Nano and Quantum Optics

Preface......Page 6
Acknowledgements......Page 8
Contents......Page 10
  1.1.1 One-Dimensional Waves......Page 14
  1.1.2 Three-Dimensional Waves......Page 19
 1.2 Evanescent Waves......Page 21
 1.3 The Realm of Nano Optics......Page 27
  1.3.1 Summary of Book Chaps.2–11......Page 29
 Exercises......Page 30
 2.1 The Concept of Fields......Page 32
  2.1.1 The Nabla Operator......Page 35
  2.1.2 Helmholtz Theorem......Page 38
  2.1.3 Gauss' and Stokes' Theorem......Page 39
 2.2 Maxwell's Equations......Page 40
  2.2.1 Electromagnetic Potentials......Page 42
 2.3 Maxwell's Equations in Matter......Page 44
  2.3.1 Linear Materials......Page 47
  2.3.2 Boundary Conditions......Page 48
 2.4 Time-Harmonic Fields......Page 50
  2.4.1 Sinusoidal Waves......Page 51
 2.5 Longitudinal and Transverse Fields......Page 53
 Exercises......Page 55
3 Angular Spectrum Representation......Page 58
 3.1 Fourier Transform of Fields......Page 59
 3.2 Far-Field Representation......Page 60
 3.3 Field Imaging and Focusing......Page 64
 3.4 Paraxial Approximation and Gaussian Beams......Page 68
 3.5 Fields of a Tightly Focused Laser Beam......Page 71
  3.6.1 Focusing of Far-Fields......Page 73
   Transformation Matrix......Page 75
   How to Compute the Focal Fields......Page 76
  3.6.2 Imaging of Far-Fields......Page 78
 Exercises......Page 82
 4.1 Optical Forces......Page 84
  4.1.1 Dipole Approximation......Page 85
  4.1.2 Geometrical Optics......Page 89
  4.1.3 Optical Tweezers......Page 92
 4.2 Continuity Equation......Page 93
 4.3 Poynting's Theorem......Page 94
 4.4 Optical Cross Sections......Page 97
 4.5 Conservation of Momentum......Page 99
 4.6 Optical Angular Momentum......Page 103
 Exercises......Page 105
 5.1 What Are Green's Functions?......Page 107
 5.2 Green's Function for the Helmholtz Equation......Page 109
  5.2.1 Representation Formula for Helmholtz Equation......Page 110
  5.2.2 Green's Function vs. Fundamental Solution......Page 114
 5.3 Green's Function for the Wave Equation......Page 115
  5.3.1 Far-field Limit......Page 117
  5.3.2 Representation Formula for Wave Equation......Page 118
 5.4 Optical Theorem......Page 119
 5.5 Details for Representation Formula of Wave Equation......Page 120
 Exercises......Page 124
 6.1 Imaging a Single Dipole......Page 127
 6.2 Diffraction Limit of Light......Page 133
 6.3 Scanning Nearfield Optical Microscopy......Page 138
  6.3.1 Bethe–Bouwkamp Model......Page 139
  6.4.1 Position Accuracy......Page 142
  6.4.2 Photo-Activated Localization Microscopy......Page 144
  6.4.3 Stimulated Depletion Microscopy......Page 146
   Can Localization Microscopy Beat the Diffraction Limit?......Page 148
 Exercises......Page 149
7 Material Properties......Page 150
 7.1 Drude–Lorentz and Drude Models......Page 152
 7.2 From Microscopic to Macroscopic Electromagnetism......Page 158
 7.3 Nonlocality in Time......Page 161
  7.3.1 Poynting's Theorem Revisited......Page 164
  7.3.2 Kramers–Kronig Relation......Page 166
 7.4 Reciprocity Theorem in Optics......Page 169
 Exercises......Page 171
 8.1 Surface Plasmons......Page 172
  8.1.1 Kretschmann and Otto Geometry......Page 179
 8.2 Graphene Plasmons......Page 182
  8.3.1 Fresnel Coefficients......Page 185
  8.3.2 Transfer Matrices......Page 188
   Reflection and Transmission Coefficients of Slab......Page 191
  8.3.3 Surface Plasmons Revisited......Page 192
   Coupled Surface Plasmons......Page 194
 8.4 Negative Refraction......Page 198
  8.4.2 The Perfect Lens......Page 201
 8.5 Green's Function for Stratified Media......Page 203
  8.5.1 Source Located Above Topmost Layer......Page 206
  8.5.2 Imaging with an Imperfect Veselago Lens......Page 208
  8.5.3 Far-field Limit......Page 209
  8.5.4 Source Located Inside Layer......Page 213
 Exercises......Page 214
 9.1 Quasistatic Limit......Page 217
  9.2.1 Quasistatic Mie Theory......Page 219
   Dielectric Sphere......Page 222
   Metallic Sphere......Page 223
  9.2.2 Mie–Gans Theory......Page 225
  9.2.3 Optical Cross Sections......Page 227
 9.3 Boundary Integral Method for Quasistatic Limit......Page 231
  9.3.1 Plasmonic Eigenmodes......Page 236
   Plasmon Sensors......Page 240
  9.3.2 Coupled Particles......Page 241
 9.4 Conformal Mapping......Page 245
  9.4.1 A Few Selected Examples......Page 247
  9.4.2 Details About Conformal Mapping......Page 249
  9.4.3 Kissing Cylinders......Page 250
 9.5 Mie Theory......Page 254
 9.6 Boundary Integral Method for Wave Equation......Page 257
  9.6.1 Eigenmodes for Full Maxwell's Equations......Page 260
  9.7.1 Eigenmode Analysis of Ouyang and Isaacson......Page 261
  9.7.2 Eigenmode Decomposition of Green's Function......Page 263
 Exercises......Page 264
 10.1 Decay Rate of Quantum Emitter......Page 268
  10.1.1 Photonic Local Density of States......Page 273
  10.2.1 Quantum Emitter Above Metal Slab......Page 275
  10.2.2 Quasistatic Approximation......Page 276
  10.2.3 Mie Theory......Page 279
 10.3 Surface-Enhanced Raman Scattering......Page 282
 10.4 Förster Resonance Energy Transfer......Page 287
 10.5 Electron Energy Loss Spectroscopy......Page 290
  10.5.1 Fields Produced by Swift Electrons......Page 293
  10.5.2 Decomposition Into Bulk and Surface Losses......Page 295
  10.5.3 Expressing EELS Through the Green's Dyadics......Page 298
  10.5.4 Quasistatic Limit......Page 301
 Exercises......Page 302
 11.1 Finite Difference Time Domain Simulations......Page 305
  11.1.1 The Magic of the FDTD Approach......Page 308
   Two-Dimensional Case......Page 310
  11.1.2 Stability and Dispersion......Page 312
  11.1.3 Perfectly Matched Layers......Page 314
  11.1.4 Material Properties......Page 316
 11.2 Boundary Element Method......Page 317
 11.3 Galerkin Scheme......Page 322
  11.3.1 Grand Idea of Galerkin Scheme......Page 323
  11.3.2 Unstructured Grid......Page 325
   Vector Solution......Page 327
  11.4.1 Raviart–Thomas Basis Functions......Page 328
  11.4.2 Galerkin Scheme for Full Maxwell's Equations......Page 330
  11.5.1 Finite Element Method in Frequency Domain......Page 332
  11.5.2 Nedelec Elements......Page 336
  11.5.3 Discontinuous Galerkin Scheme......Page 338
 11.6 Details of Potential Boundary Element Method......Page 342
 Exercises......Page 345
12 Quantum Effects in Nano Optics......Page 348
 12.1 Going Quantum in Three Steps......Page 350
 12.2 The Quantum Optics Toolbox......Page 354
 12.3 Summary of Book Chaps. 13–18......Page 356
 13.1 Preliminaries......Page 358
  13.1.1 A First Glimpse of Quantum Electrodynamics......Page 362
 13.2 Canonical Quantization......Page 364
  13.2.1 Euler–Lagrange Equations......Page 367
  13.2.2 Hamilton Formalism......Page 368
  13.2.3 Canonical Quantization......Page 370
   Example of Harmonic Oscillator......Page 372
   Complex Coordinates......Page 375
 13.3 Coulomb Gauge......Page 377
 13.4 Canonical Quantization of Maxwell's Equations......Page 379
  13.4.1 Lagrange Formalism......Page 380
  13.4.2 Quantization of Matter Part......Page 381
   Light–Matter Interaction for Many-Particle Systems......Page 382
  13.4.3 Quantization of Maxwell's Equations......Page 384
  13.4.4 Photons......Page 389
  13.4.5 Quantization of Coupled Light-Matter System......Page 391
  13.4.6 States of the Harmonic Oscillator......Page 395
 13.5 Multipolar Hamiltonian......Page 398
  13.6.1 Lagrange Function for Charged Particle......Page 404
  13.6.2 Lagrange Function for Maxwell's Equations......Page 405
  13.6.3 Lagrange Function in Coulomb Gauge......Page 407
 Exercises......Page 410
14 Correlation Functions......Page 413
 14.1 Statistical Operator......Page 414
 14.2 Kubo Formalism......Page 417
  14.2.1 Spectral Function......Page 419
  14.2.2 Cross-Spectral Density......Page 421
 14.3 Correlation Functions for Electromagnetic Fields......Page 424
  14.4.1 Response to Longitudinal Fields......Page 428
  14.4.2 Lindhard's Dielectric Function......Page 432
  14.4.3 Response to Longitudinal and Transverse Fields......Page 435
  14.4.4 Fluctuation–Dissipation Theorem......Page 437
 14.5 Quantum Plasmonics......Page 439
  14.5.1 Nonlocality in Plasmonics......Page 440
  14.5.2 Additional Boundary Conditions......Page 443
   Approach of Dasgupta and Fuchs for Spherical Nanoparticle......Page 445
  14.5.3 Feibelman Parameters......Page 453
  14.5.4 Charge Transfer Plasmons......Page 459
 14.6 Electron Energy Loss Spectroscopy Revisited......Page 462
  14.6.1 Energy Loss of a Swift Electron......Page 464
 Exercises......Page 469
15 Thermal Effects in Nano Optics......Page 472
 15.1 Cross-Spectral Density and What We Can Do with It......Page 474
  15.1.1 Cross-Spectral Density in Free Space......Page 475
  15.1.2 What We Can Do with Cross-Spectral Densities......Page 477
 15.2 Noise Currents......Page 478
  15.2.1 Green's Function Solution......Page 482
 15.3 Cross-Spectral Density Revisited......Page 484
  15.3.1 Representation Formula for Green's Functions......Page 486
  15.3.2 Cross-Spectral Density for Absorbing Media......Page 487
 15.4 Photonic Local Density of States Revisited......Page 490
  15.4.1 Lamb Shift......Page 493
  15.5.1 Casimir–Polder Forces......Page 498
  15.5.2 Casimir Forces......Page 499
   Casimir Force Between Two Perfectly Conducting Plates......Page 500
   Casimir Force Exerted by Field Fluctuations......Page 501
 15.6 Heat Transfer at the Nanoscale......Page 506
 15.7 Details of Derivation of Representation Formula......Page 510
  15.7.1 Evaluation of Boundary Term......Page 512
 Exercises......Page 513
 16.1 Bloch Sphere......Page 516
  16.1.1 Pauli Matrices......Page 517
 16.2 Two-Level Dynamics......Page 519
  16.2.1 Optically Driven Two-Level System......Page 520
   Time-Harmonic Fields......Page 522
 16.3 Relaxation and Dephasing......Page 526
 16.4 Jaynes–Cummings Model......Page 532
 Exercises......Page 535
 17.1 Density Operator......Page 537
  17.1.1 Time Evolution of Density Operator......Page 540
   Optically Driven Few-Level System......Page 541
 17.2 Master Equation of Lindblad Form......Page 544
 17.3 Solving the Master Equation of Lindblad Form......Page 547
  17.3.1 Quantum Dot Coupled to Metallic Nanosphere......Page 550
  17.3.2 Lasers and Spasers......Page 552
  17.4.1 Boltzmann's Equation......Page 556
  17.4.2 Nakajima–Zwanzig Equation......Page 560
   Master Equation Revisited......Page 563
  17.4.3 Fermi's Golden Rule......Page 566
 Exercises......Page 569
18 Photon Noise......Page 571
 18.1 Photon Detectors and Spectrometers......Page 572
  18.1.1 Photodetector......Page 573
  18.1.2 Spectrometer......Page 574
  18.1.3 Photon Correlations......Page 576
 18.2 Quantum Regression Theorem......Page 579
 18.3 Photon Correlations and Fluorescence Spectra......Page 581
  18.3.1 Incoherently Driven Two-Level System......Page 582
  18.3.2 Quantum Regression Theorem and Eigenmodes......Page 587
  18.3.3 Three-Level System......Page 589
 18.4 Molecule Interacting with Metallic Nanospheres......Page 592
 Exercises......Page 594
 A.1 Cauchy's Theorem......Page 596
 A.2 Residue Theorem......Page 598
 B.1 Spectral Decomposition of Scalar Green's Function......Page 600
 B.2 Spectral Representation of Dyadic Green's Function......Page 603
 B.3 Sommerfeld Integration Path......Page 606
C Spherical Wave Equation......Page 611
 C.1 Legendre Polynomials......Page 613
 C.2 Spherical Harmonics......Page 614
 C.3 Spherical Bessel and Hankel Functions......Page 616
D Vector Spherical Harmonics......Page 620
 D.1 Vector Spherical Harmonics......Page 622
 D.2 Orthogonality Relations......Page 623
 Exercises......Page 627
 E.1 Multipole Expansion of Electromagnetic Fields......Page 628
 E.2 Mie Coefficients......Page 630
 E.3 Plane Wave Excitation......Page 633
 E.4 Dipole Excitation......Page 638
F Dirac's Delta Function......Page 646
 F.1 Transverse and Longitudinal Delta Function......Page 647
References......Page 651
Index......Page 659