Tailored Light 1 (eBook)

Prof. Dr. Reinhart Poprawe holds a M. A. in Physics degree from the California State University in Fresno which he received in 1977. After completion of his diploma and PhD in physics (Darmstadt 1984) he joined the Fraunhofer Institute for Laser Technology in Aachen where he began working as head of the department „Laser oriented process development" in 1985. From 1989 to 1/1996 he has been managing director of Thyssen Laser Technik GmbH in Aachen. Since February 1996 he is managing director of the Fraunhofer Institute for Laser Technology and holds the University Chair for Laser Technology at the RWTH Aachen. Currently he is a member of the board in the AKL Arbeitskreis Lasertechnik e. V. Aachen. Prof. Poprawe has been elected to the grade of Fellow in the Society of Manufacturing Engineers in USA (SME) since 1998. Since 2001 he is a member of the board of the Laser Institute of America (LIA) and serves in many national and international boards as advisor, referee or consultant. Since 09/2005 he is Vice-Rector for Structure, Research and Junior Academic Staff. In 2006 he became Fellow of the Laser Institute of America LIA.

Preface 6
Who Should Read in this Book? 6
Contents 8
1 The History of Laser 13
2 An Introduction to Laser Technology 19
2.1 The Laser 19
2.1.1 Stimulated Emission 20
2.1.2 Population Inversion and Amplification 22
2.2 The Laser Medium 24
2.2.1 The Laser Pumping Process 25
2.2.2 Cooling 27
2.3 Feedback and Self-Excitation 28
2.4 The Laser Resonator 30
2.5 Laser Radiation 32
2.5.1 Characteristic Properties 32
2.5.2 Laser Mode 34
2.5.3 Coherence 35
2.6 Fields of Applications of Laser Technology 36
3 Electromagnetic Radiation 39
3.1 The Spectrum of Electromagnetic Radiation 39
3.2 The Wave Equation 41
3.2.1 Maxwell’s Equations 41
3.2.2 The General Wave Equation 43
3.2.3 Wave Equation in Vacuum 44
3.2.4 Wave Equations in Material 45
3.2.5 Scalar Wave Equations 47
3.3 Elementary Solutions of the Wave Equation 48
3.3.1 Introduction to Complex Field Parameters 48
3.3.2 Planar Waves 50
3.3.3 Polarization of Electromagnetic Waves 51
3.3.4 Spherical Waves 56
3.3.5 Energy Density of Electromagnetic Waves 59
3.4 Superposition of Waves 63
3.4.1 Superposition with Different Phases 63
3.4.2 Superposition of Differently Polarized Waves 64
3.4.3 Superposition of Waves of Different Frequency 65
3.4.4 Group Velocity and Dispersion 67
3.4.5 Superposition of Waves with Different Propagation Directions 68
4 The Propagation of Electromagnetic Waves 70
4.1 Propagation Regimes and Fresnel Number 70
4.2 Geometrical Optics 73
4.2.1 Fermat’s Principle 73
4.3 Reflection and Refraction 75
4.3.1 Law of Reflection 76
4.3.2 Law of Refraction 76
4.3.3 Total Reflection 77
4.4 Transmission and Reflection Coefficients 78
4.4.1 The Fresnel Equations 79
4.4.2 Reflectance and Transmittance 82
4.4.3 The Brewster Angle 83
4.5 Basic Optical Elements 84
4.5.1 Refraction at a Prism 85
4.5.2 The Thin Lens 86
4.5.3 The Thick Lens 91
4.5.4 Spherically Curved Mirrors 93
4.6 Matrix Formalism of Geometrical Optics 94
4.7 Aberration 94
4.7.1 Spherical Aberration 98
4.7.2 Coma 99
4.7.3 Astigmatism 100
4.7.4 Field Curvature 102
4.7.5 Distortion 102
4.7.6 Chromatic Aberration 103
4.7.7 Diffraction Limit 104
4.8 Diffraction 105
4.8.1 Huygens’ Principle and Kirchhoff’s Diffraction Integral 106
4.8.2 The Fresnel Diffraction 108
4.8.3 The Fraunhofer Diffraction 110
4.8.4 Diffraction at the Slit 110
4.9 Nonlinear Optics 112
4.9.1 Maxwell’s and Material Equations 112
4.9.1.1 First Order Polarization 113
4.9.1.2 Second-Order Polarization 114
4.9.2 Wave Equation 116
4.9.2.1 Separating the Fast Oscillating Factors 116
4.9.3 Three Wave Mixing 116
4.9.3.1 Polarization of the Pump Wave 117
4.9.3.2 Phase Matching 118
4.9.3.3 Signal and Idler Waves 118
4.9.3.4 Walk-off 119
References 120
5 Laser Beams 121
5.1 The SVE Approximation 122
5.2 The Gaussian Beam 123
5.2.1 The Amplitude Factor 124
5.2.2 The Phase Factor 125
5.2.3 The Intensity Distribution of the Gaussian Beam 126
5.3 Higher-Order Modes 128
5.3.1 The Hermite-Gaussian Modes 128
5.3.2 The Laguerre-Gaussian Modes 131
5.3.3 Doughnut Modes 132
5.3.4 The Beam Radius of Higher-Order Modes 133
5.4 Real Laser Beams and Beam Quality 136
5.5 Transformation of Gaussian Beams 138
5.5.1 The ABCD Law 139
5.5.2 Focusing of a Gaussian Beam by a Thin Lens 140
5.5.3 Adjustment of the Focus Radius 143
5.5.4 Influence of Spherical Aberrations 147
6 Optical Resonators 150
6.1 Eigenmodes of the Electromagnetic Field 151
6.1.1 Eigenmode of a One-Dimensional Resonator 151
6.1.2 Eigenmodes of a Rectangular Cavity 152
6.2 Selection of Modes and Resonator Quality 154
6.2.1 The Open Resonator 155
6.2.2 Frequency Selection: The Fabry-Perot-Resonator 156
6.2.3 Eigen Modes and the Threshold of Self-Excitation 157
6.2.4 Line Width and Resonator Quality 158
6.3 Resonators with Spherical Mirrors 161
6.3.1 Beam Geometry in the Resonator 161
6.3.2 The Stability Criterion 164
6.3.3 Eigenfrequencies of Stable Spherical Resonators 167
6.4 Influence of Mirror Boundaries 169
6.4.1 The Diffraction Integral Between Curved Mirrors 170
6.4.2 Eigenvalue Equation for Open Spherical Resonators 171
6.4.3 Eigenmodes According to the Methods from Fox and Li 172
6.5 Unstable Resonators 173
6.5.1 Field Distribution of Unstable Resonators 176
6.6 Resonator Losses 177
6.6.1 Diffraction Losses 179
6.6.2 Absorption and Scattering at the Mirrors 180
6.6.3 Misalignment 182
6.6.4 Influence of the Laser Medium 185
7 Interaction of Light and Matter 187
7.1 Absorption and Emission of Light—Spectral Lines 188
7.2 The Dipole Model 190
7.2.1 The Lorentz Model 191
7.2.2 The Complex Index of Refraction 193
7.2.3 The Dispersion Relation 194
7.2.4 Absorption 196
7.3 Quantum Physics, Photons and Rate Equations 198
7.3.1 The Quantum Mechanical Model of the Atom 199
7.3.2 Photons 202
7.3.3 Absorption and Emission of Photons 204
7.3.4 Einstein’s Rate Equations 207
7.3.5 Planck’s Law 209
7.3.6 Population Inversion and Amplification 211
Reference 212
8 The Production of Laser Radiation 213
8.1 The Laser Principle 213
8.2 Producing Population Inversion 214
8.2.1 Three-Level Systems 215
8.2.2 Four-Level Systems 216
8.2.3 Pump Mechanisms 218
8.3 The Rate Equations of the Laser 219
8.3.1 Solving the Rate Equations for Stationary Operation 222
8.3.2 The Laser Threshold 226
8.3.3 Amplification 227
8.4 Laser Output Power and Efficiency 231
8.4.1 Available Amplification Power 231
8.4.2 Laser Output Power 232
8.4.3 Optimal Degree of Outcoupling and Optimal Laser Power 236
8.4.4 Laser Efficiency 236
8.5 Hole Burning and Multimode Operation 238
8.5.1 Ideally Homogeneously Enhanced Laser Line 239
8.5.2 Homogeneous Line Broadening 241
8.5.3 Inhomogeneous Broadening and Spectral Hole Burning 241
8.5.4 Spatial Hole Burning 243
8.6 Nonstationary Behavior and Pulse Generation 244
8.6.1 Spiking 244
8.6.2 Nonstationary Pulse Generation: The Q-Switch Laser 247
8.6.2.1 Inversion Build-up (t  lessthan  tR) 250
8.6.2.2 Start-up Phase (t  greaterthan  tR) 250
8.6.2.3 Maximum of the Pulses (t = tmax) 252
8.6.2.4 Pulse End (t  greaterthan  tmax) 252
8.6.3 Modulators for Q-Switching 255
8.6.4 Cavity Dumping 258
8.6.5 Examples on how to Control the Pulse Form 258
8.7 Stationary Pulse Generation: Mode Locking 260
8.7.1 Superpositioning of Longitudinal Resonator Modes 260
8.7.2 Active and Passive Mode Locking 267