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Theoretical Optics: An Introduction

Theoretical Optics: An Introduction

Hartmann Römer

ISBN: 978-3-527-60475-3 March 2006 375 Pages

 E-Book

$156.99

Description

Starting from basic electrodynamics, this volume provides a solid, yet concise introduction to theoretical optics, containing topics such as nonlinear optics, light-matter interaction, and modern topics in quantum optics, including entanglement, cryptography, and quantum computation.
The author, with many years of experience in teaching and research, goes way beyond the scope of traditional lectures, enabling readers to keep up with the current state of knowledge. Both content and presentation make it essential reading for graduate and phD students as well as a valuable reference for researchers.

Preface to the German edition IX

Preface to the English edition XIII

1 A short survey of the history of optics 1

2 The electrodynamics of continuous media 15

2.1 Maxwell's equations 15

2.2 Molecularvs.macroscopicfields 18

2.3 Asimplemodel for the electric current 20

2.4 Dispersion relations and the passivity condition 23

2.5 Electric displacement density and magnetic field strength 27

2.6 Indexof refraction andcoefficientof absorption 33

2.7 The electromagnetic material quantities 35

2.8 The oscillator model for the electric susceptibility 39

2.9 Material equations inmovingmedia 40

3 Linear waves in homogeneous media 45

3.1 Elasticwaves in solids 45

3.2 Isotropic elasticmedia 48

3.3 Wave surfaces and ray surfaces 51

4 Crystal optics 55

4.1 The normal ellipsoid 55

4.2 Planewaves in crystals 58

4.3 Opticallyuniaxial crystals 62

4.4 Opticallybiaxial crystals 65

4.5 Reflection and refraction at interfaces 66

4.6 Fresnel's equations 69

4.7 TheFabry–Perot interferometer 72

5 Electro-, magneto- and elastooptical phenomena 75

5.1 Polarization effects up to first order – optical activity 75

5.2 Polarization effectsof higherorder 79

5.2.1 Dependenceon distortions 80

5.2.2 Dependenceon shearflows 80

5.2.3 Influence of electricfields 80

5.2.4 Dependenceonmagneticfields 81

6 Foundations of nonlinear optics 83

6.1 Nonlinear polarization – combination frequencies 83

6.2 Nonlinearwaves in amedium 85

6.3 Surveyof phenomena innonlinear optics 89

6.4 Parametric amplification and frequency doubling 91

6.5 Phasematching 93

6.6 Self-focussing, optical bistability, phase self-modulation 95

6.7 Phase conjugation 98

6.8 Fiber optics andoptical solitons 101

7 Short-wave asymptotics 107

7.1 Introductory remarks 107

7.2 Short-wave expansion of Maxwell's equations 109

7.3 The scalarwave equation 111

7.4 Phase surfaces and rays 113

7.5 Fermat's principle 115

7.6 Analogy between mechanics and geometrical optics 116

8 Geometrical optics 121

8.1 Fermat's principle and focalpoints 121

8.2 Perfect optical instruments 122

8.3 Maxwell'sfish-eye 123

8.4 Canonical transformations and eikonal functions 125

8.5 Imaging points close to the optic axis by wide spread ray bundles 128

8.6 Linear geometrical optics and symplectic transformations 131

8.7 Gaussianoptics and imagematrices 134

8.8 Lensdefects andSeidel's theoryof aberrations 139

9 Geometric theory of caustics 143

9.1 Short-wave asymptotics for linear partial differential equations 143

9.2 Solution of the characteristic equation 146

9.3 Solution of the transport equation 151

9.4 Focalpoints and caustics 153

9.5 Behaviorof phases inthe vicinity of caustics 156

9.6 Caustics, Lagrangian submanifolds and Maslov index 158

9.7 Supplementary remarks on geometrical short-wave asymptotics 161

10 Diffraction theory 167

10.1 Survey 167

10.2 The principles of Huygens and Fresnel 167

10.3 The method of stationary phases 171

10.4 Kirchhoff's representation of the wave amplitude 175

10.5 Kirchhoff's theory of diffraction 179

10.6 Diffraction at an edge 184

10.7 Examples of Fraunhofer diffraction 186

10.7.1 Diffraction by a rectangle 187

10.7.2 Diffraction by a circular aperture 188

10.7.3 Arrangements of several identical structures 189

10.8 Optical image processinginFourier space 191

10.9 Morse families 195

10.10 Oscillatory functions and Fourier integral operators 198

11 Holography 203

11.1 The principleof holography 203

11.2 Modifications andapplications 205

11.2.1 Observing small object deformations 206

11.2.2 Holographic optical instruments 206

11.2.3 Pattern recognition 207

11.3 Volumeholograms 207

12 Coherence theory 211

12.1 Coherent and incoherent light 211

12.2 Real andanalytical signals 213

12.3 The lightwavefield as a stochasticprocess 217

12.4 Gaussianstochasticprocesses 220

12.5 The quasi-monochromatic approximation 222

12.6 Coherence and correlationfunctions 224

12.7 The propagation of the correlation function 227

12.8 Amplitude andintensity interferometry 230

12.8.1 Amplitude interferometry: Michelson interferometer 230

12.8.2 Photon correlation spectroscopy 231

12.9 Dynamical light scattering 232

12.10 Granulation 236

12.11 Imageprocessingbyfiltering 237

12.12 Polarization of partially coherent light 239

13 Quantum states of the electromagnetic field 245

13.1 Quantization of the electromagnetic field and harmonic oscillators 245

13.2 Coherent and squeezed states 251

13.3 Operators, ordering procedures and star products 259

13.4 The Q, P, and Wigner functions of a density operator 266

14 Detection of radiation fields 273

14.1 Beam splitters and homodyne detection 273

14.2 Correlation functions and quantum coherence 279

14.3 Measurementof correlation functions 281

14.4 Anti-bunching and sub-Poissonian light 285

15 Interaction of radiation and matter 289

15.1 The electricdipole interaction 289

15.2 Simple laser theory 294

15.3 Three-level systems and atomic interference 296

15.3.1 Electromagnetically induced transparency 299

15.3.2 Refractive indexenhancement 301

15.3.3 Lasing without inversion 301

15.3.4 Correlated emissionlaser 301

15.4 The Jaynes–Cummingsmodel 302

15.5 Themicromaser 308

15.6 Quantumstate engineering 310

15.7 ThePaul trap 313

15.8 Motion of a two-level atom in a quantized light field 320

16 Quantum optics and fundamental quantum theory 323

16.1 Quantumentanglement 323

16.2 Bell's inequalities 328

16.3 Quantum erasers and measurement without interaction 332

16.4 No cloning and quantum teleportation 337

16.5 Quantum cryptography 342

16.6 Quantumcomputation 343

Selected references 351

Index 355

"…this book delivers on its promise as an introduction to theoretical optics for graduate students, applied physicists, and professional researchers." (E-STREAMS, October 2006)

"...for more experienced and mathematically interested readers, the book is highly recommended." (Mathematical Reviews)