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Analytic description of optical bistability including spatial effects

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Zeitschrift für Physik B Condensed Matter

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.

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References

  1. Seidel, J.: U.S. Patent no. 3610731

  2. Szöke, A., Daneu, V., Goldhar, J., Kurnit, N.A.: Appl. Phys. Lett.15, 376 (1969)

    Google Scholar 

  3. Austin, J.W., De Shazer, L.G.: J. Opt. Soc. Am.61, 650 (1971)

    Google Scholar 

  4. Spiller, E.: J. Opt. Soc. Am.61, 699 (1971); J. Appl. Phys.43, 1673 (1972)

    Google Scholar 

  5. McCall, S.L.: Phys. Rev. A9, 1515 (1974)

    Google Scholar 

  6. Gibbs, H.M., McCall, S.L., Venkatesan, T.N.C.: Phys. Rev. Lett.36, 1135 (1976)

    Google Scholar 

  7. Venkatesan, T.N.C.: Ph. D. thesis (1977) unpublished

  8. Venkatesan, T.N.C., McCall, S.L.: Appl. Phys. Lett.30, 282 (1977)

    Google Scholar 

  9. McCall, S.L., Gibbs, H.M.: J. Opt. Soc. Am.68, 1378 (1978)

    Google Scholar 

  10. 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. Smith, P.W., Turner, E.H.: Appl. Phys. Lett.30, 280 (1977)

    Google Scholar 

  12. Smith, P.W., Turner, E.H., Mumford, B.B.: Opt. Lett.2, 55 (1978)

    Google Scholar 

  13. Smith, P.W., Turner, E.H., Maloney, P.J.: IEEE J. Quant. Elec. QE14, 207 (1978)

    Google Scholar 

  14. Smith, P.W., Kaminow, I.P., Maloney, P.J., Stulz, L.W.: Appl. Phys. Lett.33, 24 (1978),34, 62 (1979)

    Google Scholar 

  15. Garmire, E., Marburger, J.H., Allen, S.D.: Appl. Phys. Lett.32, 320 (1978)

    Google Scholar 

  16. Garmire, E., Allen, S.D., Marburger, J., Verber, C.M.: Opt. Lett.3, 69 (1978)

    Google Scholar 

  17. Marburger, J.H., Allen, S.D., Garmire, E., Levenson, M., Winful, H.: J. Opt. Soc. Am.,68, 642 (1978)

    Google Scholar 

  18. Garmire, E., Marburger, J.H., Allen, S.D., Winful, H.G.: Appl. Phys. Lett.34, 374 (1979)

    Google Scholar 

  19. 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. Bonifacio, R., Lugiato, L.A.: Opt. Commun.19, 172 (1976)

    Google Scholar 

  21. Bonifacio, R., Lugiato, L.A.: Phys. Rev. A18, 1129 (1978)

    Google Scholar 

  22. Bonifacio, A., Lugiato, L.A.: Phys. Rev. Lett.40, 1023 (1978)

    Google Scholar 

  23. Bonifacio, R., Gronchi, M., Lugiato, L.A.: Phys. Rev. A18, 2266 (1978)

    Google Scholar 

  24. Lugiato, L.A.: Nuovo Cimento B50, 89 (1979)

    Google Scholar 

  25. Carmichael, H.J., Walls, D.F.: J. Phys. B10, L685 (1977)

    Google Scholar 

  26. Walls, D.F., Drummond, P.D., Hassan, S.S., Carmichael, H.J.: Prog. of Theor. Phys., Suppl.64, 307 (1978)

    Google Scholar 

  27. Narducci, L.M., Gilmore, R., Feng, Da Hsuang, Agarwal, G.S.: Opt. Lett.2, 88 (1978)

    Google Scholar 

  28. Agarwal, G.S., Narducci, L.M., Gilmore, R., Feng, Da Hsuang: Phys. Rev. A18, 620 (1978)

    Google Scholar 

  29. Willis, C.R.: Opt. Commun.23, 151 (1977). Opt. Commun.26, 62 (1978)

    Google Scholar 

  30. Willis, C.R., Day, J.: Opt. Commun.28, 137 (1979)

    Google Scholar 

  31. Bulsara, A.R., Schieve, W.C., Gragg, R.F.: Phys. Lett.68A, 294 (1978)

    Google Scholar 

  32. Schenzle, A., Brand, H.: Opt. Commun.27, 485 (1978)

    Google Scholar 

  33. 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 1977

    Google Scholar 

  34. Bonifacio, R., Lugatio, L.A.: Lett. Nuovo Cimento21, 505 (1978)

    Google Scholar 

  35. Meystre, P.: Opt. Commun.26, 277 (1978)

    Google Scholar 

  36. Carmichael, H.J.: Opt. Acta, to be published

  37. Hermann, J.: Opt. Acta, to be published

  38. Bonifacio, R., Lugiato, L.A.: Lett. Nuovo Cimento21, 517 (1978)

    Google Scholar 

  39. Hassan, S.S., Drummond, P.D., Walls, D.F.: Opt. Commun.27, 480 (1978)

    Google Scholar 

  40. Agrawal, G.P., Carmichael, H.J.: Phys. Rev. A9, 2074 (1979)

    Google Scholar 

  41. Agrawal, G.P., Carmichael, H.J.: Opt. Acta, to be published

  42. Schwendimann, P.: J. Phys. A12, L39 (1979)

    Google Scholar 

  43. Bowden, C.M., Sung, C.C.: Phys. Rev. A19, 2392 (1979)

    Google Scholar 

  44. Abraham, E., Bullough, R.K., Hassan, S.S.: Opt. Commun.29, 109 (1979)

    Google Scholar 

  45. Marburger, J.H., Felber, F.S.: Phys. Rev. A17, 335 (1978)

    Google Scholar 

  46. Gradshteyn, I.S., Ryzhik, I.M.: Table of integrals series and products, pp. 81–85. New York, London: Academic Press 1965

    Google Scholar 

  47. Drummond, P.D.: D. Phil. thesis (1979) unpublished

  48. McCall, S.L.: Appl. Phys. Lett.32, 284 (1978)

    Google Scholar 

  49. Bonifacio, R., Lugiato, L.A.: Lett. Nuovo Cimento21, 510 (1978)

    Google Scholar 

  50. Bonifacio, R., Meystre, P.: Opt. Commun.27, 147 (1978)

    Google Scholar 

  51. Ikeda, K., Optics Comm.30, 257 (1979)

    Google Scholar 

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Authors and Affiliations

  1. Center for Statistical Mechanics and Thermodynamics, University of Texas at Austin, TX, Austin, 78712, USA

    H. I. Carmichael

  2. Optics Section, Physics Department, Imperial College, SW7 2BZ, London, England

    J. A. Hermann

Authors
  1. H. I. Carmichael
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  2. J. A. Hermann
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Work supported in part by the Science Research Council and by a grant from the Robert A. Welch Foundation

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Carmichael, H.I., Hermann, J.A. Analytic description of optical bistability including spatial effects. Z. Physik B - Condensed Matter 38, 365–380 (1980). https://doi.org/10.1007/BF01315329

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  • DOI: https://doi.org/10.1007/BF01315329

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