Laser Physics OXFORD UNIVERSITY PRESS SIMON HOOKER COLIN WEBB. and. Department of Physics, University of Oxford

Transcription

1 Laser Physics SIMON HOOKER and COLIN WEBB Department of Physics, University of Oxford OXFORD UNIVERSITY PRESS

2 Contents 1 Introduction 1.1 The laser 1.2 Electromagnetic radiation in a closed cavity The density of modes 1.3 Planck's law The energy density of blackbody radiation 2 The interaction of radiation and matter 2.1 The Einstein treatment Relations between the Einstein coefficients 2.2 Conditions for optical gain Conditions for steady-state inversion Necessary, but not sufficient condition 2.3 The semi-classical treatment ^ Outline Selection rules for electric dipole transitions 2.4 Atomic population kinetics^ Rate equations Semi-classical equations Validity of the rate-equation approach 3 Broadening mechanisms and lineshapes 3.1 Homogeneous broadening mechanisms Natural broadening Pressure broadening Phonon broadening 3.2 Inhomogeneous broadening mechanisms Doppler broadening Broadening in amorphous solids 3.3 The interaction of radiation and matter in the presence spectral broadening Homogeneously broadened transitions Inhomogeneously broadened atoms ^ 3.4 The formation of spectral lines: The Voigt profile^

3 viii contents 3.5 Other broadening effects Self-absorption 4 Light amplification by the stimulated emission of radiation 4.1 The optical gain cross-section Condition for optical gain Frequency dependence of the gain cross-section The gain coefficient Gain narrowing 4.2 Narrowband radiation Amplification of narrowband radiation Form of rate equations 4.3 Gain cross-section for inhomogeneous broadening* 4.4 Orders of magnitude 4.5 Absorption The absorption cross-section Self-absorption Radiation trapping 5 Gain saturation Saturation in a steady-state amplifier Homogeneous broadening Inhomogeneous broadening 1 ' Saturation in a homogeneously broadened pulsed amplifier* Design of laser amplifiers The laser oscillator Introduction Amplified spontaneous emission (ASE) lasers Optical cavities General considerations Low-loss (or 'stable') optical cavities High-loss (or 'unstable') optical cavities* Beam quality* The M 2 beam-propagation factor The approach to laser oscillation The 'cold' cavity The laser threshold condition Laser oscillation above threshold Condition for steady-state laser oscillation Homogeneously broadened systems 113

4 contents ix Inhomogeneously broadened systems^ 6.7 Output power Low-gain lasers High-gain lasers: the Rigrod analysis^ Output power in other cases 7 Solid-state lasers 7.1 General considerations Energy levels of ions doped in solid hosts ^ Radiative transitions* Non-radiative transitions* Line broadening* Three- and four-level systems Host materials Techniques for optical pumping 7.2 Nd 3+ :YAG and other trivalent rare-earth systems Energy-level structure Transition linewidth Nd:YAG laser Other crystalline hosts Nd:glass laser Erbium lasers Praseodymium ions 7.3 Ruby and other trivalent iron-group systems Energy-level structure* The ruby laser Alexandrite laser CnLiSAF and CnLiCAF Ti:sapphire 8 Dynamic cavity effects 8.1 Laser spiking and relaxation oscillations Rate-equation analysis Analysis of relaxation oscillations Numerical analysis of laser spiking 8.2 Q-switching Techniques for Q-switching Rate-equation analysis of Q-switching Comparison with numerical simulations 8.3 Modelocking General ideas Simple treatment of modelocking Active modelocking techniques Passive modelocking techniques

5 x contents 8.4 Other forms of pulsed output Semiconductor lasers Basic features of a typical semiconductor diode laser Review of semiconductor physics Band structure Density of states and the Fermi energy (T = OK) The Fermi-Dirac distribution {T ^ 0 K) Doped semiconductors Radiative transitions in semiconductors Gain at a p-i-n junction Gain in diode lasers Carrier and photon confinement: the double heterostructure Laser materials Quantum-well lasers 1 " Laser threshold Diode laser beam properties Beam shape Transverse modes of edge-emitting lasers Longitudinal modes of diode lasers Single longitudinal mode diode lasers Diode laser linewidth Tunable diode laser cavities^ Diode laser output power 1 " VCSEL lasers 1 " Strained-layer lasers Quantum cascade lasers 1^ Fibre lasers Optical fibres The importance of optical-fibre technology Optical-fibre properties: Ray optics Optical-fibre properties: Wave optics Dispersion in optical fibres Fabrication of optical fibres Fibre-optic components Wavelength bands for fibre-optic telecommunications Erbium-doped fibre amplifiers Energy levels and pumping schemes Gain spectra EDFA design and layout Fabrication of erbium-doped fibre amplifiers Fibre Raman amplifiers Introduction 285

6 contents xi Raman scattering Fibre Raman amplifiers Long-haul optical transmission systems High-power fibre lasers The revolution in fibre-laser performance Cladding-pumped fibre-laser design Materials and mechanisms of cladding-pumped fibre-laser systems High-power fibre lasers: Linewidth considerations High-power pulsed fibre lasers Large mode area (LMA) fibres Q-switched fibre lasers Oscillator-amplifier pulsed fibre lasers Applications of high-power fibre lasers Atomic gas lasers Discharge physics interlude Low-pressure and high-pressure discharges Low-pressure glow discharge Temperatures The steady-state positive column Ionization rates Excitation rates Second-kind or superelastic collisions Excited-state populations in low-pressure discharges The helium-neon laser Introduction Energy levels, transitions and excitation mechanisms Laser construction and operating parameters Output-power limitations of the He-Ne laser Applications of He-Ne lasers The argon-ion laser Introduction Energy levels, transitions and excitation mechanisms Laser construction and operating parameters Argon-ion laser: Power limitations Krypton-ion lasers Applications of ion lasers Infra-red molecular gas lasers Efficiency considerations Energy levels of atoms and molecules Quantum ratio 333

7 12.2 Partial population inversion between vibrational energy levels of molecules Physics of the C0 2 laser Levels and lifetimes The effect of adding N Effect of adding He CO2 laser parameters Low-pressure c.w. CO2 lasers High-pressure pulsed CO2 lasers Other types of C0 2 laser Gas-dynamic C0 2 lasers Waveguide C0 2 lasers Applications of CO2 lasers Ultraviolet molecular gas lasers The UV and VUV spectral regions Energy levels of diatomic molecules Separation of the overall wave function Vibrational eigenfunctions Electronic transitions in diatomic molecules: The Franck-Condon principle Absorption transitions The'Franck-Condon loop' The VUV hydrogen laser The UV nitrogen laser Excimer molecules Rare-gas excimer lasers Rare-gas halide excimer lasers Spectroscopy of the rare-gas halides Rare-gas halide laser design Pulse-length limitations of discharge-excited RGH lasers Cavity design and beam properties of RHG lasers Performance and applications of RGH excimer laser Dye lasers Introduction Dye molecules Energy levels and spectra of dye molecules in solution Energy-level scheme Singlet-singlet absorption Singlet-singlet emission spectra Triplet-triplet absorption Rate-equation models of dye laser kinetics 387

8 contents xiii 14.5 Pulsed dye lasers Flashlamp-pumped systems Dye lasers pumped by pulsed lasers Continuous-wave dye lasers Population kinetics Continuous waves dye laser design Solid-state dye lasers Applications of dye lasers Non-linear frequency conversion Introduction Linear optics of crystals Classes of anisotropic crystals Vectors Field directions for o- and e-rays in a uniaxial crystal Basics of non-linear optics Maxwell's equations for non-linear media Second-harmonic generation in anisotropic crystals The requirement for phase matching Phase-matching techniques Birefringent phase matching in uniaxial crystals Critical and non-critical phase matching Poynting vector walk-off in birefringent phase matching Other factors affecting SHG conversion efficiency Phase-matched SHG in biaxial crystals Birefringent materials for SHG Quasi-phase matching techniques SHG: practical aspects Three-wave mixing and third-harmonic generation (THG) Three-wave mixing processes in general Third-harmonic generation (THG) Optical parametric oscillators (OPOs) Parametric interactions Optical parametric oscillators (OPOs) Practical parametric devices Precision frequency control of lasers^ Frequency pulling Single longitudinal mode operation Short cavity Intra-cavity etalons Ring resonators Other techniques 440

9 xiv contents 16.3 Output linewidfh The Schawlow-Townes limit Practical limitations Intensity noise Frequency locking Locking to atomic or molecular transitions Locking to an external cavity Frequency combs Ultrafast lasers Propagation of ultrafast laser pulses in dispersive media The time-bandwidth product General considerations Propagation through a dispersive system Propagation of Gaussian pulses Non-linear effects: self-phase modulation and the B-integral Dispersion control Geometric dispersion control Chirped mirrors Pulse shaping Sources of ultrafast optical pulses Modelocked lasers Oscillators Chirped-pulse amplification (CPA) Measurement of ultrafast pulses Autocorrelators Methods for exact reconstruction of the pulse Short-wavelength lasers Definition of wavelength ranges Difficulties in achieving optical gain at short wavelengths Pump-power scaling General properties of short-wavelength lasers Travelling-wave pumping Threshold and saturation behaviour in an ASE laser Spectral width of the output Coherence properties of ASE lasers Laser-generated plasmas^ Inverse bremsstrahlung heating Generation of highly ionized plasmas from laser-solid interactions Optical field ionization Collisionally excited lasers 517

10 contents xv Ne-likeions t Ni-likeions t Methods of pumping Collisionally excited OFI lasers Recombination lasers H-like carbon OFI recombination lasers Other sources High-harmonic generation Free-electron lasers Appendix A: The semi-classical theory of the interaction of radiation and matter 548 A.l The amplitude equations 548 A. 1.1 Derivation of the amplitude equations 548 A. 1.2 Solution of the amplitude equations 550 A.2 Calculation of the Einstein B coefficient 551 A.2.1 Polarized atoms and radiation 551 A.2.2 Unpolarized atoms and/or radiation 553 A.2.3 Treatment of degeneracy 554 A.3 Relations between the Einstein coefficients 555 A.4 Validity of rate equations 555 Appendix B: The spectral Einstein coefficients 557 Appendix C: Kleinman's conjecture 560 Bibliography 563 Index 579