Advertisement

Zeitschrift für Physik B Condensed Matter

, Volume 38, Issue 4, pp 365–380 | Cite as

Analytic description of optical bistability including spatial effects

  • H. I. Carmichael
  • J. A. Hermann
Article

Abstract

Steady-state features for both absorptive and dispersive bistability are obtained analytically with the inclusion of spatial effects. Both Fabry-Perot and ring-cavity geometries are treated using an analytic integration of coupled field equations for counter-propagating waves in a homogeneously broadened two-level medium. The mean-field limit is rigorously introduced starting from exact solutions. Mean-field state equations for both Fabry-Perot and ring cavities are obtained. In the former case explicit comparisons are made with results arising in the approximate treatment of standing waves.

Keywords

Neural Network Exact Solution Analytic Description Field Equation State Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1a.
    Seidel, J.: U.S. Patent no. 3610731Google Scholar
  2. 1b.
    Szöke, A., Daneu, V., Goldhar, J., Kurnit, N.A.: Appl. Phys. Lett.15, 376 (1969)Google Scholar
  3. 1c.
    Austin, J.W., De Shazer, L.G.: J. Opt. Soc. Am.61, 650 (1971)Google Scholar
  4. 1d.
    Spiller, E.: J. Opt. Soc. Am.61, 699 (1971); J. Appl. Phys.43, 1673 (1972)Google Scholar
  5. 2.
    McCall, S.L.: Phys. Rev. A9, 1515 (1974)Google Scholar
  6. 3a.
    Gibbs, H.M., McCall, S.L., Venkatesan, T.N.C.: Phys. Rev. Lett.36, 1135 (1976)Google Scholar
  7. 3b.
    Venkatesan, T.N.C.: Ph. D. thesis (1977) unpublishedGoogle Scholar
  8. 4a.
    Venkatesan, T.N.C., McCall, S.L.: Appl. Phys. Lett.30, 282 (1977)Google Scholar
  9. 4b.
    McCall, S.L., Gibbs, H.M.: J. Opt. Soc. Am.68, 1378 (1978)Google Scholar
  10. 4c.
    Gibbs, H.M., Venkatesan, T.N.C., McCall, S.L., Passner, A., Gossard, A.C., Wiegmann, W.: Appl. Phys. Lett.34, 511 (1979)Google Scholar
  11. 5a.
    Smith, P.W., Turner, E.H.: Appl. Phys. Lett.30, 280 (1977)Google Scholar
  12. 5b.
    Smith, P.W., Turner, E.H., Mumford, B.B.: Opt. Lett.2, 55 (1978)Google Scholar
  13. 5c.
    Smith, P.W., Turner, E.H., Maloney, P.J.: IEEE J. Quant. Elec. QE14, 207 (1978)Google Scholar
  14. 5d.
    Smith, P.W., Kaminow, I.P., Maloney, P.J., Stulz, L.W.: Appl. Phys. Lett.33, 24 (1978),34, 62 (1979)Google Scholar
  15. 6a.
    Garmire, E., Marburger, J.H., Allen, S.D.: Appl. Phys. Lett.32, 320 (1978)Google Scholar
  16. 6b.
    Garmire, E., Allen, S.D., Marburger, J., Verber, C.M.: Opt. Lett.3, 69 (1978)Google Scholar
  17. 6c.
    Marburger, J.H., Allen, S.D., Garmire, E., Levenson, M., Winful, H.: J. Opt. Soc. Am.,68, 642 (1978)Google Scholar
  18. 6d.
    Garmire, E., Marburger, J.H., Allen, S.D., Winful, H.G.: Appl. Phys. Lett.34, 374 (1979)Google Scholar
  19. 7a.
    Bischofberger, T., Shen, Y.R.: Appl. Phys. Lett.32, 156 (1978); J. Opt. Soc. Am.68, 642 (1978); Phys. Rev. A19, 1169 (1979)Google Scholar
  20. 8.
    Bonifacio, R., Lugiato, L.A.: Opt. Commun.19, 172 (1976)Google Scholar
  21. 9.
    Bonifacio, R., Lugiato, L.A.: Phys. Rev. A18, 1129 (1978)Google Scholar
  22. 10a.
    Bonifacio, A., Lugiato, L.A.: Phys. Rev. Lett.40, 1023 (1978)Google Scholar
  23. 10b.
    Bonifacio, R., Gronchi, M., Lugiato, L.A.: Phys. Rev. A18, 2266 (1978)Google Scholar
  24. 10c.
    Lugiato, L.A.: Nuovo Cimento B50, 89 (1979)Google Scholar
  25. 11a.
    Carmichael, H.J., Walls, D.F.: J. Phys. B10, L685 (1977)Google Scholar
  26. 11b.
    Walls, D.F., Drummond, P.D., Hassan, S.S., Carmichael, H.J.: Prog. of Theor. Phys., Suppl.64, 307 (1978)Google Scholar
  27. 12a.
    Narducci, L.M., Gilmore, R., Feng, Da Hsuang, Agarwal, G.S.: Opt. Lett.2, 88 (1978)Google Scholar
  28. 12b.
    Agarwal, G.S., Narducci, L.M., Gilmore, R., Feng, Da Hsuang: Phys. Rev. A18, 620 (1978)Google Scholar
  29. 13a.
    Willis, C.R.: Opt. Commun.23, 151 (1977). Opt. Commun.26, 62 (1978)Google Scholar
  30. 13b.
    Willis, C.R., Day, J.: Opt. Commun.28, 137 (1979)Google Scholar
  31. 14.
    Bulsara, A.R., Schieve, W.C., Gragg, R.F.: Phys. Lett.68A, 294 (1978)Google Scholar
  32. 15.
    Schenzle, A., Brand, H.: Opt. Commun.27, 485 (1978)Google Scholar
  33. 16.
    See for example the books by Nicolis, G., Prigogine, I.: Self-Organization in non-equilibrium systems. London, New York: Wiley 1977, and Haken, H.: Synergetics. Berlin, Heidelberg, New York: Springer 1977Google Scholar
  34. 17.
    Bonifacio, R., Lugatio, L.A.: Lett. Nuovo Cimento21, 505 (1978)Google Scholar
  35. 18.
    Meystre, P.: Opt. Commun.26, 277 (1978)Google Scholar
  36. 19.
    Carmichael, H.J.: Opt. Acta, to be publishedGoogle Scholar
  37. 20.
    Hermann, J.: Opt. Acta, to be publishedGoogle Scholar
  38. 21.
    Bonifacio, R., Lugiato, L.A.: Lett. Nuovo Cimento21, 517 (1978)Google Scholar
  39. 22.
    Hassan, S.S., Drummond, P.D., Walls, D.F.: Opt. Commun.27, 480 (1978)Google Scholar
  40. 23.
    Agrawal, G.P., Carmichael, H.J.: Phys. Rev. A9, 2074 (1979)Google Scholar
  41. 24.
    Agrawal, G.P., Carmichael, H.J.: Opt. Acta, to be publishedGoogle Scholar
  42. 25.
    Schwendimann, P.: J. Phys. A12, L39 (1979)Google Scholar
  43. 26.
    Bowden, C.M., Sung, C.C.: Phys. Rev. A19, 2392 (1979)Google Scholar
  44. 27.
    Abraham, E., Bullough, R.K., Hassan, S.S.: Opt. Commun.29, 109 (1979)Google Scholar
  45. 28.
    Marburger, J.H., Felber, F.S.: Phys. Rev. A17, 335 (1978)Google Scholar
  46. 29.
    Gradshteyn, I.S., Ryzhik, I.M.: Table of integrals series and products, pp. 81–85. New York, London: Academic Press 1965Google Scholar
  47. 30.
    Drummond, P.D.: D. Phil. thesis (1979) unpublishedGoogle Scholar
  48. 31.
    McCall, S.L.: Appl. Phys. Lett.32, 284 (1978)Google Scholar
  49. 32.
    Bonifacio, R., Lugiato, L.A.: Lett. Nuovo Cimento21, 510 (1978)Google Scholar
  50. 33.
    Bonifacio, R., Meystre, P.: Opt. Commun.27, 147 (1978)Google Scholar
  51. 34.
    Ikeda, K., Optics Comm.30, 257 (1979)Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • H. I. Carmichael
    • 1
  • J. A. Hermann
    • 2
  1. 1.Center for Statistical Mechanics and ThermodynamicsUniversity of Texas at AustinAustinUSA
  2. 2.Optics Section, Physics DepartmentImperial CollegeLondonEngland

Personalised recommendations