1 Gaussian beams ............................................... 1
1.1 Introduction ............................................ 1
1.2 The paraxial wave equation .............................. 1
1.3 Gaussian beam functions and the complex beam
parameter, q ............................................ 2
1.4 Some Gaussian beam properties ........................... 3
1.5 The phase term: Gouy phase .............................. 5
1.6 Simple transformation properties of the complex beam
parameter ............................................... 6
1.7 Matrix formulation of paraxial ray optics: ABCD rule .... 8
1.8 Further reading ........................................ 10
1.9 Problems ............................................... 11
2 Optical resonators - geometrical properties ................. 12
2.1 Introduction ........................................... 12
2.2 The two-mirror standing-wave cavity .................... 12
2.3 Stability .............................................. 14
2.4 Solution for an arbitrary two-mirror stable cavity ..... 16
2.5 Higher-order modes ..................................... 18
2.6 Resonant frequencies ................................... 20
2.7 The traveling-wave (ring) cavity ....................... 21
2.8 Astigmatism in a ring cavity ........................... 25
2.9 Mode matching .......................................... 29
2.10 Beam quality characterization: the M2 parameter ........ 31
2.11 Further reading ........................................ 33
2.12 Problems ............................................... 34
3 Energy relations in optical cavities ........................ 35
3.1 Introduction ........................................... 35
3.2 Reflection and transmission at an interface ............ 35
3.3 Reflected fields from standing-wave cavity ............. 36
3.4 Internal (circulating) field in a standing-wave
cavity ................................................. 37
3.5 Reflected and internal intensities ..................... 38
3.6 The resonant character of the reflected and
circulating intensities ................................ 39
3.7 Impedance matching ..................................... 40
3.8 Fields and intensities in ring cavity .................. 43
3.9 A novel "reflective" coupling scheme using a tilted
wedge .................................................. 44
3.10 Photon lifetime ........................................ 45
3.11 The quality factor, Q .................................. 46
3.12 Relation between Q and finesse ......................... 46
3.13 Alternative representation of cavity loss .............. 47
3.14 Experimental determination of cavity parameters ........ 47
3.15 Further reading ........................................ 50
3.16 Problems ............................................... 50
4 Optical cavity as frequency discriminator ................... 52
4.1 Introduction ........................................... 52
4.2 A simple example ....................................... 52
4.3 Side of resonance discriminant ......................... 54
4.4 The manipulation of polarized beams: the Jones
calculus ............................................... 55
4.5 The polarization technique ............................. 57
4.6 Frequency modulation ................................... 60
4.7 The Pound-Drever-Hall approach ......................... 62
4.8 Frequency response of a cavity-based discriminator ..... 66
4.9 Further reading ........................................ 69
4.10 Problems ............................................... 69
5 Laser gain and some of its consequences .................... 71
5.1 Introduction ........................................... 71
5.2 The wave equation ...................................... 71
5.3 The interaction term ................................... 72
5.4 The rotating-wave approximation ........................ 73
5.5 Density matrix of two-level system ..................... 74
5.6 The classical Bloch equation ........................... 76
5.7 Connection between two-level atom and spin-1/2 system .. 79
5.8 Radiative and collision-induced damping ................ 82
5.9 The atomic susceptibility and optical gain ............. 87
5.10 The Einstein A and В coefficients ...................... 91
5.11 Doppler broadening: an example of inhomogeneous
broadening ............................................. 95
5.12 Comments on saturation ................................. 97
5.13 Further reading ....................................... 101
5.14 Problems .............................................. 101
6 Laser oscillation and pumping mechanisms .................. 103
6.1 Introduction .......................................... 103
6.2 The condition for laser oscillation ................... 103
6.3 The power output of a laser ........................... 104
6.4 Pumping in three-level and four-level laser systems ... 106
6.5 Laser oscillation frequencies and pulling ............. 109
6.6 Inhomogeneous broadening and multimode behavior ....... 110
6.7 Spatial hole burning .................................. 112
6.8 Some consequences of the photon model for laser
radiation ............................................. 113
6.9 The photon statistics of laser radiation .............. 115
6.10 The ultimate linewidth of a laser ..................... 121
6.11 Further reading ....................................... 122
6.12 Problems .............................................. 122
7 Descriptions of specific CW laser systems .................. 124
7.1 Introduction .......................................... 124
7.2 The He-Ne laser ....................................... 124
7.3 The argon-ion laser ................................... 126
7.4 The continuous-wave organic dye laser ................. 129
7.5 The titanium-sapphire laser ........................... 133
7.6 The CW neodymium-yttrium-aluminum-garnet (Nd:YAG)
laser ................................................. 135
7.7 The YAG non-planar ring oscillator: a novel ring
laser geometry ........................................ 137
7.8 Diode-pumped solid-state (DPSS) YAG lasers ............ 138
7.9 Further reading ....................................... 139
8 Laser gain in a semiconductor .............................. 140
8.1 Introduction .......................................... 140
8.2 Solid-state physics background ........................ 140
8.3 Optical gain in a semiconductor ....................... 151
8.4 Further reading ....................................... 160
8.5 Problems .............................................. 160
9 Semiconductor diode lasers ................................. 162
9.1 Introduction .......................................... 162
9.2 The homojunction semiconductor laser .................. 162
9.3 The double heterostructure laser ...................... 165
9.4 Quantum-well lasers ................................... 170
9.5 Distributed feedback lasers ........................... 176
9.6 The rate equations and relaxation oscillations ........ 182
9.7 Diode laser frequency control and linewidth ........... 190
9.8 External cavity diode lasers (ECDLs) .................. 195
9.9 Semiconductor laser amplifiers and injection locking .. 205
9.10 Miscellaneous characteristics of semiconductor
lasers ................................................ 211
9.11 Further reading ....................................... 213
9.12 Problems .............................................. 213
10 Guided-wave devices and fiber lasers ....................... 215
10.1 Introduction .......................................... 215
10.2 Slab waveguide: preliminary analysis .................. 215
10.3 Wave propagation in a slab waveguide .................. 219
10.4 Wave propagation in a fiber - ray theory .............. 230
10.5 Wave propagation in a fiber - wave theory ............. 233
10.6 Dispersion in fibers and waveguides ................... 241
10.7 Coupling into optical fibers .......................... 245
10.8 Fiber-optic components ................................ 249
10.8.1 Directional coupler ............................ 250
10.8.2 The loop reflector ............................. 253
10.8.3 Fiber Bragg gratings ........................... 256
10.8.4 Optical isolators and circulators .............. 259
10.8.5 Amplitude and phase modulation ................. 261
10.8.6 Polarization-preserving fibers ................. 263
10.8.7 Polarization controller ........................ 267
10.9 The physics of rare earth ions in glasses ............. 269
10.10 Some specific fiber lasers ........................... 280
10.10.1 Fiber laser resonators ........................ 280
10.10.2 Erbium and erbium/ytterbium lasers ............ 283
10.10.3 Neodymium lasers .............................. 284
10.10.4 Ytterbium lasers .............................. 285
10.10.5 Thulium lasers ................................ 286
10.11 Further reading ...................................... 287
10.12 Problems ............................................. 287
11 Mode-locked lasers and frequency metrology ................. 289
11.1 Introduction .......................................... 289
11.2 Theory of mode locking ................................ 289
11.3 Mode-locking techniques ............................... 294
11.4 Dispersion and its compensation ....................... 298
11.5 The mode-locked Ti-sapphire laser ..................... 302
11.6 Mode-locked fiber lasers .............................. 305
11.7 Frequency metrology using a femtosecond laser ......... 309
11.8 The carrier envelope offset ........................... 313
11.9 Comb generation in a microresonator ................... 315
11.10 Further reading ...................................... 321
11.11 Problems ............................................. 321
12 Laser frequency stabilization and control systems .......... 323
12.1 Introduction .......................................... 323
12.2 Laser frequency stabilization - a first look .......... 323
12.3 The effect of the loop filter ......................... 325
12.4 Elementary noise considerations ....................... 326
12.5 Some linear system theory ............................. 329
12.6 The stability of a linear system ...................... 333
12.7 Negative feedback ..................................... 335
12.8 Some actual control systems ........................... 344
12.9 Temperature stabilization ............................. 350
12.10 Laser frequency stabilization ........................ 354
12.11 Optical-fiber phase noise and its cancellation ....... 363
12.12 Characterization of laser frequency stability ........ 365
12.13 Frequency locking to a noisy resonance ............... 371
12.14 Further reading ...................................... 373
12.15 Problems ............................................. 373
13 Atomic and molecular discriminants ......................... 375
13.1 Introduction .......................................... 375
13.2 Sub-Doppler saturation spectroscopy ................... 375
13.3 Sub-Doppler dichroic atomic vapor laser locking and
polarization spectroscopy ............................. 381
13.4 An example of a side-of-line atomic discriminant ...... 386
13.5 Further reading ....................................... 387
13.6 Problems .............................................. 387
14 Nonlinear optics ........................................ 389
14.1 Introduction .......................................... 389
14.2 Anisotropic crystals .................................. 389
14.3 Second-harmonic generation ............................ 397
14.4 Birefringent phase matching ........................... 402
14.5 Quasi-phase matching .................................. 408
14.6 Second-harmonic generation using a focused beam ....... 413
14.7 Second-harmonic generation in a cavity ................ 420
14.8 Sum-frequency generation .............................. 425
14.9 Periodically poled optical waveguides ................. 426
14.10 Parametric interactions .............................. 430
14.11 Further reading ...................................... 443
14.12 Problems ............................................. 443
15 Frequency and amplitude modulation ......................... 444
15.1 Introduction .......................................... 444
15.2 The linear electro-optic effect ....................... 444
15.3 Bulk electro-optic modulators ......................... 446
15.4 Traveling-wave electro-optic modulators ............... 451
15.5 Acousto-optic modulators .............................. 452
15.6 Further reading ....................................... 464
15.7 Problems .............................................. 464
References ................................................. 466
Index ......................................................... 471
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