Singular Hopf bifurcation to strongly pulsating oscillations in lasers containing a saturable absorber

The equations describing the pulsating output of a laser containing a saturable absorber are investigated numerically and analytically. The laser admits a singular Hopf bifurcation to a nearly vertical branch of periodic solutions. Using asymptotic methods, we determine a simplified problem that describes the transition from harmonic to pulsating oscillations as the bifurcation parameter is changed. This transition occurs in a layer bounded by the Hopf bifurcation point, and by a critical point near which the branch of solutions becomes vertical.

[1]  Tadao Shimizu,et al.  Comprehensive interpretation of passive Q switching and optical bistability in a CO 2 laser with an intracavity saturable absorber , 1987 .

[2]  Paul Mandel,et al.  Theoretical Problems in Cavity Nonlinear Optics , 1997 .

[3]  Niloy K. Dutta,et al.  Long wavelength semiconductor lasers , 1988, Technical Digest., International Electron Devices Meeting.

[4]  Hitoshi Kawaguchi,et al.  Bistabilities and Nonlinearities in Laser Diodes , 1994 .

[5]  Barteld Braaksma,et al.  Phantom ducks and models of excitability , 1992 .

[6]  B. Krauskopf,et al.  Self-pulsations of lasers with saturable absorber: dynamics and bifurcations , 1999 .

[7]  D. Renner,et al.  Long-wavelength semiconductor lasers , 1987, IEEE Journal of Quantum Electronics.

[8]  Pierre Glorieux,et al.  Repetitive passive Q-switching and bistability in lasers with saturable absorbers , 1983 .

[9]  Rüdiger Paschotta,et al.  Experimentally confirmed design guidelines for passively Q-switched microchip lasers using semiconductor saturable absorbers , 2001 .

[10]  Pierre Glorieux,et al.  Pulse shape and phase diagram in the passive Q switching of CO 2 lasers , 1985 .

[11]  I︠A︡kov Izrailevich Khanin,et al.  Principles of laser dynamics , 1995 .

[12]  Minoru Yamada,et al.  A theoretical analysis of self-sustained pulsation phenomena in narrow-stripe semiconductor lasers , 1993 .

[13]  P. Peterson,et al.  The pulse shape of a passively Q-switched microchip laser , 2000 .

[14]  Huw D. Summers,et al.  Theoretical optimization of self-pulsating 650-nm-wavelength AlGaInP laser diodes , 1999 .

[15]  Thomas Erneux.  Q-switching bifurcation in a laser with a saturable absorber , 1988 .

[16]  S. Baer,et al.  Sungular hopf bifurcation to relaxation oscillations , 1986 .

[17]  Ultraviolet generation with passively Q-switchedmicrochip lasers. , 1996, Optics letters.

[18]  Thomas Erneux,et al.  Nearly Vertical Hopf Bifurcation for a Passively Q-Switched Microchip Laser , 2000 .

[19]  J J Zayhowski.  Ultraviolet generation with passively Q-switched microchip lasers: errata. , 1996, Optics letters.

[20]  J. Zayhowski,et al.  Diode-pumped passively Q-switched picosecond microchip lasers. , 1994, Optics letters.

[21]  Tadao Shimizu,et al.  Laser instability and chaotic pulsation in a CO 2 laser with intracavity saturable absorber , 1988 .

[22]  B. Braaksma,et al.  Singular Hopf Bifurcation in Systems with Fast and Slow Variables , 1998 .

[23]  J. Grasman.  Asymptotic Methods for Relaxation Oscillations and Applications , 1987 .

[24]  Heinz Georg Schuster,et al.  Dynamics of Lasers , 1991 .

[25]  Thomas Erneux,et al.  Dimensionless rate equations and simple conditions for self-pulsing in laser diodes , 2001 .

[26]  Huw D. Summers,et al.  Thermal limitation of self-pulsation in 650 nm AlGaInP laser diodes with an epitaxially integrated absorber , 1997 .

[27]  C. R. Mirasso,et al.  Self-pulsating semiconductor lasers: theory and experiment , 1999, physics/9906027.

[28]  M. San Miguel,et al.  Optical feedback on self-pulsating semiconductor lasers , 1996 .