Khanin Ya.I. Fundamentals of laser dynamics

Cambridge International Science Publishing Ltd, Cambridge, UK, 2006, 361 pages, ISBN: 1-904602-11-8The book explores the current state of laser dynamics and provides reference data and basic experimental facts for old and new generation lasers. The most frequently used mathematical models are presented. The author discusses the reasons for spontaneous occurrence of pulsation of the intensity of the radiation of solid-state lasers, the influence of the nonstationary nature of parameters and non-linearity of laser elements on the generation characteristics. Special emphasis is placed on the problems of low-frequency dynamics of multimode lasers.Preface

Quantum Oscillators: General Considerations
Principle of operation and practical implementation
Induced and spontaneous emission
Methods of producing an inverted population
Amplification in quantum systems without population inversion
Time-dependent processes in quantum oscillators
Dynamic properties of lasers and their relation to relaxation rates
Widespread types of lasers
Some experimental factsBasic Equations for the Dynamical Behaviour of Lasers
Equations for the electromagnetic field
Wave equation
Modal decomposition
Ring-cavity field equations
Equations for the dynamics of the material
Master equations
Two-level medium
Three-level medium: Coherent pumping
Three- and four-level media; transition to an equivalent two-level description
Material equations specialized to an ensemble of moving atoms
Self-Consistent semiclassical set of laser equationsSingle-Mode Lasers
Dynamical models of homogeneously broadened lasers
Equations for the quadratic quantities
Adiabatic elimination of the atomic polarization; Singlemode rate equations
Traveling-wave laser with homogeneous active medium
Steady states and relaxation oscillations
Phase portrait of laser; Spikes characteristics
The linear stage of the onset
Single-mode standing-wave class B laser
Model with extended laser medium
Model with the sinusoidal inversion grating
Power characteristics
Instabilities and chaos in a travelling-wave single-mode laser
Some history
The Lorenz-Haken model
Bifurcations and their sequences
Parametric origin of the second laser threshold
Effect of detuning on the laser dynamic properties
Phase dynamics of a single-mode laser
Dynamics of three-level lasers with coherent pumping
Self-consistent model and ways to its simplification
Self-excitation conditions
Lasing modes
Experimental investigations of optically pumped ammonia lasers
Effect of inhomogeneous broadening on the laser dynamic characteristic
Lowering of the instability threshold
Time-dependent laser modesMultimode Lasers with Frequency-Nondegenerate Modes
Rate equations model with spatial mode competition and its time independent solutions
Combination tone mode-mode coupling. The rate equations of the multimode lasers
Stationary oscillation spectrum of the Fabry-Perot laser
Uniqueness of the stable steady-state solution
Relaxation oscillations as low-frequency normal laser modes
The model with spatially extended laser medium
Approximation of the spatial inversion gratings
Dependence of the dynamical features on the distribution of unsaturated gain over the perimeter of laser cavity
Time-dependent processes
Features of spiking in multimode lasers
Onset of laser spectrum
Alternative mechanisms of laser multimodality
Combination tone mode-mode coupling and its influence on laser dynamics
Competition between dispersion and nonlinearity of the laser medium
Time-dependent regimes due to nonlinear mode interaction
Inhomogeneously broadened solid-state lasers
Mathematical model
Steady-state solution in the spatially uniform field approximation: The threshold for laser spectrum splitting1
Connection between the spatial mode structure and the spectral structure of laser emission
Transients in the presence of cross-relaxation
Dynamical instability of steady state of a multimode traveling wave laser (Risken-Nummedal-Graham-Haken theory)Multimode Lasers with Quasi-Frequency-Degenerate Modes
Two-mode class B laser with a Fabry-Perot resonator
Equations of class B two-mode laser
Steady-state solutions and relaxation oscillations
Bidirectional class B laser
The model of single-frequency class B ring laser
Steady states in the absence of backscattering and their stability
Influence of fine structure of the gain line on the stability of the steady states
Steady states in the presence of backscattering and their stability
Competition of two instability mechanisms
Role of phase nonreciprocity in the dynamics of a class B ring laser
Frequency dynamics of a bidirectional ring laser
Vector model of a fibre laserLasers with Time-Dependent Parameters
Lasers with periodic parameter modulation
Linear response of a single-mode laser to low-frequency modulation
Linear response of a multimode laser to low-frequency loss modulation
Nonlinear response of a single-mode laser to periodic loss modulation
Bifurcations and Chaos
Monotonic adiabatic variation of parameters
Sweeping of the losses
Sweeping of the detuning
Mechanisms of undamped pulsations in solid-state free-running lasers
Origin of the pulsations of a two-level paramagnetic Maser
Laser parameter oscillations under free-running conditions
Instabilities due to sweeping of the cavity eigenfrequency
Role of spatial effectsLasers with Nonlinear Parameters
Laser with an opto-electronic feedback
Single-mode laser with self-controlling of the cavity losses
Multimode laser with selective and combined feedback
Laser with a nonlinear absorber
Two-level rate equation model of laser with a nonlinear filter; steady states and their stability
Nonlinear pulsations in a laser with saturable absorber
Experiments with a CO2 laser. The rate equation model of a three-level laser with a two-level nonlinear filter
Laser with a Nonlinear Dielectric
Examples showing the influence of the refractive index nonlinearity on laser dynamics
Passive modulation of diffraction losses by a dielectric with cubic nonlinearity (Kerr medium inside a cavity with aperture)
Passive modulation of the mode filling factor (Kerr-medium inside a cavity without aperture)
Passive Mode Locking in Lasers
Role of the laser medium nonlinearity in mode locking
Threshold conditions of passive mode locking
Processes in a travelling wave laser with saturable absorber
Rate equation model of a travelling wave laser without bulk losses
Instability threshold of single-frequency operation of a travelling-wave laser with nonlinear filter
Soft and hard regimes of ultrashort pulse formation in lasers with nonlinear filtersGiant Pulse Regime (Q-Switching)
Active Q-switching
Active methods of generating giant pulses
Pulse delay time with instantaneous Q-Switching
Energy characteristics of a giant pulse
Pulse duration and shape
Angular and frequency spectra of a giant pulse with instantaneous Q-switching
Giant pulse generation with passive Q-switching