1 Introduction 1
1.1 Nano-optics in a nutshell 3
1.2 Historical survey 4
1.3 Scope of the book 7
References 9
2 Theoretical foundations 12
2.1 Macroscopic electrodynamics 12
2.2 Wave equations 14
2.3 Constitutive relations 14
2.4 Spectral representation of time-dependent fields 15
2.5 Fields as complex analytic signals 16
2.6 Time-harmonic fields 16
2.7 Longitudinal and transverse fields 17
2.8 Complex dielectric constant 18
2.9 Piecewise homogeneous media 18
2.10 Boundary conditions 19
2.10.1 Fresnel reflection and transmission coefficients 20
2.11 Conservation of energy 22
2.12 Dyadic Green functions 25
2.12.1 Mathematical basis of Green functions 25
2.12.2 Derivation of the Green function for the electric field 27
2.12.3 Time-dependent Green functions 30
2.13 Reciprocity 31
2.14 Evanescent fields 32
2.14.1 Energy transport by evanescent waves 34
2.14.2 Frustrated total internal reflection 36
2.15 Angular spectrum representation of optical fields 38
2.15.1 Angular spectrum representation of the dipole field 41
Problems 42
References 43
3 Propagation and focusing of optical fields 45
3.1 Field propagators 45
3.2 Paraxial approximation of optical fields 47
3.2.1 Gaussian laser beams 47
3.2.2 Higher-order laser modes 49
3.2.3 Longitudinal fields in the focal region 50
3.3 Polarized electric and polarized magnetic fields 52
3.4 Far-fields in the angular spectrum representation 53
3.5 Focusing of fields 56
3.6 Focal fields 60
3.7 Focusing of higher-order laser modes 64
3.8 The limit of weak focusing 68
3.9 Focusing near planar interfaces 70
3.10 The reflected image of a strongly focused spot 75
Problems 82
References 84
4 Resolution and localization 86
4.1 The point-spread function 86
4.2 The resolution limit（s） 92
4.2.1 Increasing resolution through selective excitation 94
4.2.2 Axial resolution 96
4.2.3 Resolution enhancement through saturation 98
4.3 Principles of confocal microscopy 100
4.4 Axial resolution in multiphoton microscopy 105
4.5 Localization and position accuracy 106
4.5.1 Theoretical background 107
4.5.2 Estimating the uncertainties of fit parameters 110
4.6 Principles of near-field optical microscopy 114
4.6.1 Information transfer from near-field to far-field 118
4.7 Structured-illumination microscopy 122
Problems 126
References 128
5 Nanoscale optical microscopy 131
5.1 The interaction series 131
5.2 Far-field optical microscopy techniques 134
5.2.1 Confocal microscopy 134
5.2.2 The solid immersion lens 143
5.2.3 Localization microscopy 145
5.3 Near-field excitation microscopy 148
5.3.1 Aperture scanning near-field optical microscopy 148
5.4 Near-field detection microscopy 150
5.4.1 Scanning tunneling optical microscopy 150
5.4.2 Field-enhanced near-field microscopy with crossed polarization 153
5.5 Near-field excitation and detection microscopy 154
5.5.1 Field-enhanced near-field microscopy 154
5.5.2 Double-passage near-field microscopy 159
5.6 Conclusion 160
Problems 160
References 161
6 Localization of light with near-field probes 165
6.1 Light propagation in a conical transparent dielectric probe 165
6.2 Fabrication of transparent dielectric probes 166
6.2.1 Tapered optical fibers 167
6.3 Aperture probes 170
6.3.1 Power transmission through aperture probes 171
6.3.2 Field distribution near small apertures 176
6.3.3 Field distribution near aperture probes 181
6.3.4 Enhancement of transmission and directionality 182
6.4 Fabrication of aperture probes 184
6.4.1 Aperture formation by focused-ion-beam milling 186
6.4.2 Alternative aperture-formation schemes 187
6.5 Optical antenna probes 188
6.5.1 Solid metal tips 188
6.6 Conclusion 195
Problems 196
References 197
7 Probe—sample distance control 201
7.1 Shear-force methods 202
7.1.1 Optical fibers as resonating beams 202
7.1.2 Tuning-fork sensors 205
7.1.3 The effective-harmonic-oscillator model 206
7.1.4 Response time 209
7.1.5 Equivalent electric circuit 211
7.2 Normal-force methods 213
7.2.1 Tuning fork in tapping mode 213
7.2.2 Bent-fiber probes 214
7.3 Topographic artifacts 214
7.3.1 Phenomenological theory of artifacts 216
7.3.2 Example of optical artifacts 219
7.3.3 Discussion 220
Problems 221
References 221
8 Optical interactions 224
8.1 The multipole expansion 224
8.2 The classical particle—field Hamiltonian 228
8.2.1 Multipole expansion of the interaction Hamiltonian 231
8.3 The radiating electric dipole 233
8.3.1 Electric dipole fields in a homogeneous space 234
8.3.2 Dipole radiation 238
8.3.3 Rate of energy dissipation in inhomogeneous environments 239
8.3.4 Radiation reaction 240
8.4 Spontaneous decay 242
8.4.1 QED of spontaneous decay 243
8.4.2 Spontaneous decay and Green’s dyadics 245
8.4.3 Local density of states 248
8.5 Classical lifetimes and decay rates 249
8.5.1 Radiation in homogeneous environments 249
8.5.2 Radiation in inhomogeneous environments 254
8.5.3 Frequency shifts 254
8.6 Dipole—dipole interactions and energy transfer 256
8.6.1 Multipole expansion of the Coulombic interaction 256
8.6.2 Energy transfer between two particles 257
8.7 Strong coupling （delocalized excitations） 264
8.7.1 Coupled oscillators 265
8.7.2 Adiabatic and diabatic transitions 267
8.7.3 Coupled two-level systems 272
8.7.4 Entanglement 276
Problems 277
References 279
9 Quantum emitters 282
9.1 Types of quantum emitters 282
9.1.1 Fluorescent molecules 282
9.1.2 Semiconductor quantum dots 286
9.1.3 Color centers in diamond 291
9.2 The absorption cross-section 294
9.3 Single-photon emission by three-level systems 296
9.3.1 Steady-state analysis 297
9.3.2 Time-dependent analysis 298
9.4 Single molecules as probes for localized fields 303
9.4.1 Field distribution in a laser focus 305
9.4.2 Probing strongly localized fields 306
9.5 Conclusion 309
Problems 310
References 310
10 Dipole emission near planar interfaces 313
10.1 Allowed and forbidden light 314
10.2 Angular spectrum representation of the dyadic Green function 315
10.3 Decomposition of the dyadic Green function 317
10.4 Dyadic Green functions for the reflected and transmitted fields 318
10.5 Spontaneous decay rates near planar interfaces 321
10.6 Far-fields 323
10.7 Radiation patterns 326
10.8 Where is the radiation going？ 329
10.9 Magnetic dipoles 332
10.10 The image dipole approximation 333
10.10.1 Vertical dipole 334
10.10.2 Horizontal dipole 334
10.10.3 Including retardation 335
Problems 335
References 336
11 Photonic crystals，resonators，and cavity optomechanics 338
11.1 Photonic crystals 338
11.1.1 The photonic bandgap 339
11.1.2 Defects in photonic crystals 343
11.2 Metamaterials 345
11.2.1 Negative-index materials 345
11.2.2 Anomalous refraction and left-handedness 348
11.2.3 Imaging with negative-index materials 348
11.3 Optical microcavities 350
11.3.1 Cavity perturbation 356
11.4 Cavity optomechanics 359
Problems 365
References 366
12 Surface plasmons 369
12.1 Noble metals as plasmas 370
12.1.1 Plasma oscillations 370
12.1.2 The ponderomotive force 372
12.1.3 Screening 372
12.2 Optical properties of noble metals 374
12.2.1 Drude—Sommerfeld theory 374
12.2.2 Interband transitions 375
12.3 Surface plasmon polaritons at plane interfaces 377
12.3.1 Properties of surface plasmon polaritons 380
12.3.2 Thin-film surface plasmon polaritons 381
12.3.3 Excitation of surface plasmon polaritons 383
12.3.4 Surface plasmon sensors 387
12.4 Surface plasmons in nano-optics 388
12.4.1 Plasmons supported by wires and particles 391
12.4.2 Plasmon resonances of more complex structures 403
12.4.3 Surface-enhanced Raman scattering 403
12.5 Nonlinear plasmonics 407
12.6 Conclusion 408
Problems 409
References 411
13 Optical antennas 414
13.1 Significance of optical antennas 414
13.2 Elements of classical antenna theory 416
13.3 Optical antenna theory 420
13.3.1 Antenna parameters 421
13.3.2 Antenna-coupled light—matter interactions 433
13.3.3 Coupled-dipole antennas 434
13.4 Quantum emitter coupled to an antenna 437
13.5 Quantum yield enhancement 440
13.6 Conclusion 443
Problems 443
References 445
14 Optical forces 448
14.1 Maxwell’s stress tensor 449
14.2 Radiation pressure 452
14.3 Lorentz force density 453
14.4 The dipole approximation 453
14.4.1 Time-averaged force 455
14.4.2 Monochromatic fields 456
14.4.3 Self-induced back-action 458
14.4.4 Saturation behavior for near-resonance excitation 459
14.4.5 Beyond the dipole approximation 462
14.5 Optical tweezers 463
14.6 Angular momentum and torque 465
14.7 Forces in optical near-fields 466
14.8 Conclusion 470
Problems 471
References 472
15 Fluctuation-induced interactions 474
15.1 The fluctuation—dissipation theorem 474
15.1.1 The system response function 475
15.1.2 Johnson noise 479
15.1.3 Dissipation due to fluctuating external fields 481
15.1.4 Normal and antinormal ordering 482
15.2 Emission by fluctuating sources 483
15.2.1 Blackbody radiation 485
15.2.2 Coherence，spectral shifts，and heat transfer 486
15.3 Fluctuation-induced forces 488
15.3.1 The Casimir—Polder potential 490
15.3.2 Electromagnetic friction 494
15.4 Conclusion 497
Problems 497
References 498
16 Theoretical methods in nano-optics 500
16.1 The multiple-multipole method 500
16.2 Volume-integral methods 506
16.2.1 The volume-integral equation 508
16.2.2 The method of moments （MOM） 513
16.2.3 The coupled-dipole method （CDM） 514
16.2.4 Equivalence of the MOM and the CDM 515
16.3 Effective polarizability 517
16.4 The total Green function 518
16.5 Conclusion 519
Problems 519
References 520
Appendix A Semi-analytical derivation of the atomic polarizability 523
A.1 Steady-state polarizability for weak excitation fields 526
A.2 Near-resonance excitation in the absence of damping 528
A.3 Near-resonance excitation with damping 530
Appendix B Spontaneous emission in the weak-coupling regime 532
B.1 Weisskopf—Wigner theory 532
B.2 Inhomogeneous environments 534
References 536
Appendix C Fields of a dipole near a layered substrate 537
C.1 Vertical electric dipole 537
C.2 Horizontal electric dipole 538
C.3 Definition of the coefficients Aj，Bj，and Cj 541
Appendix D Far-field Green functions 543
Index 545