Issues

 / 

1980

 / 

November

  

Reviews of topical problems


Limits of applicability of the method of geometric optics and related problems

 a,
a Space Research Institute, Russian Academy of Sciences, Profsoyuznaya str. 84/32, Moscow, 117997, Russian Federation

We present on a heuristic basis the universal sufficient conditions for applicability of the method of geometric optics. In formulating the criteria, we make essential use of the concept of the ``Fresnel volume'' of a ray, whose boundary links the first Fresnel zones ``threaded'' on the ray. The fundamental criterion of applicability requires that the parameters of the medium and of the wave should vary little over the transverse section of the Fresnel volume. The second criterion, which stems from the first, requires that rays incident on the same given point should lie mostly outside the Fresnel volume of an adjacent ray. The effectiveness of these criteria has been demonstrated in many problems of electrodynamics and acoustics that allow a solution more precise than the ray solution. On the basis of the presented criteria, one can reveal the regions of inapplicability of the ray method (focal and caustic regions, penumbra regions in diffraction by screens and convex bodies, regions where lateral waves arise, etc.). If we know the dimensions of the regions of inapplicability, we can also solve a number of related problems. The most important of these problems are: the problem of determining the field in the neighborhood of caustics and foci and the problem of analyzing the wave pattern as a whole. The proposed criteria also allow a generalization to three-dimensional quantummechanical problems, while outlining the limits of applicability of the quasiclassical approximation.

Fulltext pdf (1.2 MB)
Fulltext is also available at DOI: 10.1070/PU1980v023n11ABEH005060
PACS: 42.10.Dy
DOI: 10.1070/PU1980v023n11ABEH005060
URL: https://ufn.ru/en/articles/1980/11/c/
Citation: Kravtsov Yu A, Orlov Yu I "Limits of applicability of the method of geometric optics and related problems" Sov. Phys. Usp. 23 750–762 (1980)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Кравцов Ю А, Орлов Ю И «Границы применимости метода геометрической оптики и смежные вопросы» УФН 132 475–496 (1980); DOI: 10.3367/UFNr.0132.198011c.0475

Cited by (45) ↓ Similar articles (20)

  1. Knizhin S I, Tinin M V Radiophys Quantum El 65 668 (2023)
  2. Butyrskiy E Theoretical foundations of hydroacoustics and ocean acoustics 1 (2022)
  3. Minin O V, Minin I V Photonics 8 591 (2021)
  4. Khirianova A, Parkevich E et al Opt. Express 29 14941 (2021)
  5. Moeini S, Memoli G, Subramanian S J. Phys.: Conf. Ser. 1461 012107 (2020)
  6. Maj O, Mariani A et al 20 (4) (2013)
  7. Dean C E, Parker K 131 2459 (2012)
  8. Bertelli N, Maj O et al 19 (8) (2012)
  9. Fleischer K, Arca E, Shvets I V Solar Energy Materials And Solar Cells 101 262 (2012)
  10. Frolov V P, Shoom A A Phys. Rev. D 84 (4) (2011)
  11. Afanasiev A N Sol Phys 261 295 (2010)
  12. Rypina I I, Brown M G 122 1440 (2007)
  13. Kravtsov Yu A, Zhu N Ya Wave Motion 43 206 (2006)
  14. Poli E, Peeters A G, Pereverzev G V Computer Physics Communications 136 90 (2001)
  15. Poli E, Pereverzev G V et al Fusion Engineering And Design 53 9 (2001)
  16. Kravtsov Yu A, Orlov Yu I Springer Series On Wave Phenomena Vol. Caustics, Catastrophes and Wave FieldsRays and Caustics15 Chapter 2 (1999) p. 8
  17. Marston P L 102 1628 (1997)
  18. Kravtsov Yu A, Naida O N, Fuki A A Uspekhi Fizicheskikh Nauk 166 141 (1996)
  19. Nishiyama Y J. Opt. Soc. Am. A 12 1390 (1995)
  20. Asatryan A A, Kravtsov Yu A Wave Motion 19 1 (1994)
  21. Clarke T J 115 421 (1993)
  22. Kravtsov Yu A, Orlov Yu I Springer Series On Wave Phenomena Vol. Caustics, Catastrophes and Wave FieldsTypical Integrals of Catastrophe Theory15 Chapter 4 (1993) p. 48
  23. Kravtsov Yu A, Orlov Yu I Springer Series On Wave Phenomena Vol. Caustics, Catastrophes and Wave FieldsRays and Caustics15 Chapter 2 (1993) p. 8
  24. MARSTON PHILIP L Physical Acoustics Vol. 21 (1992) p. 1
  25. Kim W, Cormier V F 103 639 (1990)
  26. Fradkin L Ju J. Opt. Soc. Am. A 6 1315 (1989)
  27. Beydoun W B, Mendes M 97 151 (1989)
  28. Virovlyanskii A L, Kosterin A G Radiophys Quantum Electron 32 360 (1989)
  29. Cormier V F J. Geophys. Res. 94 3006 (1989)
  30. Kravtsov Yu A Progress In Optics Vol. 26 (1988) p. 227
  31. Asatryan A A, Kravtsov Yu A Wave Motion 10 45 (1988)
  32. Borovikov V A, Kinber B E Radiophys Quantum Electron 30 902 (1987)
  33. Frank A I Uspekhi Fizicheskikh Nauk 151 229 (1987)
  34. Cormier V F Geophysical Journal International 87 1159 (1986)
  35. Solimeno S, Crosignani B, DiPorto P Guiding, Diffraction, and Confinement of Optical Radiation (1986) p. 316
  36. Yomogida K, Aki K J. Geophys. Res. 90 7665 (1985)
  37. Yomogida K Geophysical Journal International 82 511 (1985)
  38. Brodsky A M, Urbakh M I Progress In Surface Science 15 121 (1984)
  39. Orlov Yu I, Fedorov N N Radiophys Quantum Electron 27 794 (1984)
  40. Nowack R, Aki K J. Geophys. Res. 89 7797 (1984)
  41. Cormier V F, Spudich P Geophysical Journal International 79 135 (1984)
  42. Dargeiko M M, Kravtsov Yu A et al Radiophys Quantum Electron 27 516 (1984)
  43. Brambilla M Heating in Toroidal Plasmas 1982 (1982) p. 505
  44. Orlov Yu I Radiophys Quantum Electron 25 486 (1982)
  45. Kravtsov Yu A, Orlov Yu I Radiophys Quantum Electron 25 582 (1982)

© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions