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Statistical Properties of Laser Light

  • Chapter
The Fokker-Planck Equation

Part of the book series: Springer Series in Synergetics ((SSSYN,volume 18))

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Abstract

The Fokker-Planck equation has become a very useful tool for treating noise in quantum optics. In this chapter we investigate noise in a laser, which is the most important device in quantum optics. This subject together with other applications of the Fokker-Planck equation in quantum optics are already treated in a number of handbooks, books and review articles [12.1 – 13, 1.28, 4.81. The main purpose of this chapter is to demonstrate how some of the methods of Chaps. 2–9 can be applied to a simple laser model (one mode, adiabatic elimination of all variables with the exception of the laser field, threshold region). The following two points make it difficult but also interesting to investigate the statistical properties of laser light.

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References

  1. H. Haken: Laser Theory, Encylopedia of Physics, Vol. XXV/2c (Springer, Berlin, Heidelberg, New York 1970)

    Google Scholar 

  2. F. T. Arecchi, E. O. Schulz-Dubois (eds.): Laser Handbook (North-Holland, Amsterdam 1972)

    Google Scholar 

  3. M. Sargent III, M. O. Scully, W. E. Lamb: Laser Physics (Addison-Wesley, Reading, MA 1974)

    Google Scholar 

  4. A. Yariv: Quantum Electronics (Wiley, New York 1967)

    Google Scholar 

  5. B. Saleh: Photoelectron Statistics, Springer Ser. Opt. Sci., Vol. 6 (Springer, Berlin, Heidelberg, New York 1978)

    Google Scholar 

  6. H. Haken: Licht und Materie II (Bibliographisches Institut, Mannheim 1981)

    Google Scholar 

  7. M. Lax: 1966 Brandeis University Summer Institute in Theoretical Physics (Gordon and Breach, New York 1968)

    Google Scholar 

  8. H. Risken: Fortschr. Physik 16, 261 (1968)

    Article  Google Scholar 

  9. H. Risken: Progress in Optics 8 (North-Holland, Amsterdam 1970) p. 239

    Google Scholar 

  10. S. M. Kay, A. Maitland (eds.): Quantum Optics (Academic, London 1970)

    Google Scholar 

  11. J. Perina: Coherence of Light (Van Nostrand Reinhold, London 1971)

    Google Scholar 

  12. R. Graham: In Fluctuations, Instabilities, and Phase Transitions, ed. by T. Riste (Plenum, New York 1975)

    Google Scholar 

  13. V. Dohm: Phasenübergänge und Chaos im Laser, Ferienkurs über nichtlineare Dynamik in kondensierter Materie, Kernforschungsanlage, Julien (1983)

    Google Scholar 

  14. B. Van der Pol: Phil. Mag 3, 65 (1927)

    Google Scholar 

  15. J. W. S. Rayleigh: Theory of Sound, Vol. 1 (1894), reprint (Dover, New York 1945)

    MATH  Google Scholar 

  16. H. Haken: Z. Physik 181, 96 (1964)

    Article  ADS  Google Scholar 

  17. H. Risken: Z. Physik 186, 85 (1965) (a) and 191, 302 (1966) (b)

    Article  ADS  Google Scholar 

  18. 191, 302 (1966)

    Article  MathSciNet  ADS  Google Scholar 

  19. H. Risken, H. D. Vollmer: Z. Physik 201, 323 (1967)

    Article  ADS  Google Scholar 

  20. H. Risken, H. D. Vollmer: Z. Physik 204, 240 (1967)

    Article  ADS  Google Scholar 

  21. R. D. Hempstead, M. Lax: Phys. Rev. 161, 350 (1967)

    Article  ADS  Google Scholar 

  22. J. P. Gordon, E. W. Aslaksen: IEEE J. QE-6, 428 (1970)

    Article  Google Scholar 

  23. F. T. Arecchi, V. Degiorgio: Phys. Rev. A3, 1108 (1971)

    ADS  Google Scholar 

  24. M. Suzuki: Prog. Theor. Phys. 56, 77 (1976) and 56, 477 (1976)

    Article  ADS  MATH  Google Scholar 

  25. M. Suzuki: Physica A86, 622 (1977) and T. Arimitsu, M. Suzuki: Physica A90, 303 (1978)

    ADS  Google Scholar 

  26. F. Haake: Phys. Lett. 41, 1685 (1978)

    Article  Google Scholar 

  27. S. Grossmann: Phys. Rev. A17, 1123 (1978)

    ADS  Google Scholar 

  28. F. De Pasquale, P. Tartaglia, P. Tombesi: Physica A99, 581 (1979)

    ADS  Google Scholar 

  29. H. King, U. Deker, F. Haake: Z. Physik B36, 205 (1979)

    ADS  Google Scholar 

  30. K. Ziegler, H. Homer: Z. Physik B37, 339 (1980)

    ADS  Google Scholar 

  31. H. Risken, H. D. Vollmer: Z. Physik B39, 89 (1980)

    MathSciNet  ADS  Google Scholar 

  32. J. Fiutak, J. Mizerski: Z. Physik B39, 347 (1980)

    ADS  Google Scholar 

  33. T. Arimitsu: Physica 107A, 71 (1981)

    ADS  Google Scholar 

  34. J. Mizerski: Z. Physik B49, 173 (1982)

    ADS  Google Scholar 

  35. R. L. Stratonovich: Topics in the Theory of Random Noise, Vol. II (Gordon and Breach, New York 1967) Chap. 5

    MATH  Google Scholar 

  36. H. Haken, H. Risken, W. Weidlich: Z. Physik 206, 355 (1967)

    Article  ADS  Google Scholar 

  37. M. Lax: Phys. Rev. 157, 213 (1967)

    Article  MathSciNet  ADS  Google Scholar 

  38. M. Lax, W. H. Louisell: IEEE J. QE-3, 47 (1967)

    Article  Google Scholar 

  39. M. O. Scully, W. E. Lamb: Phys. Rev. 159, 208 (1967)

    Article  ADS  Google Scholar 

  40. J. P. Gordon: Phys. Rev. 161, 367 (1967)

    Article  ADS  Google Scholar 

  41. A. W. Smith, J. A. Armstrong: Phys. Rev. Lett. 16, 1169 (1966)

    Article  ADS  Google Scholar 

  42. J. A. Armstrong, A. W. Smith: Progress in Optics 6, 211 (North-Holland, Amsterdam 1967)

    Google Scholar 

  43. F. T. Arecchi, G. S. Rodari, A. Sona: Phys. Lett. 25A, 59 (1967) (a)

    ADS  Google Scholar 

  44. F. T. Arecchi, M. Giglio, A. Sona: Phys. Lett. 25A, 341 (1967) (b);

    ADS  Google Scholar 

  45. F. T. Arecchi, V. Degiorgio, B. Querzola: Phys. Rev. Lett. 19, 1168 (1967) (c)

    Article  ADS  Google Scholar 

  46. F. Davidson, L. Mandel: Phys. Lett. 25A, 700 (1967)

    ADS  Google Scholar 

  47. R. F. Chang, V. Korenman, C. O. Alley, R. W. Detenbeck: Phys. Rev. 178, 612 (1969)

    Article  ADS  Google Scholar 

  48. D. Meltzer, L. Mandel: Phys. Rev. A3, 1763 (1971)

    ADS  Google Scholar 

  49. S. Chopra, L. Mandel: IEEE J. QE-8, 324 (1972)

    Article  Google Scholar 

  50. S. Grossmann, P. H. Richter: Z. Physik 249, 43 (1971)

    Article  ADS  Google Scholar 

  51. F. T. Hioe: J. Math. Phys. 19, 1307 (1978)

    Article  MathSciNet  ADS  Google Scholar 

  52. F. T. Hioe, S. Singh: Phys. Rev. A24, 2050 (1981)

    ADS  Google Scholar 

  53. R. K. Wangsness, F. Bloch: Phys. Rev. 89, 728 (1953)

    Article  ADS  MATH  Google Scholar 

  54. A. L. Schawlow, C. H. Townes: Phys. Rev. 112, 1940 (1958)

    Article  ADS  Google Scholar 

  55. R. Graham: Phys. Rev. 25A, 3234 (1982)

    ADS  Google Scholar 

  56. K. Seybold, H. Risken: Z. Physik 267, 323 (1974)

    Article  ADS  Google Scholar 

  57. M. Born, E. Wolf: Principles of Optics (Pergamon, London 1964)

    Google Scholar 

  58. L. Mandel, E. Wolf: Phys. Rev. 124, 1696 (1961)

    Article  ADS  MATH  Google Scholar 

  59. H. Gerhardt, H. Welling, A. Güttner: Z. Physik 253, 113 (1972)

    Article  ADS  Google Scholar 

  60. F. Haake, J. W. Haus, R. Glauber: Phys. Rev. A23, 3255 (1981)

    MathSciNet  ADS  Google Scholar 

  61. M. Mangel: Phys. Rev. A24, 3226 (1981)

    MathSciNet  ADS  Google Scholar 

  62. U. Weiss: In Chaos and Order in Nature, ed. by H. Haken, Springer Ser. Synergetics, Vol. 11, (Springer, Berlin, Heidelberg, New York 1981) p. 177

    Google Scholar 

  63. L. Mandel: Proc. Phys. Soc. 72, 1037 (1958)

    Article  ADS  Google Scholar 

  64. L. Mandel: Progress in Optics 2, 181 (North-Holland, Amsterdam 1963)

    MATH  Google Scholar 

  65. P. L. Kelley, W. H. Kleiner: Phys. Rev. 136A, 316 (1964)

    Article  MathSciNet  ADS  Google Scholar 

  66. M. Lax, M. Zwanziger: Phys. Rev. Lett. 24, 937 (1970)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Abteilung für Theoretische Physik, Universität Ulm, Oberer Eselsberg, D-7900, Ulm, Fed. Rep. of Germany

    Professor Dr. Hannes Risken

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  1. Professor Dr. Hannes Risken
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© 1984 Springer-Verlag Berlin Heidelberg

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Risken, H. (1984). Statistical Properties of Laser Light. In: The Fokker-Planck Equation. Springer Series in Synergetics, vol 18. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-96807-5_12

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  • DOI: https://doi.org/10.1007/978-3-642-96807-5_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-96809-9

  • Online ISBN: 978-3-642-96807-5

  • eBook Packages: Springer Book Archive

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