Author	Haken, Hermann. author
Title	Laser Theory [electronic resource] / by Hermann Haken
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 1984
Connect to	http://dx.doi.org/10.1007/978-3-642-45556-8
Descript	XVI, 322 p. online resource

This book, written by one of the pioneers of laser theory, is now considered a classic by many laser physicists. Originally published in the prestigious Encyclopedia of Physics series, it is now being republished in paperback to make it available not only to professors and scientists, but also to students. It presents a thorough treatment of the theory of laser resonators, the quantum theory of coherence, and the quantization of electromagnetic fields. Especial emphasis is placed on the quantum-mechanical treatment of laser light by means of quantum-mechanical Langevin equations, the density matrix equation, and the Fokker-Planck equation. The semiclassical approach and the rate equaยญ tion approach are also presented. The principles underlying these approaches are used to derive the relevant equations, from which, in turn, the various properties of laser light are derived. Preface. The concept of the laser came into existence more than a decade ago when SCHAWLOW and TOWNES showed that the maser principle could be extended to the optical region. Since then this field has developed at an incredible pace which hardly anybody could have foreseen. The laser turned out to be a meeting place for such different disciplines as optics (e. g. spectroscopy). optical pumping, radio engineering, solid state physics, gas discharge physics and many other fields. The underlying structure of the laser theory is rather simple

I. Introduction -- 1.1. The maser principle -- 1.2. The laser condition -- 1.3. Properties of laser light -- a) Spatial coherence -- b) Temporal coherence -- c) Photon statistics -- d) High intensity -- e) Ultrashort pulses -- 1.4. Plan of the article -- II. Optical resonators -- II.1. Introduction -- II.2. The Fabry-Perot resonator with plane parallel reflectors -- a) Spatial distribution of modes -- b) Diffraction losses -- c) Three-dimensional resonator -- II.3. Confocal resonator -- a) Field outside the resonator -- b) Field inside the resonator -- c) Far field pattern of the confocal resonator -- d) Phase shifts and losses -- II.4. More general configurations -- a) Confocal resonators with unequal square and rectangular apertures -- b) Resonators with reflectors of unequal curvature -- ?) Large circular apertures -- ?) Large square aperture -- II.5. Stability -- III. Quantum mechanical equations of the light field and the atoms without losses -- III.1. Quantization of the light field -- III.2. Second quantization of the electron wave field -- III.3. Interaction between radiation field and electron wave field -- III.4. The interaction representation and the rotating wave approximation -- III.5. The equations of motion in the Heisenberg picture -- III.6. The formal equivalence of the system of atoms each having 2 levels with a system of ยฝ spins -- IV. Dissipation and fluctuation of quantum systems. The realistic laser equations -- IV.1. Some remarks on homogeneous and inhomogeneous broadening -- a) Natural linewidth -- b) Inhomogeneous broadening -- ?) Impurity atoms in solids -- ?) Gases -- ?) Semiconductors -- c) Homogeneous broadening -- ?) Impurity atoms in solids -- ?) Gases -- ?) Semiconductors -- IV.2. A survey of IV.2.โIV.11 -- a) Definition of heatbaths (reservoirs) -- b) The role of heatbaths -- c) Classical Langevin and Fokker-Planck equations -- ?) Langevin equations -- ?) The Fokker-Planck equation -- d) Quantum mechanical formulation: the total Hamiltonian -- e) Quantum mechanical Langevin equations, Fokker-Planck equation and density matrix equation -- ?) Langevin equations -- ?) Density matrix equation -- ?) Generalized Fokker-Planck equation -- IV.3. Quantum mechanical Langevin equations: origin of quantum mechanical Langevin forces (the effect of heatbaths) -- a) The field (one mode) -- b) Electrons (โatomsโ) -- IV.4. The requirement of quantum mechanical consistency -- a) The field -- b) Dissipation and fluctuations of the atoms -- IV. 5. The explicit form of the correlation functions of Langevin forces -- a) The field -- b) The N-level atom -- IV. 6. The complete laser equations -- a) Quantum mechanically consistent equations for the operators b?+ and (ai+ak)? -- ?) The field equations -- ?) The matter equations -- b) Semiclassical equations -- ?) The field equations -- ?) The matter equations -- IV.7. The density matrix equation -- a) General derivation -- b) Specialization of Eq. (IV.7.31) -- ?) Light mode -- ?) Atom -- ?) The density matrix equation of the complete system of M laser modes and N atoms -- IV. 8. The evaluation of multi-time correlation functions by the single-time density matrix -- IV.9. Generalized Fokker-Planck equation: definition of distribution functions -- a) Field -- ?) Wigner distribution function and related representations -- ?) Transforms of the distribution functions: characteristic functions -- ?) Calculation of expectation values by means of the distribution functions -- b) Electrons -- ?) Distribution functions for a single electron -- ?) Characteristic functions -- ?) Electrons and fields -- IV. 10. Equation for the laser distribution function (IV.9.22) -- a) Comparison of the advantages of the Heisenberg and the Schrรถdinger representations -- ?) The Heisenberg representation -- ?) The Schrรถdinger representation -- b) Final form of the generalized Fokker-Planck equation -- IV.11. The calculation of multi-time correlation functions by means of the distribution function -- V. Properties of quantized electromagnetic fields -- V.1. Coherence properties of the classical and the quantized electromagnetic field -- a) Classical description: definitions -- ?) The complex analytical signal -- ?) The average -- ?) The mutual coherence function -- b) Quantum theoretical coherence functions -- ?) Elementary introductions -- ?) Coherence functions -- ?) Coherent wave functions -- ?) Generation of coherent fields by classical sources (the forced harmonic oscillator) -- V.2. Uncertainty relations and limits of measurability -- a) Field and photon number -- b) Phase and photon number -- ?) Heuristic considerations -- ?) Exact treatment -- c) Field strength -- V.3. Spontaneous and stimulated emission and absorption -- a) Spontaneous emission -- b) Stimulated emission -- c) Comparison between spontaneous and stimulated emission rates -- d) Absorption -- V.4. Photon counting -- a) Quantum mechanical treatment, correlation functions -- b) Classical treatment of photon counting -- V.5. Coherence properties of spontaneous and stimulated emission. The spontaneous linewidth -- VI. Fully quantum mechanical solutions of the laser equations -- VI.1. Disposition -- VI.2. Summary of theoretical results and comparison with the experiments -- a) Qualitative discussion of the characteristic features of the laser output: homogeneously broadened line -- b) Quantitative results: single mode action -- ?) The spectroscopic linewidth well above threshold -- ?) The spectroscopic linewidth somewhat below threshold -- ?) The intensity (or amplitude) fluctuations -- ?) Photon statistics -- VI.3. The quantum mechanical Langevin equations for the solid state laser -- a) Field equations -- b) Matter equations -- ?) The motion of the atomic dipole moment -- 1. Dipole moment between levels j and k -- 2. Dipole moment between levels l and l?k, j and between levels k and l=j, k -- 3. Dipole moment between levels i? k, j and l ? k, j -- ?) The occupation numbers change -- 1. For the laser levels j and k -- 2. For the non-laser levels -- VI.4. Qualitative discussion of single mode operation -- a) The linear range (subthreshold region) -- b) The nonlinear range (at threshold and somewhat above) -- ?) Phase diffusion -- ?) Amplitude (intensity) fluctuations -- c) The nonlinear range at high inversion -- d) Exact elimination of all atomic coordinates -- VI.5. Quantitative treatment of a homogeneously broadened transition: emission below threshold (intensity, linewidth, amplification of signals) -- a) No external signals -- ?) Single-mode linewidth below threshold -- ?) Many modes below threshold -- b) External signals -- VI.6. Exact elimination of atomic variables in the case of a homogeneously broadened line. Running or standing waves -- ?) Standing waves -- ?) Running waves -- VI.7. Single mode operation above threshold, homogeneously broadened line -- a) Lowest order -- b) First order -- c) Phase noise. Linewidth formula -- d) Amplitude fluctuations -- ?) The special case of a moderate photon number -- ?) The special case of a big photon number -- VI.8. Stability of amplitude. Spiking and damped oscillations. Single-mode operation, homogeneously broadened line -- a) Qualitative discussion -- b) Quantitative treatment -- c) The special case w13?? (โtwo level systemโ) -- VI.9. Qualitative discussion of two-mode operation -- a) Some transformations -- b) Both modes well below threshold -- c) Modes somewhat above or somewhat below threshold -- d) Both modes above threshold -- ?) |?1 ? ?2| ? 1/T -- ?) |?1 ? ?2| ? 1/T -- VI. 10. Gas laser and solid-state laser with an inhomogeneously broadened line. The van der Pol equation, single-mode operation -- a) Solid-state laser with an inhomogeneously broadened line and an arbitrary number of levels -- b) Gas laser -- VI.11. Direct solution of the density matrix equation -- VI.12. Reduction of the generalized Fokker-Planck equation for single-mode action -- a) Expansion in powers of N?ยฝ (N: number of atoms) -- b) Adiabatic elimination of the atomic variables -- c) The Fokker-Planck equation -- VI. 13. Solution of the reduced Fokker-Planck equation -- a) Steady state solution -- b) Transient solution -- VI. 14. The Fokker-Planck equation for multimode action near threshold. Exact or nearly exact stationary solution -- a) The explicit form of the Fokker-Planck equation -- b) Theorem on the exact stationary solution of a Fokker-Planck equation -- c) Nearly exact solution of (VI. 14.1) -- ?) Normal multimode action -- ?) Phase locking of many modes -- ?) A qualitative discussion of phase locking (example of three modes) -- VI. 15. The linear and quasi-linear solution of the general Fokker-Planck equation -- a) Far below threshold -- b) Well above threshold -- VII. The semiclassical approach and its applications -- VII.1. Spirit of the semiclassical approach. The equations for the solid state laser -- a) The field equations -- b) The material equations -- c) Macroscopic treatment -- ?) Wave picture, inhomogeneous atomic line -- ?) Wave picture, homogeneous atomic line -- ?) Wave picture, homogeneous atomic line, rotating wave approximation, slowly varying amplitude approximation -- ?) Mode picture, polarization waves -- d) Extension to multilevel atoms -- e) Systematics of the semiclassical approach -- VII.2. Method of solution for the stationary state -- a) Single-mode operation, general features -- b) Two-mode operation, general features -- ?) Time-independent atomic response -- ?) Time-dependent atomic response -- VII.3. The solid-state laser with a homogeneously broadened line. Single and multimode laser action -- a) Single-mode operation -- b) Multiple-mode operation -- ?) Equations for the photon densities of M modes -- ?) Equations for the frequency shift -- VII.4. The solid-state laser with an inhomogeneously broadened Gaussian line. Single-and two-mode operation -- a) One mode -- ?) Equation for the frequency shift -- ?) Equation for the ph

1. Physics
2. Quantum optics
3. Lasers
4. Photonics
5. Physics
6. Laser Technology
7. Photonics
8. Quantum Optics