Principles of Nano-Optics

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Preface......Page 17
Acknowledgements......Page 19
1 Introduction......Page 21
1.1 Nano-optics in a nutshell......Page 23
1.2 Historical survey......Page 25
1.3 Scope of the book......Page 27
References......Page 31
2 Theoretical foundations......Page 33
2.1 Macroscopic electrodynamics......Page 34
2.3 Constitutive relations......Page 35
2.5 Time-harmonic fields......Page 37
2.6 Complex dielectric constant......Page 38
2.8 Boundary conditions......Page 39
2.8.1 Fresnel reflection and transmission coefficients......Page 41
2.9 Conservation of energy......Page 43
2.10.1 Mathematical basis of Green’s functions......Page 45
2.10.2 Derivation of the Green’s function for the electric field......Page 46
2.10.3 Time-dependent Green’s functions......Page 50
2.11 Evanescent fields......Page 51
2.11.1 Energy transport by evanescent waves......Page 55
2.11.2 Frustrated total internal reflection......Page 56
2.12 Angular spectrum representation of optical fields......Page 58
2.12.1 Angular spectrum representation of the dipole field......Page 62
References......Page 63
3.1 Field propagators......Page 65
3.2.1 Gaussian laser beams......Page 67
3.2.3 Longitudinal fields in the focal region......Page 70
3.3 Polarized electric and polarized magnetic fields......Page 73
3.4 Far-fields in the angular spectrum representation......Page 74
3.5 Focusing of fields......Page 76
3.6 Focal fields......Page 81
3.7 Focusing of higher-order laser modes......Page 86
3.8 Limit of weak focusing......Page 91
3.9 Focusing near planar interfaces......Page 93
3.10 Reflected image of a strongly focused spot......Page 98
Problems......Page 106
References......Page 107
4.1 The point-spread function......Page 109
4.2 The resolution limit(s)......Page 115
4.2.1 Increasing resolution through selective excitation......Page 118
4.2.2 Axial resolution......Page 120
4.2.3 Resolution enhancement through saturation......Page 122
4.5 Position accuracy......Page 131
4.5.1 Theoretical background......Page 132
4.5.2 Estimating the uncertainties of fit parameters......Page 135
4.6 Principles of near-field optical microscopy......Page 141
4.6.1 Information transfer from near-field to far-field......Page 145
Problems......Page 151
References......Page 152
5.1.1 Confocal microscopy......Page 154
Experimental set-up......Page 155
The confocal principle......Page 157
Nonlinear excitation and saturation......Page 160
The solid immersion lens......Page 164
5.2 Near-field illumination and far-field detection......Page 167
5.2.1 Aperture scanning near-field optical microscopy......Page 168
5.2.2 Field-enhanced scanning near-field optical microscopy......Page 169
Modulation techniques......Page 173
5.3.1 Scanning tunneling optical microscopy......Page 177
Characterization of field distributions by photon tunneling microscopy......Page 179
Amplitude and phase of recorded field distributions......Page 180
5.3.2 Collection mode near-field optical microscopy......Page 182
5.4 Near-field illumination and near-field detection......Page 183
5.5 Other configurations: energy-transfer microscopy......Page 185
References......Page 189
6.1 Dielectric probes......Page 193
Etching......Page 194
Heating and pulling......Page 197
6.2 Light propagation in a conical dielectric probe......Page 199
6.3 Aperture probes......Page 202
6.3.1 Power transmission through aperture probes......Page 204
6.3.2 Field distribution near small apertures......Page 209
Plane wave at normal incidence......Page 210
Bethe–Bouwkamp theory applied to aperture probes......Page 212
6.3.3 Near-field distribution of aperture probes......Page 213
6.3.4 Enhancement of transmission and directionality......Page 215
6.4 Fabrication of aperture probes......Page 217
6.4.1 Aperture formation by focused ion beam milling......Page 220
6.4.2 Electrochemical opening and closing of apertures......Page 221
6.4.3 Aperture punching......Page 222
6.4.4 Microfabricated probes......Page 223
6.5.1 Solid metal tips......Page 228
Fabrication of solid metal tips......Page 232
6.5.2 Particle-plasmon probes......Page 235
6.5.3 Bowtie antenna probes......Page 238
6.6 Conclusion......Page 239
References......Page 240
7 Probe–sample distance control......Page 245
7.1 Shear-force methods......Page 246
7.1.1 Optical fibers as resonating beams......Page 247
7.1.2 Tuning-fork sensors......Page 250
7.1.3 The effective harmonic oscillator model......Page 252
7.1.4 Response time......Page 254
7.1.5 Equivalent electric circuit......Page 256
7.2 Normal force methods......Page 258
7.2.1 Tuning fork in tapping mode......Page 259
7.3 Topographic artifacts......Page 260
Constant-height mode......Page 263
Constant-gap mode......Page 264
7.3.2 Example of near-field artifacts......Page 265
7.3.3 Discussion......Page 266
Problems......Page 267
References......Page 268
8 Light emission and optical interactions in nanoscale environments......Page 270
8.1 The multipole expansion......Page 271
8.2 The classical particle–field Hamiltonian......Page 275
8.2.1 Multipole expansion of the interaction Hamiltonian......Page 278
8.3 The radiating electric dipole......Page 280
8.3.1 Electric dipole fields in a homogeneous space......Page 281
8.3.2 Dipole radiation......Page 285
8.3.3 Rate of energy dissipation in inhomogeneous environments......Page 286
8.3.4 Radiation reaction......Page 288
8.4 Spontaneous decay......Page 289
8.4.1 QED of spontaneous decay......Page 290
8.4.2 Spontaneous decay and Green’s dyadics......Page 293
8.4.3 Local density of states......Page 296
8.5.1 Homogeneous environment......Page 297
The Lorentzian lineshape function......Page 299
8.5.2 Inhomogeneous environment......Page 301
8.5.3 Frequency shifts......Page 302
8.5.4 Quantum yield......Page 303
8.6.1 Multipole expansion of the Coulombic interaction......Page 304
8.6.2 Energy transfer between two particles......Page 305
Example: Energy transfer (FRET) between two molecules......Page 311
8.7 Delocalized excitations (strong coupling)......Page 314
8.7.1 Entanglement......Page 319
Problems......Page 320
References......Page 322
9.1 Fluorescent molecules......Page 324
9.1.1 Excitation......Page 325
9.1.2 Relaxation......Page 326
9.2 Semiconductor quantum dots......Page 329
9.2.1 Surface passivation......Page 330
9.2.2 Excitation......Page 332
9.2.3 Coherent control of excitons......Page 333
9.3 The absorption cross-section......Page 335
9.4 Single-photon emission by three-level systems......Page 338
9.4.1 Steady-state analysis......Page 339
9.4.2 Time-dependent analysis......Page 340
9.5 Single molecules as probes for localized fields......Page 345
9.5.1 Field distribution in a laser focus......Page 347
Field distribution near subwavelength apertures......Page 349
Field distribution near an irradiated metal tip......Page 351
9.6 Conclusion......Page 352
References......Page 353
10 Dipole emission near planar interfaces......Page 355
10.1 Allowed and forbidden light......Page 356
10.2 Angular spectrum representation of the dyadic Green’s function......Page 358
10.3 Decomposition of the dyadic Green’s function......Page 359
10.4 Dyadic Green’s functions for the reflected and transmitted fields......Page 360
10.5 Spontaneous decay rates near planar interfaces......Page 363
10.6 Far-fields......Page 366
10.7 Radiation patterns......Page 370
10.8 Where is the radiation going?......Page 373
10.9 Magnetic dipoles......Page 376
10.10 Image dipole approximation......Page 377
10.10.1 Vertical dipole......Page 378
10.10.3 Including retardation......Page 379
Problems......Page 380
References......Page 381
11.1 Photonic crystals......Page 383
11.1.1 The photonic bandgap......Page 384
11.1.2 Defects in photonic crystals......Page 388
11.2 Optical microcavities......Page 390
References......Page 397
12 Surface plasmons......Page 398
12.1 Optical properties of noble metals......Page 399
12.1.1 Drude–Sommerfeld theory......Page 400
12.1.2 Interband transitions......Page 401
12.2 Surface plasmon polaritons at plane interfaces......Page 402
12.2.1 Properties of surface plasmon polaritons......Page 406
12.2.2 Excitation of surface plasmon polaritons......Page 407
12.2.3 Surface plasmon sensors......Page 412
12.3 Surface plasmons in nano-optics......Page 413
12.3.1 Plasmons supported by wires and particles......Page 418
Plasmon resonance of a thin wire......Page 419
Plasmon resonance of a small spherical particle......Page 423
Local interactions with particle plasmons......Page 426
12.3.2 Plasmon resonances of more complex structures......Page 427
12.3.3 Surface-enhanced Raman scattering......Page 430
Problems......Page 434
References......Page 436
13 Forces in confined fields......Page 439
13.1 Maxwell’s stress tensor......Page 440
13.2 Radiation pressure......Page 443
13.3 The dipole approximation......Page 444
13.3.1 Time-averaged force......Page 446
13.3.2 Monochromatic fields......Page 447
13.3.3 Saturation behavior for near-resonance excitation......Page 449
13.3.4 Beyond the dipole approximation......Page 452
13.4 Optical tweezers......Page 453
13.5 Angular momentum and torque......Page 456
13.6 Forces in optical near-fields......Page 457
Problems......Page 463
References......Page 464
14.1 The fluctuation–dissipation theorem......Page 466
14.1.1 The system response function......Page 468
14.1.2 Johnson noise......Page 472
14.1.3 Dissipation due to fluctuating external fields......Page 474
14.1.4 Normal and antinormal ordering......Page 475
14.2 Emission by fluctuating sources......Page 476
14.2.1 Blackbody radiation......Page 478
14.2.2 Coherence, spectral shifts and heat transfer......Page 479
14.3 Fluctuation-induced forces......Page 481
14.3.1 The Casimir–Polder potential......Page 483
14.3.2 Electromagnetic friction......Page 487
Problems......Page 492
References......Page 493
15 Theoretical methods in nano-optics......Page 495
15.1 The multiple multipole method......Page 496
15.2 Volume integral methods......Page 503
15.2.1 The volume integral equation......Page 504
15.2.3 The coupled dipole method (CDM)......Page 510
15.2.4 Equivalence of the MOM and the CDM......Page 512
15.3 Effective polarizability......Page 514
15.4 The total Green’s function......Page 515
15.5 Conclusion and outlook......Page 516
Problems......Page 517
References......Page 518
Appendix A Semianalytical derivation of the atomic polarizability......Page 520
A.1 Steady-state polarizability for weak excitation fields......Page 524
A.2 Near-resonance excitation in absence of damping......Page 526
A.3 Near-resonance excitation with damping......Page 528
B.1 Weisskopf–Wigner theory......Page 530
B.2 Inhomogeneous environments......Page 532
References......Page 534
C.1 Vertical electric dipole......Page 535
C.2 Horizontal electric dipole......Page 536
C.3 Definition of the coef.cients Aj, Bj, and Cj......Page 539
Appendix D Far-field Green’s functions......Page 541
Index......Page 545