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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