Abstract
Passively Q-switched microchip lasers generate strongly pulsating intensity oscillations that emerge from a Hopf bifurcation point. We show that this bifurcation is nearly vertical and explain why strongly pulsating oscillations are immediately observed as we pass the Hopf bifurcation point. The laser dynamical problem is mathematically a singular perturbation problem which we investigate. The leading order problem is conservative and corresponds to Lotka–Volterra equations.
Similar content being viewed by others
REFERENCES
N. B. Abraham, L. A. Lugiato, and L. M. Narducci, JOSA B 2:1 (1985).
N. B. Abraham, P. Mandel, and L. M. Narducci, Prog. in Opt. 25:3 (1988).
P. Mandel, Theoretical Problems in Cavity Nonlinear Optics, Camb. Stud. in Modern Optics (Cambridge University Press, 1997).
E. Arimondo, F. Casagrande, L. A. Lugiato, and P. Glorieux, Appl. Phys. B 30:5 (1983); E. Arimondo, P. Bootz, P. Glorieux, and E. Menchi, JOSA B 2:193 (1985).
H. Kawaguchi, Bistabilities and Nonlinearities in Laser Diodes (Artech House, Boston, 1994).
T. Erneux, JOSA B 5:1063 (1988).
J. L. A. Dubbeldam and B. Krauskopf, Opt. Comm. 159:325 (1999).
Tachikawa, K. Tanii, and T. Shimizu, JOSA B 4:387 (1987); JOSA B 5:1077 (1988).
M. Yamada, IEEE J. Quant. Electron. QE 29:1330 (1993).
J. J. Zayhowski, Opt. Lett. 21:588 (1996); Errata Opt. Lett. 21:1618 (1996); J. J. Zayhowski and C. Dill III, Opt. Lett. 19:1427 (1994).
G. J. Spühler, R. Paschotta, R. Fluck, B. Braun, M. Moser, G. Zhang, E. Gini, and U. Keller, JOSA B 16:376 (1999).
P. Peterson, A. Gavrielides, M. P. Sharma, and T. Erneux, IEEE J. Quant. Electronics 35:1247 (1999).
T. Erneux, P. Peterson, and A. Gavrielides, Europ. J. of Physics (2000), in press.
Th. Midavaine, D. Dangoisse, and P. Glorieux, Phys. Rev. Lett. 55:1989 (1985).
L. Fabiny, P. Colet, R. Roy, and D. Lenstra, Phys. Rev. A 47:4287 (1993).
N. G. Basov, V. N. Morosov, and A. N. Oraevsky, IEEE J. of Quant. Electr. QE 2:542 (1966); V. N. Morozov, JOSA B 5:909 (1988).
G. L. Oppo and A. Politi, Z. Phys. B 59:111 (1985); G.-L. Oppo and A. Politi, Phys. Rev. A 40:1422 (1989).
T. Erneux, S. M. Baer, and P. Mandel, Phys. Rev. A 35:1165 (1987).
H. Haken, Synergetics, 2nd ed. (Springer Verlag, 1978), pp. 128-131.
S. M. Baer and T. Erneux, SIAM J. Appl. Math. 46:721 (1986); SIAM J. Appl. Mathematics 52:1651 (1992).
V. Volterra, Mem. Acad. Lincei. 2:31 (1926) (translation in R. N. Chapman's Animal Ecology (McGraw-Hill, New York, 1931), pp. 409-48).
A. J. Lotka, J. Am. Chem. Soc. 42:1595 (1920); Proc. Nat. Acad. Sci. US 6:410 (1920).
J. Grasman, Asymptotic Methods for Relaxation Oscillations and Applications, Appl. Math. Sciences, Vol. 63 (Springer Verlag, New York, 1987).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Erneux, T., Kozyreff, G. Nearly Vertical Hopf Bifurcation for a Passively Q-Switched Microchip Laser. Journal of Statistical Physics 101, 543–552 (2000). https://doi.org/10.1023/A:1026482609796
Issue Date:
DOI: https://doi.org/10.1023/A:1026482609796