Contents

Part 5 Quantum optics 
5.1 
Quantum optics 
F. 
Haug, M. Freyberger, K. Vogel, W.P. Schleich ................... 3

5.1.1 
Introduction ............................................................ 3

5.1.1.1 
A brief history of quantum optics .......................................... 3

5.1.1.2 
Outline of the review .................................................... 4

5.1.2 
Field quantization in Coulomb gauge ...................................... 5

5.1.2.1 
Mode expansion ......................................................... 5

5.1.2.1.1 
Running waves .......................................................... 6

5.1.2.1.2 
Standing waves ......................................................... 6

5.1.2.1.3 
Energy of the radiation .eld .............................................. 7

5.1.2.2 
Field quantization ....................................................... 7

5.1.2.3 
Single mode ............................................................ 8

5.1.3 
Field states ............................................................. 8

5.1.3.1 
Pure and mixed states ................................................... 9

5.1.3.2 
Photon number states .................................................... 9

5.1.3.3 
Coherent states ......................................................... 10

5.1.3.4 
Squeezed states ......................................................... 11

5.1.3.5 
Thermal states .......................................................... 12

5.1.3.6 
Measures of non-classicality ............................................... 13

5.1.3.6.1 
Mandel Q-parameter ..................................................... 13

5.1.3.6.2 
GlauberSudarshan distribution ........................................... 13

5.1.4 
Atom.eld interaction ................................................... 14

5.1.4.1 
Electric .elddipole interaction ............................................ 14

5.1.4.2 
Simple model for atom.eld interaction .................................... 14

5.1.4.2.1 
Hamiltonian ............................................................ 15

5.1.4.2.2 
Dynamics of JaynesCummingsPaul model ................................ 15

5.1.4.2.3 
Quantum motion in an ion trap ........................................... 16

5.1.4.3 
Quantum state engineering ............................................... 16

5.1.4.3.1 
Resonant case: photon number state preparation ............................ 16

5.1.4.3.2 
Far o.-resonant case: Schr
odinger cat state preparation ...................... 17

5.1.5 
Reservoir theory ........................................................ 18

5.1.5.1 
Master equation ......................................................... 18

5.1.5.1.1 
Mathematics of the model ................................................ 18

5.1.5.1.2 
Methods of solution ..................................................... 18

5.1.5.2 
Damping and ampli.cation ............................................... 19

5.1.5.3 
Decoherence ............................................................ 19

5.1.6 
One-atom maser ........................................................ 20

5.1.6.1 
Master equation ......................................................... 21

5.1.6.2 
Steady-state photon statistics ............................................. 21

5.1.7	
Atomreservoir interaction ............................................... 22

5.1.7.1	
Master equation ......................................................... 22

5.1.7.2	
Lamb shift ............................................................. 23

5.1.7.3	
WeisskopfWigner decay ................................................. 23

5.1.8	
Resonance .uorescence ................................................... 24

5.1.8.1	
Model ................................................................. 24

5.1.8.2	
Spectrum and antibunching ............................................... 24

5.1.9	
Fundamental questions of quantum mechanics ............................... 26

5.1.9.1	
Quantum jumps ......................................................... 26

5.1.9.1.1	
Continuous versus discontinuous dynamics .................................. 26

5.1.9.1.2	
Experimental observation ................................................. 27

5.1.9.2	
Waveparticle duality .................................................... 28

5.1.9.2.1	
Delayed choice experiments ............................................... 28

5.1.9.2.2	
Quantum-optical tests of complementarity .................................. 29

5.1.9.3	
Entanglement ........................................................... 30

5.1.9.4	
Bell inequality .......................................................... 31

5.1.10	
New frontiers ........................................................... 32

5.1.10.1	
Atom optics in quantized .elds ............................................ 32

5.1.10.2	
BoseEinstein condensation ............................................... 33

5.1.10.2.1	
History ................................................................ 34

5.1.10.2.2	
BoseEinstein condensation in dilute atomic gases ........................... 34

5.1.10.2.3	
GrossPitaevskii equation ................................................ 34

5.1.10.2.4	
Experiments with BoseEinstein condensates ............................... 35

5.1.10.3	
Quantum information .................................................... 36

5.1.10.3.1	
Quantum teleportation ................................................... 36

5.1.10.3.2	
Quantum cryptography .................................................. 38


X	Contents 
References for 5.1 ....................................................... 39

Part 6 Coherence and superradiance 
6.1	
Coherence 

W. 
Martienssen, H. Paul .............................................. 49

6.1.1 
Historical remarks ....................................................... 49

6.1.2 
Basic concepts .......................................................... 49

6.1.2.1 
Classical light ........................................................... 49

6.1.2.2 
Non-classical light ....................................................... 50

6.1.2.3 
Field mode ............................................................. 50

6.1.2.4 
Single-mode .eld ........................................................ 50

6.1.2.5 
Electric .eld strength .................................................... 50

6.1.2.6 
Interference ............................................................. 50

6.1.2.7 
Decoherence ............................................................ 51

6.1.3 
Coherence theory ........................................................ 51

6.1.3.1 
Field correlation functions ................................................ 51

6.1.3.1.1 
De.nitions ............................................................. 51

6.1.3.1.2 
Connections between correlation functions of di.erent order .................. 51

6.1.3.2 
First-order coherence .................................................... 52

6.1.3.2.1 
Degree of coherence ...................................................... 52

6.1.3.2.2 
Temporal coherence ..................................................... 52

6.1.3.2.3 
Spatial coherence ........................................................ 53


Filtering out coherent light from a chaotic source ............................ 55

Measurement of coherence lengths ......................................... 55

Laser light versus chaotic light ............................................ 55

Generating mechanisms and radiation characteristics ......................... 55

Chaotic light ............................................................ 55

Laser light .............................................................. 55

Interference between beams from independent sources ........................ 56

Coherent interaction ..................................................... 56

Particle interference ..................................................... 57

Higher-order coherence ................................................... 57

Intensity interference .................................................... 58

Formal description ....................................................... 58

Measurement ........................................................... 58

Spatial intensity correlations .............................................. 58

Stellar intensity interferometry ............................................ 58

Temporal intensity correlations ............................................ 59

Amplitude stabilization .................................................. 59

Photon bunching ........................................................ 59

Photon antibunching ..................................................... 59

Experiments with entangled photon pairs ................................... 60

Parametric down-conversion .............................................. 60

Two-photon mixing ...................................................... 60

HongOuMandel interferometer .......................................... 60

Photon-pair interference .................................................. 61

Interferometric devices ................................................... 61

Franson experiment ...................................................... 61

Photon counting statistics ................................................ 62

Measurement ........................................................... 62

Photon distribution functions ............................................. 62

Measurements under di.erent experimental conditions ....................... 63

Variances of the photon number ........................................... 63

References for 6.1 ....................................................... 64

Superradiance 
M.G. Benedict, E.D. Trifonov ........................................ 67

De.nitions and historical layout ........................................... 67

Superradiance theory .................................................... 68

Superradiance of a system with dimensions smaller than the radiation wavelength 68

Superradiation of an extended multiatomic system ........................... 70

Superradiance experiments ............................................... 73

A 
microscopic observation of superradiance and subradiance .................. 74

Superradiance experiments in pencil-shaped macroscopic samples .............. 75

Superradiant-type Rayleigh scattering from a BoseEinstein condensate ........ 77

Outlook ................................................................ 78

References for 6.2 ....................................................... 79



7.1	
Modulators 
B. 
Kuhlow ............................................................ 85

7.1.1	
Introduction ............................................................ 85

7.1.2	
Light propagation in crystals .............................................. 86

7.1.3	
Linear electro-optic e.ect ................................................. 87

7.1.3.1	
Modulator devices ....................................................... 87

7.1.3.1.1	
Phase modulation ....................................................... 88

7.1.3.1.2	
Polarization modulation (dynamic retardation) .............................. 89

7.1.3.1.3	
Amplitude modulation ................................................... 90

7.1.3.1.4	
Design considerations .................................................... 91

7.1.3.2	
Traveling-wave modulator ................................................ 91

7.1.3.3	
Examples .............................................................. 92

7.1.3.3.1	
Crystal classes .......................................................... 92

7.1.3.3.1.1	
Crystal class 
42m ....................................................... 92

7.1.3.3.1.2	
Crystal class 3m ........................................................ 92

7.1.3.3.1.3	
Crystal class 
43m ....................................................... 93

7.1.3.3.2	
Selected electro-optic materials and modulator systems ....................... 94

7.1.3.4	
Electro-optic beam de.ector .............................................. 94

7.1.4	
Kerr electro-optic e.ect modulators ........................................ 96

7.1.4.1	
Kerr e.ect in isotropic media ............................................. 96

7.1.5	
Acousto-optic modulators ................................................ 98

7.1.5.1	
The photoelastic e.ect ................................................... 98

7.1.5.2	
Interaction regimes ...................................................... 100

7.1.5.2.1	
RamanNath regime ..................................................... 100

7.1.5.2.2	
Bragg regime ........................................................... 101

7.1.5.2.2.1	
Isotropic interaction ..................................................... 101

7.1.5.2.2.2	
Anisotropic interaction ................................................... 102

7.1.5.2.2.3	
E.ciency .............................................................. 102

7.1.5.2.2.4	
Bandwidth ............................................................. 103

7.1.5.3	
Acousto-optic intensity modulator ......................................... 106

7.1.5.4	
Acousto-optic de.ector ................................................... 106

7.1.6	
Glossary ............................................................... 108



References for 7.1 ....................................................... 110

7.2	
Thin-.lm technology 
D. 
Ristau	.............................................................111

7.2.1	
Introduction ............................................................ 111

7.2.2	
Basic principle of optical thin-.lm systems .................................. 111

7.2.3	
Production of optical coatings ............................................. 114

7.2.4	
Quality parameters of optical laser components ............................. 116

7.2.5	
Measurement of critical parameters of laser components ...................... 117

7.2.5.1	
Calorimetric measurement of absorption .................................... 117

7.2.5.2	
Measurement of total scattering ........................................... 119

7.2.5.3	
Laser-induced damage thresholds .......................................... 120

7.2.5.4	
Quality parameters of laser components: present state ........................ 121

7.2.6	
Examples for advanced laser components ................................... 122

7.2.7	
Summary and future trends ............................................... 123



References for 7.2 ....................................................... 125

7.3	
Beam shaping 
M. 
Scholl .............................................................127

7.3.1	
Introduction ............................................................ 127

7.3.2	
Beam-shaping techniques and design procedures ............................. 129

7.3.2.1	
Beam transformation .................................................... 130

7.3.2.1.1	
Coherent beams ......................................................... 130

7.3.2.1.2	
Partially coherent beams and geometric optic approximation .................. 132

7.3.2.1.3	
Comparison of the geometric-optical solution with the solution from the
coherent techniques ...................................................... 133

7.3.2.2	
Beam integration ........................................................ 133

7.3.2.3	
Beam integration with beamlet shaping .................................... 137

7.3.2.4	
Beam shaping and coherence .............................................. 138

7.3.2.5	
Beam splitting .......................................................... 139

7.3.2.6	
Manufacturing of beam-shaping elements ................................... 140

7.3.3	
Conclusion ............................................................. 142



References for 7.3 ....................................................... 143

Part 8 Optical resonators 
8.1	
Optical resonators 


N. 
Hodgson ...........................................................147

8.1.1 
Introduction ............................................................ 147

8.1.1.1 
Linear stable resonators .................................................. 147

8.1.1.2 
Linear unstable resonators ................................................ 147

8.1.1.3 
Ring resonators ......................................................... 148

8.1.1.4 
Waveguide resonators .................................................... 148

8.1.1.5 
Reviewing the basic properties of all optical resonators ....................... 148

8.1.2 
Classi.cation of optical resonators ......................................... 149

8.1.3 
Uncon.ned stable resonators .............................................. 151

8.1.3.1 
Transverse mode structures ............................................... 152

8.1.3.1.1 
GaussLaguerre and GaussHermite modes ................................. 152

8.1.3.1.2 
Hybrid modes ........................................................... 156

8.1.3.2 
Beam propagation of stable resonator modes ................................ 157

8.1.3.2.1 
Fundamental mode ...................................................... 157

8.1.3.2.2 
Higher-order modes ...................................................... 159

8.1.3.3 
Beam quality and resonator parameters.................................... 161

8.1.3.4 
Resonance frequencies .................................................... 163

8.1.4 
Aperture-limited stable resonators ......................................... 164

8.1.4.1 
Resonators with one aperture ............................................. 164

8.1.4.2 
Resonators with two apertures ............................................ 166

8.1.5 
Misalignment sensitivity .................................................. 167

8.1.5.1 
Fundamental-mode operation............................................. 169

8.1.5.2 
Multimode operation .................................................... 170

8.1.6	
Unstable resonators ...................................................... 172

8.1.6.1	
Beam propagation ....................................................... 172

8.1.6.1.1	
Characterization of unstable resonators .................................... 172

8.1.6.1.2	
Resonator schemes ...................................................... 174

8.1.6.2	
Mode structures and losses ............................................... 176

8.1.6.3	
Beam quality ........................................................... 178

8.1.6.3.1	
Circular symmetry ...................................................... 178

8.1.6.3.2	
Rectangular symmetry ................................................... 179

8.1.6.4	
Unstable resonators with variable-re.ectivity mirrors ......................... 180

8.1.6.5	
Applications of unstable resonators ........................................ 183

8.1.7	
Output power of stable resonators ......................................... 184

8.1.7.1	
Calculation of the output power of stable resonators ......................... 184

8.1.7.2	
Optimum output coupling and maximum output power ...................... 187

8.1.7.2.1	
Homogeneous line broadening ............................................. 188

8.1.7.2.2	
Inhomogeneous line broadening ........................................... 190

8.1.8	
Thermal lensing in solid-state lasers ....................................... 190

8.1.8.1	
Fundamental-mode operation............................................. 191

8.1.8.2	
Transverse multimode operation ........................................... 194

8.1.9	
Ring resonators ......................................................... 196

8.1.9.1	
General properties of ring resonators ....................................... 196

8.1.9.2	
Unstable ring resonators ................................................. 198

8.1.9.3	
Nonplanar ring resonators ................................................ 200

8.1.10	
Waveguide resonators .................................................... 201

8.1.10.1	
Motivation ............................................................. 201

8.1.10.2	
Eigenmodes of hollow rectangular waveguides ............................... 202

8.1.10.3	
Properties of waveguide resonators ........................................ 205

8.1.10.3.1	
Waveguide resonator con.gurations ........................................ 206

8.1.10.3.1.1 
Case I resonators ........................................................ 206

8.1.10.3.1.2 
Case II resonators ....................................................... 206

8.1.10.3.1.3 
Case III resonators ...................................................... 206

8.1.10.3.2	
Calculated round-trip losses of the lowest-loss resonator mode ................. 207

8.1.10.3.3	
Mode properties of a general waveguide resonator ........................... 208

8.1.10.4	
Waveguide resonator mode and loss calculations ............................. 208

8.1.10.5	
Properties of slab waveguide lasers ........................................ 210



References for 8.1 ....................................................... 213

Part 9 Interferometry 
9.1	
Interferometry 


H.J. Tiziani,N.Kerwien,G.Pedrini ..................................221

9.1.1 
Introduction ............................................................ 221

9.1.2 
Basic principles of interference ............................................ 222

9.1.2.1 
Coherence .............................................................. 222

9.1.2.1.1 
Temporal coherence ..................................................... 222

9.1.2.1.2 
Spatial coherence ........................................................ 223

9.1.2.2 
Two-beam interference ................................................... 223

9.1.2.3 
Interference in a plane-parallel plate....................................... 224

9.1.2.4 
Vector e.ects of interference .............................................. 226

9.1.3	
Interferometry for optical testing .......................................... 228

9.1.3.1	
Basic interferometer types ................................................ 228

9.1.3.1.1	
Michelson interferometer ................................................. 228

9.1.3.1.2	
TwymanGreen interferometer ............................................ 229

9.1.3.1.3	
Fizeau interferometer.................................................... 230

9.1.3.1.4	
MachZehnder interferometer ............................................. 230

9.1.3.1.5	
Shearing interferometry.................................................. 231

9.1.3.1.6	
FabryPerot interferometer ............................................... 231

9.1.3.2	
Quantitative electronic phase evaluation techniques .......................... 231

9.1.3.2.1	
The Fourier-transform technique .......................................... 232

9.1.3.2.2	
Fringe analysis by phase shifting .......................................... 232

9.1.3.2.3	
Phase-locked interferometry .............................................. 234

9.1.4	
Interferometry for surface metrology ....................................... 234

9.1.4.1	
Interferometry with extended range and reduced sensitivity: Oblique incidence
interferometry .......................................................... 234

9.1.4.1.1	
Prismatic interferometer with oblique incidence ............................. 234

9.1.4.1.2	
Grating interferometer with oblique incidence ............................... 236

9.1.4.2	
Multiwavelength interferometry ........................................... 236

9.1.4.3	
White-light interferometry ................................................ 237

9.1.4.4	
Polarization interferometry ............................................... 239

9.1.5	
Heterodyne interferometry for velocity and distance measurement ............. 241

9.1.5.1	
Principle of heterodyne interferometry ..................................... 241

9.1.5.2	
Absolute heterodyne interferometry:
Double heterodyne interferometry (DHI) ................................... 243

9.1.6	
Interferometry with adaptive optics ........................................ 244

9.1.6.1	
Interferometry with a null corrector ........................................ 244

9.1.6.2	
Adaptive optics with optical light modulator ................................ 246

9.1.6.3	
Adaptive optics with deformable membrane mirror .......................... 247

9.1.6.4	
Adaptive optics for optical stitching using dynamically tilted reference wave .... 249

9.1.7	
Speckle pattern interferometry ............................................ 250

9.1.7.1	
Some properties of speckles ............................................... 251

9.1.7.2	
Speckle applications ..................................................... 253

9.1.7.3	
Speckle pattern interferometry for deformation measurements ................. 253

9.1.7.4	
Phase analysis in speckle interferometry .................................... 256

9.1.7.4.1	
Phase analysis by phase stepping .......................................... 256

9.1.7.4.2	
Phase analysis by spatial phase shifting .................................... 256

9.1.7.4.3	
Analysis of vibrating objects .............................................. 257

9.1.7.5	
Temporal speckle pattern interferometry (TSPI) ............................. 257

9.1.7.5.1	
Shape measurement with TSPI by using time-varying wavelength change ....... 259

9.1.7.5.2	
Laser diode with external cavity for wavelength change ....................... 259

9.1.7.5.3	
Application of TSPI for deformation measurement...........................260

9.1.7.5.4	
Deformation measurements by TSPI and digital holography, a comparison ...... 260

9.1.7.5.5	
Vibration measurement with TSPI ........................................ 262

9.1.8	
Holographic interferometry ............................................... 263

9.1.8.1	
Principle of holography .................................................. 263

9.1.8.2	
Principle of holographic interferometry ..................................... 265

9.1.8.3	
Digital holography ....................................................... 266

9.1.8.3.1	
Principle of digital holography ............................................ 266

9.1.8.3.2	
Con.gurations for recording and reconstruction of digital holograms ........... 267

9.1.8.3.2.1	
Lensless Fourier hologram ................................................ 269

9.1.8.3.2.2	
Fresnel hologram ........................................................ 270

9.1.8.3.2.3	
Image-plane hologram .................................................... 271

9.1.8.4	
Digital holographic interferometry ......................................... 272

9.1.8.4.1	
Principle of digital holographic interferometry ............................... 272

9.1.8.4.2	
Digital holographic interferometry for dynamic deformations .................. 272

9.1.8.4.2.1	
Dimensional measurements............................................... 272

9.1.8.4.2.2	
Digital holographic interferometry for deformation and vibration analysis of 3D
objects.................................................................273

9.1.8.4.3	
Pulsed digital holographic interferometry for endoscopic investigations ......... 276

9.1.8.4.4	
Temporal phase unwrapping of digital holograms ............................ 278



References for 9.1 ....................................................... 280

Index ............................................................................285



6.1.3.2.4 
6.1.3.2.5 
6.1.3.3 
6.1.3.3.1 
6.1.3.3.1.1 
6.1.3.3.1.2 
6.1.3.3.2 
6.1.3.3.3 
6.1.3.4 
6.1.3.5 
6.1.4 
6.1.4.1 
6.1.4.2 
6.1.4.3 
6.1.4.3.1 
6.1.4.4 
6.1.4.4.1 
6.1.4.4.2 
6.1.4.4.3 
6.1.4.5 
6.1.4.5.1 
6.1.4.5.2 
6.1.4.5.2.1 
6.1.4.5.3 
6.1.4.5.3.1 
6.1.4.5.3.2 
6.1.5 
6.1.5.1 
6.1.5.2 
6.1.5.3 
6.1.5.4 
6.2 
6.2.1 
6.2.2 
6.2.2.1 
6.2.2.2 
6.2.3 
6.2.3.1 
6.2.3.2 
6.2.3.3 
6.2.4 
Contents XI 
XII	Contents 
Part 7 Optical components 
Contents	XIII 
XIV	Contents 
Contents	XV 
XVI	Contents 
