## Fundamental Issues of Nonlinear Laser Dynamics: Concepts,Mathematics, Physics,and Applications International Spring School, Texel, The Netherlands 16-19 April 2000This book is the first collection of tutorials on nonlinear dynamics of lasers. The International Spring School on Fundamental Issues of Nonlinear Laser Dynamics was aimed at young researchers who are interested in working at the forefront of applied nonlinear mathematics and nonlinear laser dynamics. In a highly interdisciplinary spirit, there were tutorial presentations from 14 internationally recognized top experts from applied mathematics, theoretical and experimental physics, and engineering disciplines. Topics included are: bifurcation theory, the notion of chaos, multiple time scale systems, and delay equations. The dynamics of lasers with optical injection and optical feedback, and lasers with spatio-temporal dynamics are discussed from the theoretical, experimental, and device simulation points of view. Applications of lasers include secure communications, pulse generation and telecommunication through optical fibers. This mixture of introductory material will benefit an inderdisciplinary readership of researchers, lecturers and students in the fields of applied mathematics, physics, and electrical engineering. |

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### Contents

Chaos in Periodically Driven Systems | 31 |

Multiple Time Scale Analysis of Lasers | 54 |

The Mathematics of Delay Equations with an Application | 66 |

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amplitude attractor bandwidth broad area carrier density chaos chaotic complex computed corresponding coupling curve CW-state delayed optical feedback detuning device diode dynamical behavior dynamical systems eigenmodes eigenvalues Electron emitting encoded equilibrium Erneux excitable experimental external cavity facet fibre FIGURE filamentation filter fixed point four-wave mixing frequency function gain Gavrielides Hopf bifurcation IEEE increasing injection current intensity Krauskopf Lang-Kobayashi lasing Lenstra Lett linear linewidth enhancement factor longitudinal mode modulation Moloney nonlinear dynamics normal form operation optical feedback optical field output power parameters period-doubling periodic orbit perturbation phase space photon Phys Poincare map polarization pulses pump current quantum rate equations refractive index regime relaxation oscillation resonance saddle point saddle-node bifurcation semiconductor laser shown in Fig shows signal simulation solitary laser solution spatially spatio-temporal dynamics spectra spectrum stable emission steady-state synchronization threshold transverse modes typically unstable manifold values VCSELs vector field wavelength