Progress in Optics (eBook)

Cover 1
Contents 8
Preface 6
Chapter 1. Negative refractive index metamaterials in optics 14
1. Introduction 16
1.1. Ambidextrous light in a left-handed world 16
1.2. Negative index:Brief history 21
2. Optical negative index metamaterials:State of the art 21
2.1. Plasmonic NIMs 22
2.2. Loss management 26
2.3. Alternative approaches to negative refraction 28
3. Negative refraction and superlens 33
3.1. Negative refraction 33
3.2. Superlens 35
4. Enhanced nonlinearity and its origin in metamaterials 38
5. Optical bistability and solitons 40
5.1. Generalized nonlinear Schrödinger equation 41
5.2. Solitons in plasmonic nanostructures 43
5.3. Gap solitons 46
5.4. Optical bistability 48
5.5. Ultra-narrowspatial solitons 49
6. BackwardŽ phase-matching conditions: Implications for nonlinear optics 51
6.1. Second-harmonic generation 52
6.2. Optical parametric amplification 55
7. Surface polaritons,waveguides and resonators 57
7.1. Linear surface polaritons 57
7.2. Nonlinear surface polaritons 60
7.3. NIM slab as a linear waveguide 61
7.4. Linear waveguide in nonlinear surroundings 64
7.5. Nano-resonators 66
8. New frontiers:Metamaterials for cloaking 68
9. Summary 72
Acknowledgements 73
References 73
Chapter 2. Polarization techniques for surface nonlinear optics 82
1. Introduction 84
2. Polarization effects in the nonlinear response of surfaces and thin films 86
2.1. Functional formof themeasured signals 87
2.2. Approximation of unity refractive indices 89
2.3. Polarization arrangements for the characterization of nonlinear samples 91
2.4. Low-symmetry samples 99
2.5. Experimental considerations 100
3. Applications of polarization techniques 103
3.1. Chirality and circular-difference response 103
3.2. Higher-multipole contributions to the surface nonlinearity of isotropic materials 106
4. Complete theoretical model including linear optics 114
4.1. Geometry and notational conventions 117
4.2. Second-harmonic field exiting from a thick sample 121
4.3. Limit of zero thickness 124
4.4. Effect on the susceptibility components 126
5. Conclusions and outlook 128
Acknowledgements 129
References 130
Chapter 3. Electromagnetic fields in linear bianisotropic mediums, Myi 134
1. Introduction 136
2. The Maxwell postulates and constitutive relations 137
2.1. Maxwell postulates 138
2.2. Constitutive relations 139
2.3. The frequency domain 140
2.4. 6-vector/6 ×6 dyadic notation 142
2.5. Forminvariances 143
2.6. Constitutive dyadics 148
3. Linearmediums 155
3.1. Isotropy 156
3.2. Anisotropy 157
3.3. Bianisotropy 164
3.4. Nonhomogeneous mediums 166
4. Plane-wave propagation 169
4.1. Uniform and non-uniform plane waves 170
4.2. Eigenanalysis 171
4.3. Isotropic scenarios 173
4.4. Anisotropic scenarios 174
4.5. Bianisotropic scenarios 181
4.6. Nonhomogeneous mediums 183
4.7. Planewaveswith negative phase velocity 187
5. DyadicGreen functions 188
5.1. Definition and properties 189
5.2. Closed-formrepresentations 191
5.3. Eigenfunction representations 196
5.4. Depolarization dyadics 198
6. Homogenization 205
6.1. Constituent mediums 206
6.2. MaxwellGarnett formalism 207
6.3. Bruggeman formalism 208
6.4. Strong-property-fluctuation theory 210
6.5. Anisotropy and bianisotropy via homogenization 213
7. Closing remarks 214
References 215
Chapter 4. Ultrafast optical pulses 224
1. Overviewof ultrashort optical pulses 226
1.1. Historic developments in short optical pulse development 226
1.2. Outline of chapter 227
2. Fundamental properties of optical pulses 228
2.1. Amplitudes, envelopes, and intensity 228
2.2. Phase, frequency, and group delay 231
2.3. Time–bandwidth product 233
2.4. The zero areaŽ pulse 234
3. Ultrashort-pulse generation 235
3.1. Spectral properties of ultrafast lasermaterials 235
3.2. Modelocking issues 237
3.3. Active and passive modulation 239
3.4. Modelocking schemes 241
4. Ultrafast-pulse characterization 249
4.1. Autocorrelation 250
4.2. Frequency-resolved optical gating (FROG) 252
5. Ultrafast Ti:sapphire lasers and amplifiers 253
5.1. Dispersion control 253
5.2. Ultrashort Ti:sapphire lasers 255
5.3. Ti:sapphire amplifiers 256
6. Attosecond pulses 257
7. Conclusion 259
References 260
Chapter 5. Quantum imaging 264
1. Introduction to quantum imaging 266
1.1. Optical parametric down-conversion of type I 268
1.2. Spatially multimode versus single-mode squeezing 273
1.3. Spatial structure of squeezed vacuum states in the degenerate optical parametric oscillator below threshold 274
1.4. Quantum images in the OPO above and below threshold 277
1.5. The interference of signal and idler waves in type I PDC 284
2. Quantum spatial intensity correlations in optical parametric down-conversion 287
2.1. Degenerate OPO below threshold, spatial quantum correlation and entanglement 288
2.2. Multimode-model for single-pass parametric down-conversion 292
2.3. Single-pass PDC of type I. Near-field/far-field duality 295
2.4. Single-pass PDC of type II. Simultaneous near-field and far-field spatial correlation 298
2.5. Detection of sub-shot-noise spatial correlation in the high gain regime of type II PDC. Spatial analogue of photon antibunching 301
2.6. Detection of weak amplitude objects beyond the standard quantum limit 308
2.7. Multimode polarization entanglement in high-gain PDC 308
3. Ghost imaging 311
3.1. General theory of ghost imaging with entangled beams 313
3.2. Two paradigmatic imaging schemes 315
3.3. Spatial average in ghost diffraction: Increase of spatial bandwidth and of speed in retrieval. Homodyne detection scheme 318
3.4. Debate: Is quantum entanglement really necessary for ghost imaging? 320
3.5. Ghost imaging by splitted thermal-like beams: Theory 322
3.6. Resolution aspects, correlation aspects, visibility aspects 324
3.7. Ghost imaging with splitted thermal beams: Experiment 326
3.8. Complementarity between thermalŽ ghost imaging and the classic Hanbury-Brown. Twiss (HBT) correlation technique, with respect to spatial coherence 330
4. Image amplification by parametric down-conversion 332
4.1. Twin (quantumentangled) images 332
4.2. Noiseless amplification of images 334
4.3. Theory of noiseless amplification of optical images 337
4.4. Noiseless amplification of optical images: Experiments in the pumped regime 339
4.5. Noiseless amplification of optical images: Experiment in the cw regime. Experimental observation of twin images 341
5. The quantumlaser pointer 342
5.1. 1Dexperiment 344
5.2. 2Dquantumlaser pointer 345
6. Miscellaneous 348
6.1. Object reconstruction 349
6.2. Entangled two-photon microscopy 350
6.3. Quantum-optical coherence tomography 351
6.4. Quantum ellipsometry 351
6.5. Transverse distribution of quantum fluctuations in free-space spatial solitons 351
6.6. Quantumfluctuations in cavity solitons 352
6.7. Quantum holographic teleportation and dense coding of optical images 352
6.8. Quantum-optical lithography 354
References 356
Chapter 6. Assessment of optical systems by means of point-spread functions 362
1. Introduction 364
1.1. The optical point-spread function 365
1.2. Quality assessment by inverse problem solving 367
2. Theory of point-spread function formation 368
2.1. Field representations and the diffraction integral 368
2.2. TheDebye integral for focusedfields 372
2.3. The Rayleigh-I integral for focused fields 375
2.4. Comparison of the various diffraction integrals 377
2.5. The amplitude of the point-spread function produced by an optical system 380
2.6. Analytic expressions for the point-spread function in the focal region (scalar case) 389
2.7. Analytic expressions for the point-spread function in the vector diffraction case 397
2.8. The point-spread function in a stratified medium 402
3. Energy density and powerflowin the focal region 404
3.1. Expression for the electric energy density 404
3.2. Expression for thePoynting vector 416
4. Quality assessment by inverse problem solution 422
4.1. Intensitymeasurements and phase retrieval 423
4.2. The optical inverse problem for finite-aperture imaging systems 424
4.3. Solving the optical inverse problem using phase diversity 428
5. Quality assessment using the Extended Nijboer–Zernike diffraction theory 430
5.1. Scalar retrieval process using the Extended Nijboer–Zernike theory 432
5.2. Pupil function retrieval for high-NA imaging systems 444
5.3. Retrieval examples for high-NAsystems 448
6. Conclusion and outlook 467
Acknowledgements 468
Appendix A: Derivation of Weyl’s plane wave expansion of a spherical wave 469
Appendix B: The Debye integral in the presence of aberrations 470
Appendix C: Series expansion of the diffraction integral at large defocus 471
Appendix D: Series expansion for the diffraction integral V < sup>
D.1. Expansion using the functions V< sup>
D.2. Expansion using the functions T< sup>
AppendixE:The predictor–corrector procedure 476
Appendix F: Zernike coefficients for circularly symmetric polarization states 478
References 479
Chapter 7. The discrete Wigner function 482
1. Introduction 484
2. Continuous Wigner function 489
3. Discretefinite space andfinitefields 490
4. The generalizedPauli group 493
4.1. Prime-dimensional spaces 493
4.2. Power-of-a-prime-dimensional spaces 494
5. Mutually unbiased bases 498
6. The discreteWigner function 501
6.1. Wigner function in prime-dimensional spaces 501
6.2. Wigner function in composite-dimensional spaces 508
6.3. Wigner function for pN-dimensional space 509
7. Reconstruction of the density operator from the discrete Wigner function 511
7.1. Lines and rays 511
7.2. Marginal probability density and the density operator 513
7.3. Tomographic reconstruction 514
7.4. Rotation operators 515
7.5. The phase of the displacement operator 520
8. Applications 522
9. Discussion and outlook 525
Acknowledgements 526
References 527
Author index forVolume 51 530
Subject index for volume 51 546
Contents of previous volumes 550
Cumulative index – Volumes 1–51 562