Abstract
We develop a general formalism to describe the dynamical behavior of an ensemble of two-level systems in a Fabry-Perot cavity. Our main result is a set of space and time-dependent, integro-differential equations for the slowly varying radiation and atomic variables, which we derive through a precise analysis of the slowly-varying amplitude approximation in the presence of counter-propagating fields. With the help of new and properly chosen variables we recast these equations in a form that makes their boundary conditions formally identical to those of an ideal Fabry-Perot resonator, and introduce in a natural way a modal structure even for systems with arbitrary mirror reflectivity. We derive simplified forms of these equations in the uniform field limit and within the more general single-frequency approximation. Finally, we extend our formulation to include driven systems such as optically bistable devices and the laser with an injected signal.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abraham, N.B., Lugiato, L.A., Narducci, L.M.: J. Opt. Soc. Am. B2, 7 (1985)
Boyd, R.W., Raymer, M.G., Narducci, L.M. (eds.): Optical instabilities. Cambridge: Cambridge University Press 1986
Lugiato, L.A.: In: Progress in optics. Wolf, E. (ed.), Vol. XXI. p. 69. Amsterdam: North Holland 1984
Carmichael, H.J.: In: Laser physics. Harvey, J.D., Walls, D.H., (eds.). Lecture Notes in Physics, Vol. 182, p. 64. Berlin, Heidelberg, New York: Springer 1983
Abraham, N.B., Mandel, P., Narducci, L.M.: In: Progress in optics. Wolf, E. (ed.). Amsterdam: North Holland (in press)
See, for example, Haken, H.: Laser theory. Handbuch der Physik. Genzel, L. (ed.), Vol. XXV/2c. Berlin, Heidelberg, New York: Springer 1970; Sargent, M., III, Scully, M.O., Lamb, W.E., Jr.: Laser physics. Reading, Mass.: Addison-Wesley 1974
Drummond, R.D.: IEEE J. Quantum Electron. QE-17, 301 (1981); Sargent, M., III: Sov. J. Quantum Electron.10, 1247 (1980)
See, for example, Carmichael, H.J.: Opt. Commun.53, 122 (1985)
See, for example, Abraham, E., Firth, W.J.: Opt. Acta30, 1541 (1983)
McCall, S.L.: Phys. Rev. A9, 1515 (1974)
Carmichael, H.J.: Opt. Acta27, 147 (1980)
Hermann, J.A.: Opt. Acta27, 159 (1980)
Casperson, L.W.: Phys. Rev. A21, 911 (1980)
Hendow, S.T., Sargent, M., III: J. Opt. Soc. Am. B2, 84 (1985)
Benza, V., Lugiato, L.A.: Z. Phys. B — Condensed Matter35, 383 (1979); Lugiato, L.A.: Z. Phys. B — Condensed Matter41, 85 (1981)
Narducci, L.M., Tredicce, J.R., Lugiato, L.A., Abraham, N.B., Bandy, D.K.: Phys. Rev. A32, 1588 (1985)
Lugiato, L.A., Narducci, L.M., Bandy, D.K., Tredicce, J.R.: Phys. Rev. A33, 1109 (1986)
Hecht, E., Zajae, A.: Optics, p. 309. Reading, Mass: Addison-Wesley 1980
Haken, H.: Synergetics — an introduction. Berlin, Heidelberg, New York: Springer 1977
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lugiato, L.A., Narducci, L.M. Nonlinear dynamics in a Fabry-Perot resonator. Z. Physik B - Condensed Matter 71, 129–138 (1988). https://doi.org/10.1007/BF01310852
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01310852