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Waves in weakly anisotropic 3D inhomogeneous media: quasi-isotropic approximation of geometrical optics

 a,  b,  c
a Space Research Institute, Russian Academy of Sciences, Profsoyuznaya str. 84/32, Moscow, 117997, Russian Federation
b Kamyshin Technological Institute, ul. Lenina 6a, Kamyshin, Volgograd Region, 403850, Russian Federation
c Geophysical Center, Russian Academy of Sciences, ul. Molodezhnaya 3, Moscow, 117296, Russian Federation

The quasi-isotropic approximation (QIA) of geometrical optics is outlined. The main idea of the method is that electromagnetic waves in weakly anisotropic media preserve their transverse structure as they do in isotropic media. Advantages of the QIA are illustrated by considering electromagnetic wave propagation in plasma, a number of optical problems (liquid crystals, hiral media, single mode optical fibres), acoustical problems of weakly anisotropic elastic media, and quantum mechanical polarisation effects of the Stern-Gerlach type. New modifications of the QIA are presented, namely the method of split rays and the synthetic approach, the latter being applicable even for strongly anisotropic media.

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Fulltext is also available at DOI: 10.1070/PU1996v039n02ABEH000131
PACS: 42.15.−i, 42.25.Bs, 42.68.Ay, 92.60.Ta (all)
DOI: 10.1070/PU1996v039n02ABEH000131
URL: https://ufn.ru/en/articles/1996/2/b/
A1996UB80800002
Citation: Kravtsov Yu A, Naida O N, Fuki A A "Waves in weakly anisotropic 3D inhomogeneous media: quasi-isotropic approximation of geometrical optics" Phys. Usp. 39 129–154 (1996)
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Оригинал: Кравцов Ю А, Найда О Н, Фуки А А «Волны в слабоанизотропных трехмернонеоднородных средах: квазиизотропное приближение геометрической оптики» УФН 166 141–167 (1996); DOI: 10.3367/UFNr.0166.199602b.0141

References (120) ↓ Cited by (49) Similar articles (20)

  1. Budden K G Proc. Roy. Soc. A 215 215 (1952)
  2. Budden K G Radio Waves in the Ionosphere (Cambridge: Cambridge Univ. Press, 1961)
  3. Ginzburg V L Elektromagnitnye Volny v Plazme (Electromagnetic Waves in Plasma, Moscow: Nauka, 1967)
  4. Davis K Ionospheric Radio Waves (Wallham Mass: Blaisdell, 1969)
  5. Zheleznyakov V V Rasprostranenie Elektromagnitnykh Voln v Kosmicheskoi Plazme (Propagation of Electromagnetic Waves in a Cosmic Plasma, Moscow: Nauka, 1977)
  6. Cheng X A, Fung Z Astrophys. and Space Sci. 49 367 (1977); 50 361 (1977)
  7. Oldano C Phys. Rev. 31 1014 (1985)
  8. Zheleznyakov V V, Kocharovskii V V, Kocharovskii Vl V Usp. Fiz. Nauk 141 257 (1983) [Sov Phys.Uspekhi 26 877 (1983)]
  9. Kravtsov Yu A Dokl. Akad. Nauk SSSR 183 74 (1968) [Sov. Phys. Dokl.]
  10. Courant R, Lax P D Proc. Nat. Acad. US 42 872 (1956)
  11. Lax P D Duke Math. J. 24 627 (1957)
  12. Courant R Partial Differential Equations [Translated into Russian (Moscow: Mir, 1964)]
  13. Rytov S M Dokl. Akad. Nauk SSSR 18 263 (1938) [Compt. Rend. de l’Acad. des Sci. USSR 18 263 (1938)]
  14. Naida O N Izv. Vyssh. Uchebn. Zaved. Ser. Radiofiz. 13 1497 (1970)
  15. Naida O N Izv. Vyssh. Uchebn. Zaved. Ser. Radiofiz. 14 1843 (1971)
  16. Naida O N Izv. Vyssh. Uchebn. Zaved. Ser. Radiofiz. 15 751 (1972)
  17. Naida O N Izv. Vyssh. Uchebn. Zaved. Ser. Radiofiz. 17 896 (1974)
  18. Naida O N Izv. Vyssh. Uchebn. Zaved. Ser. Radiofiz. 20 383 (1977)
  19. Naida O N Radiotekh. Electronika 23 2489 (1978)
  20. Naida O N Izv. Vyssh. Uchebn. Zaved. Ser. Radiofiz. 17 1833 (1974)
  21. Naida O N Dokl. Akad. Nauk SSSR 236 842 (1977) [Sov. Phys. Dokl. 22 575 (1977)]
  22. Naida O N Akust. Zh. 24 731 (1978) [Sov. Phys. Acoust. 24 410 (1978)]
  23. Naida O N, Prudkovskii A G Yad. Fiz. 28 1560 (1978) [Sov. J. Nucl. Phys.]
  24. Kravtsov Yu A, Naida O N Zh. Eksp. Teor. Fiz. 71 237 (1976) [Sov. Phys. JETP 44 122 (1976)]
  25. Fuki A A, Preprint VINITI 4136-B87 (Moscow: VINITI, 1987)
  26. Tokar’ V G, Rubinshtein L I, Nikitin M A Izv. Vyssh. Uchebn. Zaved. Ser. Radiofiz. 30 36 (1987) [Radiophys. Quant. Electron. 30 29 (1987)]
  27. Goryshnik L L, Kravtsov Yu A Geomagn. Aeronomiya9 279 (1969) [Geomagn. Aeronomy 9 223 (1969)]
  28. Fuki A A, Preprint RTI AN SSSR No 881 (Moscow: RTI AN SSSR, 1988)
  29. Apresyan L A Astron. Zh. 53 53 (1976) [Sov. Astron. 20 29 (1976)]
  30. Apresyan L A, Kravtsov Yu A Teoriya Perenosa Izlucheniya (Radiation Transfer Theory, Moscow: Nauka, 1983)
  31. Naida O M Zh. Eksp. Teor. Fiz. 77 471 (1979) [Sov. Phys. JETP 50 239 (1979)]
  32. Zheleznyakov V V, Kocharovskii V V, Kocharovskii Vl V Zh. Eksp. Teor. Fiz. 79 1735 (1980) [Sov. Phys. JETP 52 877 (1980)]
  33. Pauli W Helv. Phys. Acta 5 179 (1932)
  34. Galanin A D J. Phys. of USSR 6 35 (1942)
  35. Rubinow S J, Keller J B Phys. Rev. 131 2789 (1963)
  36. Akhiezer A I, Berestetskii V B Kvantovaya Electrodinamika (Quantum Electrodynamics, Moscow: Nauka, 1981)
  37. Kravtsov Yu A Geometrical Optics of Inhomogeneous Media (Berlin, New York: Springer-Verlag, 1989)
  38. Landau L D, Lifshitz E M Electrodynamics of Continuous Media (New York, London: Pergamon Press, 1984); Kucherenko V V Izv. Akad. Nauk SSSR Ser. Matem. 38 625 (1974)
  39. Landau L D, Lifshitz E M Quantum Mechanics (New York: Pergamon Press, 1977)
  40. Erokhin N S, Moiseev S S Usp. Fiz. Nauk 109 225 (1973) [Sov. Phys. Uspekhi 16 64 (1973)]
  41. Katsenelenbaum B Z Teoriya Neregulyarnykh Volnovodov s Medlenno Menyayushchimisya Parametrami (Theory of Irregular Waveguides with Slowly Varying Parameters, Moscow: Izd. Akad. Nauk SSSR, 1961)
  42. Wasow W Asymptotic Expansions for Ordinary Differential Equations (New York: Interscience, 1966) [Translated into Russian (Moscow: Mir, 1968)]
  43. Kravtsov Yu A, Orlov Yu I Usp. Fiz. Nauk 132 475 (1980) [Sov. Phys. Uspekhi 23 750 (1980)]
  44. Kravtsov Yu A, in Progress in Optics (Amsterdam: Nord Holland, 1987)
  45. Apresyan L A, Kravtsov Yu A, Yashin Yu Ya, Yashnov V A Izv. Vyssh. Uchebn. Zaved. Ser. Radiofiz. 19 1296 (1976)
  46. Cohen M H Astrophys. J. 131 664 (1960)
  47. Melrose D B Austral. J. Phys. 27 31 (1974)
  48. Zheleznyakov V V, Zlotnik E Ya Astron. Zh. 40 633 (1963)
  49. Titheridge J E J. Atm. Terr. Phys. 33 1533 (1971)
  50. Kantor I J, Rai D B, De Mendoca F IEEE Trans. Ant. Prop. AP-19 246 (1978)
  51. Zheleznyakov V V, Zlotnik E Ya Izv. Vyssh. Uchebn. Zaved. Ser. Radiofiz. 20 1444 (1977)
  52. Goryshnik L L et al. Geomagn. Aeronomiya 9 873 (1969) [Geomagn. Aeronomy 9 813 (1969)]
  53. Kharitonova R Yu, Fuki A A, Bukatov M D, in Radiololokatsionnye Metody v Radiofizicheskikh Issledovaniyakh (Radio-location Methods in Radiophysical Research, Moscow: RTI Akad. Nauk SSSR, 1989) p. 76
  54. Zheleznyakov V V Radioizluchenie Solntsa i Planet (Radiowaves from the Sun and Planets, Moscow: Nauka, 1964)
  55. Kocharovskii V V, Kocharovskii Vl V Fizika Plazmy 6 565 (1980)
  56. Stepanov N S, Gavrilenko V G Dokl. Akad. Nauk SSSR 201 577 (1971) [Sov. Phys. Dokl.]
  57. Gavrilenko V G, Lupanov G A, Stepanov N S Izv. Vyssh. Uchebn. Zaved. Ser. Radiofiz. 15 183 (1972)
  58. Gavrilenko V G, Stepanov N S Astron. Zh. 53 291 (1976) [Sov. Astron. 20 (2) 165 (1976)]
  59. Kravtsov Yu A, Kugushev A I, Chernykh A V Zh. Eksp. Teor. Fiz. 59 2160 (1970) [Sov. Phys. JETP 32 1168 (1971)]
  60. Kertes I N et al. Zh. Eksp. Teor. Fiz. 59 1115 (1970) [Sov. Phys. JETP 32 606 (1971)]; Foster J D, Osterink L M J. Appl. Phys. 41 3656 (1970)
  61. Ginzburg V L Zh. Tekhn. Fiz. 14 181 (1944)
  62. Suvorov E V Izv. Vyssh. Uchebn. Zaved. Ser. Radiofiz. 15 1320 (1972)
  63. Bellyustin N S Izv. Vyssh. Uchebn. Zaved. Ser. Radiofiz. 23 133 (1980)
  64. Zheleznyakov V V, Kocharovskii V V, Kocharovskii Vl V Zh. Eksp. Teor. Fiz. 79 1735 (1980) [Sov. Phys. JETP 52 877 (1980)]
  65. Unger H G Planar Optical Waveguides and Fibres (Oxford: Claredon Press, 1977)
  66. Snyder A W, Love J D Optical Waveguide Theory (London -- New York: Chapman and Hall, 1983)
  67. Fang X S, Lin Z Q J. Lightwave Technology 3 789 (1985)
  68. Smith A M Appl. Opt. 19 2606 (1980)
  69. Ross J N Opt. Quant. Electr. 16 456 (1984)
  70. Itoh K, Saitoh T, Ohtsuka Y J. Lightwave Technology 5 916 (1987)
  71. Chiao R Y, Wu Y-S Phys. Rev. Lett. 57 933 (1986)
  72. Tomita A, Chiao R Y Phys. Rev. Lett. 57 937 (1986)
  73. Chiao R Y et al. Phys. Rev. Lett. 60 1214 (1988)
  74. Tjaden D L Phillips J. Res. 33 254 (1978)
  75. Love J D, Sammut R A Electron. Lett. 15 615 (1979)
  76. Garth S J, Pask C Electron. Lett. 22 27 (1986)
  77. Kaminov I P, Ramaswamy V Appl. Phys. Lett. 34 268 (1979)
  78. Eickhoff W Opt. Lett. 7 629 (1982)
  79. Varnham M P et al. J. Lightwave Technology 1 332 (1983)
  80. Berry M V Proc. Roy. Soc. London Ser. A 392 (1802) 45 (1984); Klyshko D N Usp. Fiz. Nauk 163 1 (1993) [Phys. Uspekhi 36 1005 (1993)]
  81. Kaminow I P IEEE J. Quantum. Electron. 17 15 (1981)
  82. Payne D N, Barlow A J, Ramskov-Hansen J J IEEE J. Quantum. Electron. 18 477 (1982)
  83. Rashleigh S C, Stolen R H Laser Focus 19 (5) 155 (1983)
  84. Rashleigh S C J. Lightwave Technology 1 312 (1983)
  85. Liberman V S, Zel’dovich B Ya Phys. Rev. A 46 5199 (1992)
  86. Dooghin A V, Kundikova N D, Liberman V S, Zel’dovich B Ya Phys. Rev. A 45 8204 (1992)
  87. Maker P D, Terhune R W, Savage C M Phys. Rev. Lett. 12 (18) 507 (1964)
  88. Akhmanov S A, Zharikov V I Pis’ma Zh. Eksp. Teor. Fiz. 6 644 (1967) [JETP Lett. 6 137 (1967)]
  89. Kaplan A E Opt. Lett. 8 560 (1983)
  90. Dyshman M I, Tarasov G G Zh. Eksp. Teor. Fiz. 72 2246 (1977) [Sov. Phys. JETP 45 1181 (1977)]
  91. Gibbs H M Optical Bistability: Controlling Light with Light (New York: Acad. Press, 1985)
  92. Arakelyan S M, Lyakhov G A, Chilingaryan Yu S Usp. Fiz. Nauk 131 3 (1980) [Sov. Phys. Uspekhi 23 245 (1980)]
  93. Zheludev N I Usp. Fiz. Nauk 157 683 (1989) [Sov. Phys. Uspekhi 32 357 (1989)]
  94. Evans M W Phys. Lett. A 147 364 (1986)
  95. Evans M W Phys. Rev. Lett. 64 2909 (1990)
  96. Levin M L, Rytov S M Akust. Zh. 2 173 (1956)
  97. Karal F C, Keller J B J. Accoust. Soc. Amer. 31 694 (1959)
  98. Babich V M, in Voprosy Dinamicheskoi Teorii Rasprostraneniya Seismicheskikh Voln (Questions of Dynamic Theory of Seismic Waves, Leningrad: Leningrad Univ. Press, 1961) No. 5, p. 36
  99. Cerveny V Geophys. J. R. Astron. Soc. 29 1 (1972)
  100. Cerveny V, Psencik J Z. Geophys. 38 (3) 565 (1972)
  101. Cerveny V, Molotkov I A, Psencik J Ray Method in Seismology (Praha: Univerzita Karlova, 1977)
  102. Landau L D, Lifshitz E M Theory of Elasticity 2nd edition (Oxford: Pergamon Press, 1970)
  103. Toupin R A, Bernstein B J. Acoust. Soc. Amer. 33 216 (1961)
  104. Murnaghan F D Finite Deformation of an Elastic Solid (New York: Wiley, 1951)
  105. Blackman D K, Orcutt J A, Forsyth D W, Kendall J-M Nature (London) 366 675 (1993)
  106. Romp J T Nature (London) 366 678 (1994)
  107. Miyano K, Ketterson J B, in Physical Acoustics (New York: Acad. Press, 1979) p. 93
  108. De Broglie L La Theorie des Particles de Spin 1/2 (Paris, 1952)
  109. Schiller R Phys. Rev. 125 1116 (1962)
  110. Schiller R Phys. Rev. 128 1402 (1962)
  111. Stern O Z. Phys. 7 249 (1921)
  112. Gerlach W, Stern O Z. Phys. 8 110 (1921)
  113. Gerlach W, Stern O Z. Phys. 9 349 (1922)
  114. Gerlach W, Stern O Z. Phys. 9 353 (1922)
  115. Gerlach W, Stern O Ann. Phys. 74 673 (1924)
  116. Frish R, Segre E Z. Phys. 80 610 (1933)
  117. Rabi I I Phys. Rev. 49 324 (1936)
  118. Motz L, Rose M E Phys. Rev. 50 348 (1936)
  119. Li X, Strahler A H IEEE Trans. GE-24 908 (1986)
  120. Vacek R "Chirality in nonlinear media" PIERS’95. July 24-28 1995. Seattle WA

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