1 Introduction ................................................. 1
1.1 The laser ............................................... 1
1.2 Electromagnetic radiation in a closed cavity ............ 3
1.2.1 The density of modes .............................. 7
1.3 Planck's law ............................................ 7
1.3.1 The energy density of blackbody radiation ......... 8
Further reading .............................................. 9
Exercises .................................................... 9
2 The interaction of radiation and matter ..................... 12
2.1 The Einstein treatment ................................. 12
2.1.1 Relations between the Einstein coefficients ...... 14
2.2 Conditions for optical gain ............................ 16
2.2.1 Conditions for steady-state inversion ........... 16
2.2.2 Necessary, but not sufficient condition ......... 18
2.3 The semi-classical treatment ........................... 19
2.3.1 Outline ......................................... 19
2.3.2 Selection rules for electric dipole
transitions ..................................... 20
2.4 Atomic population kinetics ............................. 21
2.4.1 Rate equations .................................. 22
2.4.2 Semi-classical equations ........................ 22
2.4.3 Validity of the rate-equation approach .......... 23
Further reading ............................................. 24
Exercises ................................................... 25
3 Broadening mechanisms and lineshapes ........................ 27
3.1 Homogeneous broadening mechanisms ...................... 27
3.1.1 Natural broadening .............................. 27
3.1.2 Pressure broadening ............................. 32
3.1.3 Phonon broadening ............................... 35
3.2 Inhomogeneous broadening mechanisms .................... 35
3.2.1 Doppler broadening .............................. 36
3.2.2 Broadening in amorphous solids .................. 38
3.3 The interaction of radiation and matter in the
presence of spectral broadening ........................ 38
3.3.1 Homogeneously broadened transitions ............. 38
3.3.2 Inhomogeneously broadened atoms ................. 39
3.4 The formation of spectral lines: The Voigt profile ..... 40
3.5 Other broadening effects ................................ 42
3.5.1 Self-absorption .................................. 42
Further reading ............................................. 43
Exercises ................................................... 43
4 Light amplification by the stimulated emission of
radiation ................................................... 46
4.1 The optical gain cross-section ......................... 46
4.1.1 Condition for optical gain ...................... 48
4.1.2 Frequency dependence of the gain cross-
section ......................................... 48
4.1.3 The gain coefficient ............................ 49
4.1.4 Gain narrowing .................................. 49
4.2 Narrowband radiation ................................... 50
4.2.1 Amplification of narrowband radiation ........... 50
4.2.2 Form of rate equations .......................... 51
4.3 Gain cross-section for inhomogeneous broadening ........ 52
4.4 Orders of magnitude .................................... 53
4.5 Absorption ............................................. 54
4.5.1 The absorption cross-section .................... 54
4.5.2 Self-absorption ................................. 55
4.5.3 Radiation trapping .............................. 56
Further reading ............................................. 56
Exercises ................................................... 57
5 Gain saturation ............................................. 60
5.1 Saturation in a steady-state amplifier ................. 60
5.1.1 Homogeneous broadening .......................... 60
5.1.2 Inhomogeneous broadening ........................ 67
5.2 Saturation in a homogeneously broadened pulsed
amplifier .............................................. 73
5.3 Design of laser amplifiers ............................. 77
Exercises ................................................... 78
6 The laser oscillator ........................................ 83
6.1 Introduction ........................................... 83
6.2 Amplified spontaneous emission (ASE) lasers ............ 83
6.3 Optical cavities ....................................... 85
6.3.1 General considerations .......................... 85
6.3.2 Low-loss (or 'stable') optical cavities ......... 89
6.3.3 High-loss (or 'unstable') optical cavities ...... 97
6.4 Beam quality .......................................... 103
6.4.1 The M2 beam-propagation factor .................. 103
6.5 The approach to laser oscillation ..................... 106
6.5.1 The 'cold' cavity .............................. 106
6.5.2 The laser threshold condition .................. 110
6.6 Laser oscillation above threshold ..................... 111
6.6.1 Condition for steady-state laser oscillation ... 112
6.6.2 Homogeneously broadened systems ................ 113
6.6.3 Inhomogeneously broadened systems' .............. 115
6.7 Output power .......................................... 117
6.7.1 Low-gain lasers ................................ 117
6.7.2 High-gain lasers: the Rigrod analysis .......... 120
6.7.3 Output power in other cases .................... 123
Further reading ............................................ 123
Exercises .................................................. 123
7 Solid-state lasers ......................................... 132
7.1 General considerations ................................ 132
7.1.1 Energy levels of ions doped in solid hosts ..... 132
7.1.2 Radiative transitions .......................... 137
7.1.3 Non-radiative transitions ...................... 138
7.1.4 Line broadening ................................ 142
7.1.5 Three-and four-level systems ................... 142
7.1.6 Host materials ................................. 146
7.1.7 Techniques for optical pumping ................. 149
7.2 Nd3+:YAG and other trivalent rare-earth systems ....... 157
7.2.1 Energy-level structure ......................... 157
7.2.2 Transition linewidth ........................... 157
7.2.3 Nd:YAG laser ................................... 158
7.2.4 Other crystalline hosts ........................ 163
7.2.5 Nd:glass laser ................................. 164
7.2.6 Erbium lasers .................................. 165
7.2.7 Praseodymium ions .............................. 169
7.3 Ruby and other trivalent iron-group systems ........... 169
7.3.1 Energy-level structure ......................... 169
7.3.2 The ruby laser ................................. 174
7.3.3 Alexandrite laser .............................. 177
7.3.4 Cn:LiSAF and Cn:LiCAF .......................... 180
7.3.5 Ti:sapphire .................................... 180
Further reading ............................................ 184
Exercises .................................................. 184
8 Dynamic cavity effects ..................................... 188
8.1 Laser spiking and relaxation oscillations ............. 188
8.1.1 Rate-equation analysis ......................... 190
8.1.2 Analysis of relaxation oscillations ............ 190
8.1.3 Numerical analysis of laser spiking ............ 192
8.2 Q-switching ........................................... 193
8.2.1 Techniques for Q-switching ..................... 194
8.2.2 Rate-equation analysis of Q-switching .......... 198
8.2.3 Comparison with numerical simulations .......... 203
8.3 Modelocking ........................................... 203
8.3.1 General ideas .................................. 204
8.3.2 Simple treatment of modelocking ................ 206
8.3.3 Active modelocking techniques .................. 208
8.3.4 Passive modelocking techniques ................. 214
8.4 Other forms of pulsed output .......................... 221
Further reading ............................................ 222
Exercises .................................................. 222
9 Semiconductor lasers ....................................... 226
9.1 Basic features of a typical semiconductor diode
laser ................................................. 226
9.2 Review of semiconductor physics ....................... 228
9.2.1 Band structure ................................. 228
9.2.2 Density of states and the Fermi energy (T =
0K) ............................................ 231
9.2.3 The Fermi-Dirac distribution (T ≠ 0К) .......... 232
9.2.4 Doped semiconductors ........................... 233
9.3 Radiative transitions in semiconductors ............... 235
9.4 Gain at a p-i-n junction .............................. 236
9.5 Gain in diode lasers .................................. 238
9.6 Carrier and photon confinement: the double
heterostructure ....................................... 241
9.7 Laser materials ....................................... 243
9.8 Quantum-well lasers1 .................................. 244
9.9 Laser threshold ....................................... 247
9.10 Diode laser beam properties ........................... 250
9.10.1 Beam shape ..................................... 250
9.10.2 Transverse modes of edge-emitting lasers ....... 250
9.10.3 Longitudinal modes of diode lasers ............. 251
9.10.4 Single longitudinal mode diode lasers .......... 253
9.10.5 Diode laser linewidth .......................... 254
9.10.6 Tunable diode laser cavities ................... 255
9.11 Diode laser output power .............................. 257
9.12 VCSEL lasers .......................................... 259
9.13 Strained-layer lasers ................................. 261
9.14 Quantum cascade lasers ................................ 262
Further reading ............................................ 264
Exercises .................................................. 264
10 Fibre lasers ............................................... 267
10.1 Optical fibres ........................................ 267
10.1.1 The importance of optical-fibre technology ..... 267
10.1.2 Optical-fibre properties: Ray optics ........... 268
10.1.3 Optical-fibre properties: Wave optics .......... 271
10.1.4 Dispersion in optical fibres ................... 274
10.1.5 Fabrication of optical fibres .................. 276
10.1.6 Fibre-optic components ......................... 277
10.2 Wavelength bands for fibre-optic telecommunications ... 280
10.3 Erbium-doped fibre amplifiers ......................... 282
10.3.1 Energy levels and pumping schemes .............. 282
10.3.2 Gain spectra ................................... 282
10.3.3 EDFA design and layout ......................... 284
10.3.4 Fabrication of erbium-doped fibre amplifiers ... 285
10.4 Fibre Raman amplifiers ................................ 285
10.4.1 Introduction ................................... 285
10.4.2 Raman scattering ............................... 285
10.4.3 Fibre Raman amplifiers ......................... 286
10.4.4 Long-haul optical transmission systems ......... 287
10.5 High-power fibre lasers ............................... 289
10.5.1 The revolution in fibre-laser performance ...... 289
10.5.2 Cladding-pumped fibre-laser design ............. 290
10.5.3 Materials and mechanisms of cladding-pumped
fibre-laser systems ............................ 291
10.5.4 High-power fibre lasers: Linewidth
considerations ................................. 291
10.6 High-power pulsed fibre lasers ........................ 293
10.6.1 Large mode area (LMA) fibres ................... 293
10.6.2 Q-switched fibre lasers ........................ 294
10.6.3 Oscillator-amplifier pulsed fibre lasers ....... 294
10.7 Applications of high-power fibre lasers ............... 295
Further reading ............................................ 296
Exercises .................................................. 296
11 Atomic gas lasers .......................................... 298
11.1 Discharge physics interlude ........................... 298
11.1.1 Low-pressure and high-pressure discharges ...... 298
11.1.2 Low-pressure glow discharge .................... 299
11.1.3 Temperatures ................................... 300
11.1.4 The steady-state positive column ............... 303
11.1.5 Ionization rates ............................... 306
11.1.6 Excitation rates ............................... 307
11.1.7 Second-kind or superelastic collisions ......... 310
11.1.8 Excited-state populations in low-pressure
discharges ..................................... 311
11.2 The helium-neon laser ................................. 314
11.2.1 Introduction ................................... 314
11.2.2 Energy levels, transitions and excitation
mechanisms ..................................... 316
11.2.3 Laser construction and operating parameters .... 318
11.2.4 Output-power limitations of the He-Ne laser .... 319
11.2.5 Applications of He-Ne lasers ................... 321
11.3 The argon-ion laser ................................... 321
11.3.1 Introduction ................................... 321
11.3.2 Energy levels, transitions and excitation
mechanisms ..................................... 322
11.3.3 Laser construction and operating parameters .... 325
11.3.4 Argon-ion laser: Power limitations ............. 327
11.3.5 Krypton-ion lasers ............................. 328
11.3.6 Applications of ion lasers ..................... 329
Further reading ............................................ 329
Exercises .................................................. 329
12 Infra-red molecular gas lasers ............................. 332
12.1 Efficiency considerations ............................. 332
12.1.1 Energy levels of atoms and molecules ........... 332
12.1.2 Quantum ratio .................................. 333
12.2 Partial population inversion between vibrational
energy levels of molecules ............................ 335
12.3 Physics of the CO2 laser .............................. 338
12.3.1 Levels and lifetimes ........................... 338
12.3.2 The effect of adding N2 ........................ 341
12.3.3 Effect of adding He ............................ 342
12.4 CO2 laser parameters .................................. 343
12.5 Low-pressure c.w. CO2 lasers .......................... 344
12.6 High-pressure pulsed CO2 lasers ....................... 346
12.7 Other types of C02 laser .............................. 349
12.7.1 Gas-dynamic CO2 lasers ......................... 349
12.7.2 Waveguide CO2 lasers ........................... 351
12.8 Applications of CO2 lasers ............................ 351
Further reading ............................................ 352
Exercises .................................................. 352
13 Ultraviolet molecular gas lasers ........................... 355
13.1 The UV and VUV spectral regions ....................... 355
13.2 Energy levels of diatomic molecules ................... 356
13.2.1 Separation of the overall wave function ........ 356
13.2.2 Vibrational eigenfunctions ..................... 357
13.3 Electronic transitions in diatomic molecules: The
Franck-Condon principle ............................... 358
13.3.1 Absorption transitions ......................... 358
13.3.2 The 'Franck-Condon loop' ....................... 360
13.4 The VUV hydrogen laser ................................ 361
13.5 The UV nitrogen laser ................................. 364
13.6 Excimer molecules ..................................... 364
13.7 Rare-gas excimer lasers ............................... 367
13.8 Rare-gas halide excimer lasers ........................ 370
13.8.1 Spectroscopy of the rare-gas halides ........... 370
13.8.2 Rare-gas halide laser design ................... 371
13.8.3 Pulse-length limitations of discharge-excited
RGH lasers ..................................... 373
13.8.4 Cavity design and beam properties of RHG
lasers ......................................... 373
13.8.5 Performance and applications of RGH excimer
laser .......................................... 375
Further reading ............................................ 377
Exercises .................................................. 378
14 Dye lasers ................................................. 380
14.1 Introduction .......................................... 380
14.2 Dye molecules ......................................... 380
14.3 Energy levels and spectra of dye molecules in
solution .............................................. 382
14.3.1 Energy-level scheme ............................ 382
14.3.2 Singlet-singlet absorption ..................... 382
14.3.3 Singlet-singlet emission spectra ............... 385
14.3.4 Triplet-triplet absorption ..................... 387
14.4 Rate-equation models of dye laser kinetics ............ 387
14.5 Pulsed dye lasers ..................................... 388
14.5.1 Flashlamp-pumped systems ....................... 388
14.5.2 Dye lasers pumped by pulsed lasers ............. 389
14.6 Continuous-wave dye lasers ............................ 391
14.6.1 Population kinetics ............................ 391
14.6.2 Continuous waves dye laser design .............. 393
14.7 Solid-state dye lasers ................................ 395
14.8 Applications of dye lasers ............................ 396
Further reading ............................................ 398
Exercises .................................................. 398
15 Non-linear frequency conversion ............................ 400
15.1 Introduction .......................................... 400
15.2 Linear optics of crystals ............................. 400
15.2.1 Classes of anisotropic crystals ................ 400
15.2.2 Vectors ........................................ 402
15.2.3 Field directions for o-and e-rays in a
uniaxial crystal ............................... 403
15.3 Basics of non-linear optics ........................... 405
15.3.1 Maxwell's equations for non-linear media ....... 405
15.3.2 Second-harmonic generation in anisotropic
crystals ....................................... 406
15.3.3 The requirement for phase matching ............. 408
15.4 Phase-matching techniques ............................. 409
15.4.1 Birefringent phase matching in uniaxial
crystals ....................................... 409
15.4.2 Critical and non-critical phase matching ....... 412
15.4.3 Poynting vector walk-off in birefringent
phase matching ................................. 414
15.4.4 Other factors affecting SHG conversion
efficiency ..................................... 414
15.4.5 Phase-matched SHG in biaxial crystals .......... 415
15.4.6 Birefringent materials for SHG ................. 416
15.4.7 Quasi-phase matching techniques ................ 418
15.5 SHG: practical aspects ................................ 420
15.6 Three-wave mixing and third-harmonic generation
(THG) ................................................. 421
15.6.1 Three-wave mixing processes in general ......... 421
15.6.2 Third-harmonic generation (THG) ................ 423
15.7 Optical parametric oscillators (OPOs) ................. 424
15.7.1 Parametric interactions ........................ 424
15.7.2 Optical parametric oscillators (OPOs) .......... 425
15.7.3 Practical parametric devices ................... 426
Further reading ............................................ 428
Exercises .................................................. 428
16 Precision frequency control of lasers ...................... 431
16.1 Frequency pulling ..................................... 431
16.2 Single longitudinal mode operation .................... 433
16.2.1 Short cavity ................................... 434
16.2.2 Intra-cavity etalons ........................... 435
16.2.3 Ring resonators ................................ 437
16.2.4 Other techniques ............................... 440
16.3 Output linewidth ...................................... 440
16.3.1 The Schawlow-Townes limit ...................... 441
16.3.2 Practical limitations .......................... 444
16.3.3 Intensity noise ................................ 446
16.4 Frequency locking ..................................... 448
16.4.1 Locking to atomic or molecular transitions ..... 450
16.4.2 Locking to an external cavity .................. 452
16.5 Frequency combs ....................................... 453
Further reading ............................................ 456
Exercises .................................................. 456
17 Ultrafast lasers ........................................... 462
17.1 Propagation of ultrafast laser pulses in dispersive
media ................................................. 462
17.1.1 The time-bandwidth product ..................... 462
17.1.2 General considerations ......................... 463
17.1.3 Propagation through a dispersive system ........ 466
17.1.4 Propagation of Gaussian pulses ................. 469
17.1.5 Non-linear effects: self-phase modulation and
the B-integral ................................. 472
17.2 Dispersion control .................................... 474
17.2.1 Geometric dispersion control ................... 474
17.2.2 Chirped mirrors ................................ 478
17.2.3 Pulse shaping .................................. 480
17.3 Sources of ultrafast optical pulses ................... 482
17.3.1 Modelocked lasers .............................. 482
17.3.2 Oscillators .................................... 483
17.3.3 Chirped-pulse amplification (CPA) .............. 483
17.4 Measurement of ultrafast pulses ....................... 489
17.4.1 Autocorrelators ................................ 489
17.4.2 Methods for exact reconstruction of the
pulse .......................................... 492
Further reading ............................................ 495
Exercises .................................................. 495
18 Short-wavelength lasers .................................... 502
18.1 Definition of wavelength ranges ....................... 503
18.2 Difficulties in achieving optical gain at short
wavelengths ........................................... 503
18.2.1 Pump-power scaling ............................. 503
18.3 General properties of short-wavelength lasers ......... 505
18.3.1 Travelling-wave pumping ........................ 505
18.3.2 Threshold and saturation behaviour in an ASE
laser .......................................... 506
18.3.3 Spectral width of the output ................... 508
18.3.4 Coherence properties of ASE lasers ............. 509
18.4 Laser-generated plasmas ............................... 510
18.4.1 Inverse bremsstrahlung heating ................. 510
18.4.2 Generation of highly ionized plasmas from
laser-solid interactions ....................... 511
18.4.3 Optical field ionization ....................... 514
18.5 Collisionally excited lasers .......................... 517
18.5.1 Ne-like ions ................................... 518
18.5.2 Ni-like ions ................................... 520
18.5.3 Methods of pumping ............................. 520
18.5.4 Collisionally excited OFI lasers ............... 528
18.6 Recombination lasers .................................. 530
18.6.1 H-like carbon .................................. 532
18.6.2 OFI recombination lasers ....................... 533
18.7 Other sources ......................................... 535
18.7.1 High-harmonic generation ....................... 535
18.7.2 Free-electron lasers ........................... 537
Further reading ............................................ 541
Exercises .................................................. 541
Appendix A: The semi-classical theory of the interaction of
radiation and matter ....................................... 548
A.1 The amplitude equations ............................... 548
A.1.1 Derivation of the amplitude equations .......... 548
A.1.2 Solution of the amplitude equations ............ 550
A.2 Calculation of the Einstein В coefficient ............. 551
A.2.1 Polarized atoms and radiation .................. 551
A.2.2 Unpolarized atoms and/or radiation ............. 553
A.2.3 Treatment of degeneracy ........................ 554
A.3 Relations between the Einstein coefficients ........... 555
A.4 Validity of rate equations ............................ 555
Appendix B: The spectral Einstein coefficients ................ 557
Appendix C: Kleinman's conjecture ............................. 560
Bibliography .................................................. 563
Index ......................................................... 579
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