Abstract
The paper is devoted to an investigation of laser-radiation statistics. The dynamics of establishment of an equilibrium photon distribution in frequency is analyzed and the results are compared with numerical experiments. The spectral density of the radiation-intensity fluctuations is obtained in analytic form in the quasiclassical laser theory. An equation that generalizes the earlier calculations is obtained for the lasing linewidth in the framework of the Scully-Lamb theory.
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Literature Cited
W. Horsthemke and R. Lefevre, Noise-Induced Transitions [Russian translation], Mir, Moscow (1987).
H. Risken, The Fokker-Planck Equation, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo (1984).
D. R. Bates, A. S. Kingston, and R. W. P. McWirter, “Recombination between electrons and atomic ions,” Proc. R. Soc.,A267, 297–312 (1962).
B. F. Gordiets, A. I. Osipov, and L. A. Shelepin, Kinetic Processes in Gases and Molecular Lasers [In Russian], Nauka, Moscow (1980).
S. A. Reshetnyak, S. M. Kharchev, and L. A. Shelepin, “Asymptotic methods in the theory of kinetic equations,” Trudy FIAN,144, 3–36 (1984).
S. A. Reshetnyak and S. M. Kharchev, “Metastable distributions of the order parameter for the description of the dynamics of second-phase transitions,” FIAN Preprint No. 273 Moscow (1985).
H. A. Kramers, “Brownian motion in a field of force and the diffusion model of chemical reactions,” Physica (The Hague),7, 284–304 (1940).
E. M. Lifshitz and L. P. Pitaevskii, Physical Kinetics, Pergamon, Oxford (1984).
A. Z. Patashinskii and B. O. Shumilo, “Theory of relaxation of metastable states,” Zh. Éksp. Teor. Fiz.,77, 1417–1431 (1979).
V. P. Silin and A. A. Rukhadze, Electromagnetic Properties of Plasma and of Plasmalike Media [in Russian], Gosatomizdat, Moscow (1961).
M. Sargent, M. O. Scully, W. E. Lamb, Laser Physics, London (1974).
E. E. Nikitin, Theory of Elementary Atomic-Molecular Processes in Gases [in Russian], Khimiya, Moscow (1970).
S. A. Reshetnyak, “Rates of biomolecular reactions in the theory of Brownian motion,” FIAN Preprint No. 250, Moscow (1987).
G. Parisi and Y., Wu, “Perturbation theory without gauge fixing,” Sci. Sin.,24 483–497 (1981).
A. S. Goncharov and A. D. Linde, “Tunneling in an expanding Universe; Euclidean and Haniltonian approaches,” Fiz. Elem. Chastits At. Yad.,17, No. 5, 837–883 (1987).
E. Witten, “Dynamical breaking of supersymmetry,” Nucl. Phys.,B188, No. 3, 513–554 (1981).
M. V. Feigel'man and A. M. Tsvelik, “Hidden supersymmetry of stochastic dissipative dynamics,” Zh. Éksp. Teor. Fiz.,83, No. 4, 1430–1443 (1982).
L. M. Biberman, V. S. Vorob'ev, and I. T. Yakubov, Kinetics of Nonequilibrium Low-Tem-perature Plasma, Consultants Bureau, New York (1987).
H. Dekker and N. G. van Kampen, “The expansion of the Fokker-Planck equation including a critical point,” Phys. Lett.,76A, No. 2, 101–105 (1980).
J. M. Sancho, M. San Miguel, S. L. Katz, and J. D. Gunton, “Analytical and numerical studies of multiplicative noise,” Phys. Rev.,A26, No. 3, 1589–1609 (1982).
H. Dekker, “Critical dynamics. The expansion of master equation including a critical point. 1. Diffusion processes,” Physica,103A, No. 1/2, 55–79 (1980).
S. A. Lomov, Introduction to the General Theory of Singular Perturbations [in Russian], Nauka, Moscow (1981).
W. Bez and P. Talkner, “A new variational method to calculate escape rates in bistable system,” Phys. Lett.,82A, No. 7, 313–316 (1981).
H. Brand, A. Schenzle, and G. Schroder, “Lower and upper bounds for the eigenvalues of the Fokker-Planck equation in detailed balance,” Phys. Rev.,A25, No. 4, 2324–2338. (1982).
V. Seshadri, B. J. West, and K. Lindenberg, “Analytical theory of extrema,” J. Chem. Phys.,72, No. 2, 1145–1150 (1980).
L. Pontryagin, A. Andronov, and W. Vitt, “Statistical analysis fo dynamic systems,” Zh. Éksp. Teor. Fiz.,3, No. 4, 165–180 (1933).
M. Suzuki, “Instability, fluctuations and critical slowing down,” Lect. Notes Phys.,132, 48–75 (1980).
W. M. Zheng, “Decay of unstable states: examination of scaling theory,” Physica,122A, No. 3, 431–440 (1983).
H. Hu, “Unified solution of the Fokker-Planck equation with a bistable potential,” Phys. Lett.,116A, No. 8, 361–364 (1980).
N. N. Bogolyubov, “Problems of a dynamical theory in statistical physics,” in: Studies in Statistical Mechanics, J. E. de Boer and G. E. Uhlenbek (eds.), Vol. 1, Wiley, N. Y. (1981).
S. A. Reshetyak and L. A. Shelepin, “Method of quasiequilibrium functions in physical kinetics,” Trudy FIAN,106, 90–118 (1979).
I. MacDonalds, Symmetric Functions and Hall Polynomials [Russian translation], Mir, Moscow (1985).
H. Dekker and N. G. van Kampen, “Eigenvalues of a diffusion process with a critical point,” Phys. Lett.,73A, No. 5/6, 374–376 (1979).
W. E. Lamb, “Theory of an optical maser,” Phys. Rev.,134, A1429-A1450 (1964).
F. Arechhi, M. Scully, H. Haken, and D. Weindlich, Quantum Fluctuations of Laser Radiation [Russian translation], Mir, Moscow (1974).
H. Risken, “Distribution and correlation functions for a laser amplitude,” Z. Phys.,186, No. 1, 85–98 (1965).
H. Risken and H. D. Vollmer, “The influence of higher order contributions to the correlation function of the intensity fluctuations in a laser threshold,” Z. Phys.,201, No. 3, 323–330 (1967).
F. T. Arecchi, G. S. Rodari, and A. Sona, “Statistics of the laser radiation at threshold,” Phys. Lett.,25A, No. 1, 59–60 (1967).
D. Meltzer, L. Mandel, “Dynamics of a Q-switched laser near threshold,” Phys. Rev.,A3, No. 4, 1763–1772 (1971).
F. T. Arecchi, M. Giglio, and A. Sona, “A dynamics of the laser radiation at threshold,” Phys. Lett.,25A, No. 4, 5341–5342 (1967).
L. D. Landau and I. M. Khalatnikov, “Anomalous absorption of sound near second-order phase-transition poitns,” Dokl. Akad. Nauk SSSR,96, 469–472 (1954).
Yu. L. Klimontovich, Kinetic Theory of Electromagnetic Processes [in Russian], Nauka, Moscow (1980).
L. D. Landau and E. M. Lifshitz, Statistical Physica, Pergamon, Oxford (1980).
N. N. Bogolyubov, Selected Works [in Russian], Vol. 3, Naukova Dumka, Kiev (1971). pp. 174–243.
Additional information
Optics Division, Lebedev Physics Institute. Translated from Preprint No. 79, Lebedev Physics Institute, Academy of Sciences of the USSR, Moscow, 1990.
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Reshetnyak, S.A., Kharchev, S.M. Kinetics of transition through lasing threshold. J Russ Laser Res 11, 466–497 (1990). https://doi.org/10.1007/BF01120735
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DOI: https://doi.org/10.1007/BF01120735