Preface ...................................................... xiii
1. Electromagnetic radiation .................................... 1
1.1. Brief history of the interaction of light and matter .... 3
1.2. Light in vacuum ......................................... 3
1.2.1. The electromagnetic spectrum ..................... 6
1.2.2. Wave equation in vacuum ......................... 26
1.2.3. Propagation of one component in one dimension ... 30
1.2.4. Phase and group velocity of a light pulse ....... 34
1.2.5. Amplitude modulation ............................ 38
1.2.6. Frequency and phase modulation .................. 38
1.2.7. Energy, momentum and angular momentum of
electromagnetic waves ........................... 41
1.2.8. Polarized light ................................. 50
1.2.9. Diffraction ..................................... 60
1.2.10.Interference .................................... 66
1.2.11.Temporal and spatial coherence .................. 72
1.2.12.Photons: quantization of the electromagnetic
field ........................................... 75
1.3. Matter-source of light ................................. 79
1.3.1. Classical expressions for the charge density
and current ..................................... 79
1.3.2. The wave equation with source terms: Lienard-
Wiechert potentials ............................. 80
2. Phenomenology of light propagation in matter ................ 87
2.1. Absorption of light .................................... 88
2.1.1. Color of materials .............................. 91
2.1.2. An aside on Einstein absorption and emission
coefficients .................................... 93
2.2. Nonlinear absorption ................................... 94
2.2.1. Saturable absorption ............................ 95
2.2.2. Reverse saturable absorption .................... 97
2.2.3. Two-photon absorption ........................... 99
2.3. Index of refraction ................................... 100
2.3.1. Reflection and refraction at a boundary
interface ...................................... 101
2.3.2. Relationship between refractive index and
absorption: Kramers - Kronig relation .......... 105
2.3.3. Dispersion ..................................... 107
2.3.4. Refractive index temperature dependence:
thermal lensing ................................ 112
2.4. Optical phenomena in nonisotropic media ............... 113
2.4.1. Introduction to crystallography and optics in
crystals ....................................... 113
2.4.2. Dichroism ...................................... 122
2.4.3. Birefringence .................................. 122
2.4.4. Optical activity, optical rotatory dispersion
and circular dichroism ......................... 140
2.5. Electric field effects ................................ 143
2.5.1. Kerr effect .................................... 143
2.5.2. Pockels effect ................................. 144
2.5.3. Piezoelectricity ............................... 149
2.5.4. Pyroelectric effect ............................ 151
2.5.5. Ferroelectric effect ........................... 152
2.5.6. Electrostriction ............................... 158
2.5.7. Photorefractive effect ......................... 161
2.6. Acousto-optic effects ................................. 163
2.6.1. Diffraction by acoustic waves: Brillouin
scattering ..................................... 163
2.6.2. Photoelastic effect (stress-birefringence) ..... 168
2.6.3. Acousto-optic detection of light ............... 169
2.7. Magnetic field effects ................................ 171
2.7.1. Faraday effect ................................. 173
2.7.2. Voigt and Cotton -Mouton effects ............... 175
2.7.3. Magnetic circular birefringence and dichroism .. 176
2.7.4. Magnetostriction and magnetoelasticity ......... 176
3. The interaction of light and matter ........................ 177
3.1. Lorentz force law ..................................... 178
3.2. Motion of a charged particle in static electric and
magnetic fields ....................................... 178
3.2.1. Motion in a magnetic field - the cyclotron
frequency ...................................... 178
3.2.2. Crossed electric and magnetic fields ........... 179
3.2.3. Conductivity, magnetoconductivity and Hall
effect ......................................... 180
3.3. Motion of a bound electron in an electromagnetic
field ................................................. 184
3.3.1. Linewidth due to spontaneous emission .......... 184
3.3.2. Rayleigh scattering, Thomson scattering,
and resonant line scattering limits ............ 186
3.3.3. Polarization of a medium ....................... 193
3.3.4. Polarization of a medium in a static magnetic
field .......................................... 202
3.3.5. Electromagnetic field and a static electric
field .......................................... 206
3.3.6. Nonlinear polarization of a medium ............. 207
3.4. Radiation due to acceleration of charges .............. 210
3.4.1. Radiation from relativistically moving
charges ........................................ 211
3.4.2. Synchrotron emission ........................... 214
3.4.3. Radiative damping force revisited .............. 215
3.4.4. Cherenkov radiation ............................ 217
3.5. Multipole radiation ................................... 217
3.5.1. Scattering of long wavelength electromagnetic
radiation from small particles ................. 221
3.6. Scattering of a light wavepacket ...................... 224
3.7. Cooling and trapping of atoms ......................... 225
3.7.1. Far off-resonance trapping, atom mirrors and
optical tweezers ............................... 226
3.7.2. Doppler cooling ................................ 228
3.7.3. Polarization gradient cooling (Sisyphus
cooling) of atoms .............................. 230
4. Magnetic phenomena, constitutive relations and plasmas ..... 235
4.1. Magnetic moments ...................................... 237
4.2. Magnetization ......................................... 242
4.2.1. Diamagnetism ................................... 243
4.2.2. Paramagnetism .................................. 244
4.2.3. Ferromagnetism ................................. 247
4.2.4. Ferrimagnetism ................................. 250
4.2.5. Antiferromagnetism ............................. 251
4.2.6. Permeability resonances ........................ 251
4.3. Magnetic resonance .................................... 252
4.3.1. Nuclear magnetic resonance ..................... 256
4.4. Polarization and magnetization as source terms ........ 259
4.5. Atomistic derivation of macroscopic electromagnetism
and the constitutive relations ........................ 261
4.6. Microscopic polarizability and macroscopic
polarization .......................................... 264
4.6.1. Clausius-Mossotti equation and the Lorentz-
Lorenz correction factor ....................... 265
4.6.2. Microscopic magnetic moment and macroscopic
magnetization .................................. 267
4.7. Dielectric relaxation ................................. 267
4.7.1. Molecular orientation (and re-orientation)
in an applied field ............................ 270
4.7.2. Dispersion relations for light in dielectric
crystals ....................................... 272
4.8. Plasmas ............................................... 275
4.8.1. Plasma parameters .............................. 277
4.8.2. Constitutive equations in a plasma ............. 280
4.8.3. Kinetic theory ................................. 282
4.8.4. Hydrodynamic model of plasmas .................. 284
4.8.5. Waves in a plasma .............................. 289
5. Quantum description of absorption, emission and light
scattering ................................................. 293
5.1. Charged particle in an electromagnetic field .......... 294
5.1.1. Electron spin coupling ......................... 297
5.1.2. Landau levels in a static magnetic field ....... 300
5.2. Absorption and emission ............................... 301
5.2.1. Time-dependent perturbation theory ............. 301
5.2.2. Spontaneous emission ........................... 304
5.2.3. Stimulated emission and absorption ............. 309
5.2.4. Finite lifetime considerations for stimulated
emission and absorption ........................ 309
5.2.5. Finite duration pulses ......................... 311
5.3. Rayleigh and Raman scattering ......................... 312
5.3.1. Why is the sky blue, the setting sun red and
clouds white? .................................. 316
5.4. Thomson scattering .................................... 317
6. Spectroscopy ............................................... 319
6.1. Atoms ................................................. 320
6.1.1. The hydrogen atom .............................. 327
6.1.2. Multielectron atomic systems ................... 337
6.1.3. Atomic selection rules ......................... 347
6.1.4. Broadening due to lifetime and collisions ...... 348
6.2. Molecules ............................................. 348
6.2.1. Hamiltonian for molecular systems .............. 348
6.2.2. The Born - Oppenheimer approximation and
potential energy surfaces ...................... 349
6.2.3. Molecular orbitals ............................. 350
6.3. Diatomic molecules .................................... 353
6.3.1. Diatomic rotational and vibrational states
and transitions ................................ 354
6.3.2. Electric dipole transitions .................... 360
6.3.3. The Franck-Condon principle .................... 361
6.3.4. More about rotational states and transitions:
microwave spectroscopy ......................... 363
6.3.5. H2+ ion ........................................ 364
6.3.6. H2 molecule .................................... 366
6.4. Polyatomic molecules .................................. 367
6.4.1. Multidimensional Born-Oppenheimer potential
surfaces ....................................... 367
6.4.2. The nuclear Hamiltonian for molecular systems .. 369
6.4.3. Rotational degrees of freedom .................. 370
6.4.4. Large molecules ................................ 377
6.5. Condensed-phase materials ............................. 381
6.5.1. Crystals doped with metal ions ................. 381
6.5.2. Metals ......................................... 392
6.5.3. Semiconductor materials ........................ 397
7. Lasers ..................................................... 409
7.1. Laser dynamics ........................................ 410
7.1.1. Three- and four-level lasers ................... 410
7.1.2. Laser rate equations ........................... 412
7.2. Threshold ............................................. 414
7.3. Steady state .......................................... 416
7.3.1. Small signal gain and gain saturation .......... 417
7.3.2. Circulating intracavity intensity .............. 417
7.3.3. cw output vs input ............................. 419
7.4. Pulsed laser operation ................................ 420
7.4.1. Relaxation oscillations ........................ 420
7.4.2. Q-switching .................................... 422
7.4.3. Mode-locking ................................... 426
7.4.4. Extra-cavity pulse compressor .................. 429
7.4.5. Chirped pulse amplifiers ....................... 429
7.5. Cavity modes .......................................... 430
7.5.1. Longitudinal modes ............................. 430
7.5.2. Transverse modes ............................... 432
7.6. Amplified spontaneous emission ........................ 435
7.7. Laser linewidth ....................................... 437
7.8. Laser coherence ....................................... 437
7.9. Specific laser systems ................................ 437
7.9.1. He-Ne laser .................................... 438
7.9.2. Ar ion and Krion lasers ........................ 439
7.9.3. CO2 laser ...................................... 441
7.9.4. Nitrogen laser ................................. 443
7.9.5. Excimer and exciplex lasers .................... 444
7.9.6. Dye lasers ..................................... 444
7.9.7. Solid-state lasers ............................. 445
7.9.8. Semiconductor diode lasers: GaAs, AlGaAs
heterostructures ............................... 451
8. Nonlinear optics ........................................... 455
8.1. Expansion of the polarization in the electric field ... 456
8.1.1. Symmetry relations of the nonlinear
susceptibilities ............................... 460
8.1.2. Electromagnetic energy density in a nonlinear
medium ......................................... 462
8.1.3. Local field corrections to nonlinear
susceptibilities ............................... 464
8.1.4. The nonlinear wave equation for the slowly
varying envelope ............................... 465
8.1.5. Manley-Rowe relations .......................... 469
8.2. Phase-matching ........................................ 470
8.2.1. Collinear phase-matching ....................... 471
8.2.2. Noncollinear phase-matching .................... 472
8.3. Second harmonic generation ............................ 473
8.3.1. Second harmonic generation with multimode
light .......................................... 473
8.3.2. Short-pulse second harmonic generation ......... 476
8.4. Three-wave mixing ..................................... 478
8.4.1. Sum frequency generation ....................... 478
8.4.2. Difference frequency generation ................ 484
8.5. Third harmonic generation ............................. 485
8.5.1. Third harmonic generation in rare gas
mixtures ....................................... 487
8.5.2. Effects of self-phase modulation on third
harmonic generation ............................ 487
8.6. Self-focusing and self-phase modulation ............... 488
8.6.1. The nonlinear Schrodinger equation ............. 490
8.6.2. Optical solitons ............................... 492
8.7. Four-wave mixing ...................................... 495
8.8. Stimulated Raman processes ............................ 496
8.8.1. Coherent anti-Stokes and Stokes Raman
spectroscopy ................................... 498
8.9. Stimulated Bnllouin processes ......................... 498
8.10.Nonlinear matter-wave optics .......................... 501
9. Quantum-optical processes .................................. 503
9.1. Interaction of a two-level system with an
electromagnetic field ................................. 504
9.1.1. Rotating wave approximation .................... 505
9.1.2. Rabi oscillations .............................. 506
9.1.3. Dressed states ................................. 508
9.1.4. Adiabatic passage and the adiabatic theorem .... 512
9.2. Liouville-von Neumann equation for the density
matrix ................................................ 514
9.2.1. The density matrix description of matter ....... 515
9.2.2. The steady-state density matrix solution ....... 524
9.2.3. Rate equation limit ............................ 526
9.2.4. Atom cooling and trapping revisited ............ 527
9.2.5. The adiabatic theorem for density matrix
dynamics ....................................... 528
9.2.6. Inhomogeneous broadening ....................... 529
9.2.7. Optical coherent transient processes ........... 530
9.3. Three-level system .................................... 536
9.3.1. Wavefunction treatment of a three-level
system ......................................... 537
9.3.2. Population transfer using stimulated Raman
adiabatic passage .............................. 539
9.3.3. Coherent trapping dark states .................. 541
9.3.4. Density matrix treatment of a three-level
system ......................................... 541
9.4. Coherent states and squeezed states ................... 543
9.4.1. Position-momentum squeezing .................... 547
9.4.2. Number and phase squeezing and the phase
operator ....................................... 549
9.4.3. Generation of squeezed states: parametric
down-conversion ................................ 551
9.4.4. Homodyne detection of squeezed states .......... 552
9.4.5. Application of squeezed states: sub-shot-
noise phase measurements ....................... 553
9.5. The Jaynes-Cummings model ............................. 554
9.6. Interaction between modes of a quantum field .......... 556
9.6.1. Interaction representation ..................... 557
9.6.2. Quantum-field two-mode Rabi problem ............ 558
9.6.3. Parametric oscillation ......................... 559
10.Light propagation in optical fibers and introduction to
optical communication systems .............................. 561
10.1.Fiber characteristics ................................. 562
10.1.1.Attenuation in fibers .......................... 564
10.1.2.Dispersion in fibers ........................... 564
10.1.3.Polarization- maintenance and single-
polarization fibers ............................ 566
10.1.4.Gain in doped fibers ........................... 566
10.2. Transverse modes of an optical fiber ................. 567
10.2.1.Single-mode fiber .............................. 571
10.2.2.Imperfections in the fiber ..................... 572
10.2.3.Coupling between fiber modes ................... 572
10.2.4.Fiber-Bragg gratings ........................... 572
10.3. Nonlinear processes in fibers ........................ 573
10.3.1.Optical solitons in fibers ..................... 574
10.3.2.Stimulated Raman amplification in fibers ....... 574
10.3.3.Higher-order nonlinear effects ................. 575
10.3.4.Parametric processes ........................... 576
10.4. Fiber-optic communication systems .................... 576
10.4.1.Analogue communication ......................... 577
10.4.2.Coherent optical communication ................. 577
10.4.3.Digital communication .......................... 579
10.4.4.Multiplexing techniques ........................ 581
Appendices .................................................... 583
Appendix A: vector analysis ................................... 583
A.1. Scalar and vector products ............................ 583
A.2. Differential operators ................................ 583
A.3. Divergence and Stokes theorems ........................ 585
A.4. Curvilinear coordinates ............................... 586
Appendix B: Electromagnetism and Maxwell's equations .......... 588
B.l. The laws of electromagnetism .......................... 588
B.2. Electromagnetic units ................................. 589
B.3. Maxwell's equations ................................... 590
Appendix C: Quantum mechanics and the Schrodinger equation .... 595
C.l. Time-dependent and time-independent Schrodinger
equations ............................................. 595
C.2. Spherical harmonics ................................... 597
C.3. The radial Schrodinger equation ....................... 598
C.4. The free particle ..................................... 600
С 5. The spherical top and the distorted spherical top ..... 601
С 6. The Coulomb potential ................................. 602
C.7. Atomic units .......................................... 603
C.8. The Morse potential ................................... 606
C.9. The harmonic oscillator potential ..................... 607
Appendix D: perturbation theory ............................... 609
D.1. Nondegenerate time-independent perturbation theory .... 609
D.2. Degenerate time-independent perturbation theory ....... 611
D.3. Time-dependent perturbation theory .................... 612
Appendix E: Fundamental constants ............................. 613
References .................................................... 615
Bibliography .................................................. 619
Index ......................................................... 623
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