Preface ........................................................ xv
1. Introduction ................................................ 1
1.1. Nano-optics in a nutshell ............................. 3
1.2. Historical survey ..................................... 5
1.3. Scope of the book ..................................... 7
References 11
2. Theoretical foundations .................................... 13
2.1. Macroscopic electrodynamics .......................... 14
2.2. Wave equations ....................................... 15
2.3. Constitutive relations ............................... 15
2.4. Spectral representation of time-dependent fields ..... 17
2.5. Time-harmonic fields ................................. 17
2.6. Complex dielectric constant .......................... 18
2.7. Piecewise homogeneous media .......................... 19
2.8. Boundary conditions .................................. 19
2.8.1. Fresnel reflection and transmission
coefficients .................................. 21
2.9. Conservation of energy ............................... 23
2.10. Dyadic Green's functions ............................. 25
2.10.1.Mathematical basis of Green's functions ....... 25
2.10.2.Derivation of the Green's function for the
electric field ................................ 26
2.10.3.Time-dependent Green's functions .............. 30
2.11. Evanescent fields .................................... 31
2.11.1.Energy transport by evanescent waves .......... 35
2.11.2.Frustrated total internal reflection .......... 36
2.12. Angular spectrum representation of optical fields .... 38
2.12.1.Angular spectrum representation of the
dipole field .................................. 42
Problems ................................................... 43
References ................................................. 43
3. Propagation and focusing of optical fields ................. 44
3.1. Field propagators .................................... 45
3.2. Paraxial approximation of optical fields ............. 47
3.2.1. Gaussian laser beams .......................... 49
3.2.2. Higher-order laser modes ...................... 51
3.2.3. Longitudinal fields in the focal region ....... 51
3.3. Polarized electric and polarized magnetic fields ..... 53
3.4. Far-fields in the angular spectrum representation .... 54
3.5. Focusing of fields ................................... 56
3.6. Focal fields ......................................... 61
3.7. Focusing of higher-order laser modes ................. 66
3.8. Limit of weak focusing ............................... 71
3.9. Focusing near planar interfaces ...................... 72
3.10. Reflected image of a strongly focused spot ........... 78
Problems ................................................... 86
References ................................................. 87
4. Spatial resolution and position accuracy ................... 89
4.1. The point-spread function ............................ 89
4.2. The resolution Hmit(s) ............................... 95
4.2.1. Increasing resolution through selective
excitation ................................... 98
4.2.2. Axial resolution ............................ 100
4.2.3. Resolution enhancement through saturation ... 102
4.3. Principles of confocal microscopy ................... 105
4.4. Axial resolution in multiphoton microscopy .......... 110
4.5. Position accuracy ................................... 111
4.5.1. Theoretical background ...................... 112
4.5.2. Estimating the uncertainties of fit
parameters .................................. 115
4.6. Principles of near-field optical microscopy ......... 121
4.6.1. Information transfer from near-field to
far-field ................................... 125
Problems .................................................. 131
References ................................................ 132
5. Nanoscale optical microscopy .............................. 134
5.1. Far-field illumination and detection ................ 134
5.1.1. Confocal microscopy ......................... 134
5.2. Near-field illumination and far-field detection ..... 147
5.2.1. Aperture scanning near-field optical
microscopy .................................. 148
5.2.2. Field-enhanced scanning near-field optical
microscopy .................................. 149
5.3. Far-field illumination and near-field detection ..... 157
5.3.1. Scanning tunneling optical microscopy ....... 157
5.3.2. Collection mode near-field optical
microscopy .................................. 162
5.4. Near-field illumination and near-field detection .... 163
5.5. Other configurations: energy-transfer microscopy .... 165
5.6. Conclusion .......................................... 169
Problems .................................................. 169
References ................................................ 169
6. Near-field optical probes ................................. 173
6.1. Dielectric probes ................................... 173
6.1.1. Tapered optical fibers ...................... 174
6.1.2. Tetrahedral tips ............................ 179
6.2. Light propagation in a conical dielectric probe ..... 179
6.3. Aperture probes ..................................... 182
6.3.1. Power transmission through aperture
probes ...................................... 184
6.3.2. Field distribution near small apertures ..... 189
6.3.3. Near-field distribution of aperture
probes ...................................... 193
6.3.4. Enhancement of transmission and
directionality .............................. 195
6.4. Fabrication of aperture probes ...................... 197
6.4.1. Aperture formation by focused ion
beam milling ................................ 200
6.4.2. Electrochemical opening and closing
of apertures ................................ 201
6.4.3. Aperture punching ........................... 202
6.4.4. Microfabricated probes ...................... 203
6.5. Optical antennas: tips, scatterers, and bowties ..... 208
6.5.1. Solid metal tips ............................ 208
6.5.2. Particle-plasmon probes ..................... 215
6.5.3. Bowtie antenna probes ....................... 218
6.6. Conclusion .......................................... 219
Problems .................................................. 220
References ................................................ 220
7. Probe-sample distance control ............................. 225
7.1. Shear-force methods ................................. 226
7.1.1. Optical fibers as resonating beams .......... 227
7.1.2. Tuning-fork sensors ......................... 230
7.1.3. The effective harmonic oscillator model ..... 232
7.1.4. Response time ............................... 234
7.1.5. Equivalent electric circuit ................. 236
7.2. Normal force methods ................................ 238
7.2.1. Tuning fork in tapping mode ................. 239
7.2.2. Bent fiber probes ........................... 240
7.3. Topographic artifacts ............................... 240
7.3.1. Phenomenological theory of artifacts ........ 243
7.3.2. Example of near-field artifacts ............. 245
7.3.3. Discussion .................................. 246
Problems .................................................. 247
References ................................................ 248
8. Light emission and optical interactions in nanoscale
environments .............................................. 250
8.1. The multipole expansion ............................. 251
8.2. The classical particle-field Hamiltonian ............ 255
8.2.1. Multipole expansion of the interaction
Hamiltonian ................................. 258
8.3. The radiating electric dipole ....................... 260
8.3.1. Electric dipole fields in a homogeneous
space ....................................... 261
8.3.2. Dipole radiation ............................ 265
8.3.3. Rate of energy dissipation in
inhomogeneous environments .................. 266
8.3.4. Radiation reaction .......................... 268
8.4. Spontaneous decay ................................... 269
8.4.1. QED of spontaneous decay .................... 270
8.4.2. Spontaneous decay and Green's dyadics ....... 273
8.4.3. Local density of states ..................... 276
8.5. Classical lifetimes and decay rates ................. 277
8.5.1. Homogeneous environment ..................... 277
8.5.2. Inhomogeneous environment ................... 281
8.5.3. Frequency shifts ............................ 282
8.5.4. Quantum yield ............................... 283
8.6. Dipole-dipole interactions and energy transfer ...... 284
8.6.1. Multipole expansion of the Coulombic
interaction ................................. 284
8.6.2. Energy transfer between two particles ....... 285
8.7. Delocalized excitations (strong coupling) ........... 294
8.7.1. Entanglement ................................ 299
Problems .................................................. 300
References ................................................ 302
9. Quantum emitters .......................................... 304
9.1. Fluorescent molecules ............................... 304
9.1.1. Excitation .................................. 305
9.1.2. Relaxation .................................. 306
9.2. Semiconductor quantum dots .......................... 309
9.2.1. Surface passivation ......................... 310
9.2.2. Excitation .................................. 312
9.2.3. Coherent control of excitons ................ 313
9.3. The absorption cross-section ........................ 315
9.4. Single-photon emission by three-level systems ....... 318
9.4.1. Steady-state analysis ....................... 319
9.4.2. Time-dependent analysis ..................... 320
9.5. Single molecules as probes for localized fields ..... 325
9.5.1. Field distribution in a laser focus ......... 327
9.5.2. Probing strongly localized fields ........... 329
9.6. Conclusion .......................................... 332
Problems .................................................. 333
References ................................................ 333
10. Dipole emission near planar interfaces .................... 335
10.1. Allowed and forbidden light ......................... 336
10.2. Angular spectrum representation of the dyadic
Green's function .................................... 338
10.3. Decomposition of the dyadic Green's function ........ 339
10.4. Dyadic Green's functions for the reflected and
transmitted fields .................................. 340
10.5. Spontaneous decay rates near planar interfaces ...... 343
10.6. Far-fields .......................................... 346
10.7. Radiation patterns .................................. 350
10.8. Where is the radiation going? ....................... 353
10.9. Magnetic dipoles .................................... 356
10.10.Image dipole approximation .......................... 357
10.10.1.Vertical dipole ............................. 358
10.10.2.Horizontal dipole ........................... 359
10.10.3.Including retardation ....................... 359
Problems .................................................. 360
References ................................................ 361
11. Photonic crystals and resonators .......................... 363
11.1. Photonic crystals ................................... 363
11.1.1. The photonic bandgap ........................ 364
11.1.2. Defects in photonic crystals ................ 368
11.2. Optical microcavities ............................... 370
Problems .................................................. 377
References ................................................ 377
12. Surface plasmons .......................................... 378
12.1. Optical properties of noble metals .................. 379
12.1.1. Drude-Sommerfeld theory ..................... 380
12.1.2. Interband transitions ....................... 381
12.2. Surface plasmon polaritons at plane interfaces ...... 382
12.2.1. Properties of surface plasmon polaritons .... 386
12.2.2. Excitation of surface plasmon polaritons .... 387
12.2.3. Surface plasmon sensors ..................... 392
12.3. Surface plasmons in nano-optics ..................... 393
12.3.1. Plasmons supported by wires and particles ... 398
12.3.2. Plasmon resonances of more complex
structures .................................. 407
12.3.3. Surface-enhanced Raman scattering ........... 410
12.4. Conclusion .......................................... 414
Problems .................................................. 414
References ................................................ 416
13. Forces in confined fields ................................. 419
13.1. Maxwell's stress tensor ............................. 420
13.2. Radiation pressure .................................. 423
13.3. The dipole approximation ............................ 424
13.3.1. Time-averaged force ......................... 426
13.3.2. Monochromatic fields ........................ 427
13.3.3. Saturation behavior for near-resonance
excitation .................................. 429
13.3.4. Beyond the dipole approximation ............. 432
13.4. Optical tweezers .................................... 433
13.5. Angular momentum and torque ......................... 436
13.6. Forces in optical near-fields ....................... 437
13.7. Conclusion .......................................... 443
Problems .................................................. 443
References ................................................ 444
14. Fluctuation-induced interactions .......................... 446
14.1. The fluctuation-dissipation theorem ................. 446
14.1.1. The system response function ................ 448
14.1.2. Johnson noise ............................... 452
14.1.3. Dissipation due to fluctuating external
fields ...................................... 454
14.1.4. Normal and antinormal ordering .............. 455
14.2. Emission by fluctuating sources ..................... 456
14.2.1. Blackbody radiation ......................... 458
14.2.2. Coherence, spectral shifts and heat
transfer .................................... 459
14.3. Fluctuation-induced forces .......................... 461
14.3.1. The Casimir-Polder potential ................ 463
14.3.2. Electromagnetic friction .................... 467
14.4. Conclusion .......................................... 472
Problems .................................................. 472
References ................................................ 473
15. Theoretical methods in nano-optics ........................ 475
15.1. The multiple multipole method ....................... 476
15.2. Volume integral methods ............................. 483
15.2.1. The volume integral equation ................ 484
15.2.2. The method of moments (MOM) ................. 490
15.2.3. The coupled dipole method (CDM) ............. 490
15.2.4. Equivalence of the MOM and the CDM .......... 492
15.3. Effective polarizability ............................ 494
15.4. The total Green's function .......................... 495
15.5. Conclusion and outlook .............................. 496
Problems .................................................. 497
References ................................................ 498
Appendix A. Semianalytical derivation of the atomic
polarizability ............................................ 500
A.1. Steady-state polarizability for weak
excitation fields .................................... 504
A.2. Near-resonance excitation in absence of damping ...... 506
A.3. Near-resonance excitation with damping ............... 508
Appendix В. Spontaneous emission in the weak coupling
regime ............................................ 510
B.1. Weisskopf-Wigner theory .............................. 510
B.2. Inhomogeneous environments ........................... 512
References ................................................ 514
Appendix С. Fields of a dipole near a layered substrate ....... 515
C.1. Vertical electric dipole ............................. 515
C.2. Horizontal electric dipole ........................... 516
C.3. Definition of the coefficients Aj, Вj, and Сj ......... 519
Appendix D. Far-field Green's functions ....................... 521
Index ......................................................... 525
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