characteristic matrix methods with applications to measurements of material parameters of linear media, Opt. Commun. 94, 159–174.CrossRefGoogle Scholar
  42. 42.
    Borzdov, G.N. (1993) An intrinsic tensor technique in Minkowski space with applications to boundary value problems, J. Math. Phys. 34, 3162–3196.MathSciNetzbMATHCrossRefGoogle Scholar
  43. 43.
    Borzdov, G.N. (1996) Waves with linear, quadratic and cubic coordinate dependence of amplitude in crystals, Pramana-journal of physics 46, 245–257.CrossRefGoogle Scholar
  44. 44.
    Barkovskii, L.M., Borzdov, G.N., Zhilko, V.V., Lavrinenko, A.V., Borzdov, A.N., Fedorov, F.I. and Kamach, Yu.E. (1996) The impedance operator method for calculation of electro-optic systems for control laser radiation. I–III, J. Phys. D29, 289–306.Google Scholar
  45. 45.
    Barkovskii, L.M. and Hang, F.T.N. (1990) Tensor of eikonal in geometrooptical approximations for anisotropic media, Opt. Spektrosk. 68, 670–674.Google Scholar
  46. 46.
    Barkovskii, L.M. and Hang, F.T.N. (1991) Cauchy operators and ray operators in geometrooptics of anisotropic media, Opt. Spektrosk. 70, 61–64.Google Scholar
  47. 47.
    Semchenko, I.V., Tretyakov, S.A. and Serdyukov, A.N. (1996) Research on chiral and bianisotropic media in Byelorussia and Russia in the last ten years, Progress in Electromagnetic Research PIER12, 335–370.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1997

Authors and Affiliations

  • L. M. Barkovskii
    • 1
  • G. N. Borzdov
    • 1
  1. 1.Department of Theoretical PhysicsByelorussian State UniversityMinskBelarus

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