Nonlinear optical systems:
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge Univ. Press
2015
|
| Ausgabe: | 1. publ. |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027989436&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027989436&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XIV, 454 S. graph. Darst. |
| ISBN: | 9781107062672 1107062675 |
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Datensatz im Suchindex
| _version_ | 1819333450261331968 |
|---|---|
| adam_text | Guiding graduate students and researchers through the complex world of
laser physics and nonlinear optics, this book provides an in-depth exploration
of the dynamics of lasers and other relevant optical systems, under the
umbrella of a unitary spatio-temporal vision.
Adopting a balanced approach, the book covers traditional as well as
special topics in laser physics, quantum electronics and nonlinear optics,
treating them from the viewpoint of nonlinear dynamical systems. These
include laser emission, frequency generation, solitons, optically bistable
systems, pulsations and chaos and optical pattern formation. It also provides
a coherent and up-to-date treatment of the hierarchy of nonlinear optical
models and of the rich variety of phenomena they describe, helping readers
to understand the limits of validity of each model and the connections among
the phenomena. It is ideal for graduate students and researchers in nonlinear
optics, quantum electronics, laser physics and photonics.
LUIGI LUGIATO is Professor Emeritus at Università dell’lnsubria, Como, Italy.
He has received numerous national and international honors as a result of
his many pioneering contributions in nonlinear and quantum optics.
FRANCO PRATI is Associate Professor at Università dell’lnsubria, Como,
Italy, where he works in laser physics and nonlinear optics.
MASSIMO BRAMBILLA is Associate Professor at Politecnico di Bari, Italy,
where he works in the field of nonlinear optical systems.
Contents
Preface
Part I Models, propagation, stationary phenomena
Introduction to Part I
1 The rate-equation model for the laser
1.1 Absorption, stimulated emission and spontaneous emission
1.2 Calculation of the B coefficient
1.3 The laser
2 The interaction of a system of two-level atoms with the electromagnetic field
2.1 The interaction Hamiltonian in the dipole approximation
2.2 The two-level atom and its analogy with spin 1/2
2.3 The rotating-wave approximation. Optical Bloch equations
2.4 The Bloch vector and its nutation
3 The Maxwell-Bloch equations
3.1 The Maxwell equations. Paraxial and slowly varying
envelope approximations
3.2 The Maxwell-Bloch equations. The plane-wave approximation
3.3 Self-induced transparency, the sine-Gordon equation and solitons
3.4 Superradiance and superfluorescence
4 Inclusion of the irreversible processes in the atomic equations
4.1 Irreversible transition processes between the two levels
4.2 Irreversible decay of the atomic polarization
4.3 Damped Rabi oscillations and the approach to a stationary state
4.4 The complete Maxwell—Bloch equations
5 Propagation in irreversible Maxwell-Bloch equations
5.1 Linear theory
5.2 Saturation and power broadening
5.3 Nonlinear propagation for a monochromatic input field: The role of
saturation and nonlinear phase shift
5.4 Background linear dispersion and absorption
page xiii
1
3
5
5
7
9
15
15
17
19
21
29
29
33
34
37
43
43
45
47
48
49
49
53
55
57
viii
Contents
6 Optical nonlinearities. Materials with quadratic nonlinearities 60
6.1 Linear and nonlinear polarization 61
6.2 Media with a quadratic nonlinearity 63
6.3 The stationary state in the plane-wave approximation 67
7 Optical nonlinearities. Materials with cubic nonlinearities 74
7.1 The Kerr medium nonlinearity. Self-phase modulation 74
7.2 Temporal Kerr solitons 76
7.3 Spatial Kerr solitons 78
7.4 The case of three frequency bands. Cross-phase modulation and
four-wave mixing 79
7.5 Optical phase conjugation 81
8 Optical resonators. The planar ring cavity. Empty cavity. Linear cavity 85
8.1 Optical cavities 85
8.2 Beam splitters 86
8.3 The planar ring cavity. Boundary condition, input and output fields.
Transmission of the cavity 87
8.4 The empty cavity 90
8.5 The linear cavity. Frequency pulling and pushing, mode splitting 92
9 A nonlinear active ring cavity: the ring laser, stationary states 95
9.1 Calculation of the nontrivial stationary solutions 95
9.2 The low-transmission limit 99
9.3 The analogy with second-order phase transitions 101
10 The adiabatic elimination principle 105
10.1 General formulation of the principle 105
10.2 Adiabatic elimination of the atomic polarization in the Bloch equations.
Limits of the optical pumping between two levels 107
10.3 The three-level optical-pumping scheme 108
10.4 The four-level optical-pumping scheme 110
11 A nonlinear passive ring cavity: optical bistability 112
11.1 Absorptive optical bistability 112
11.2 Dispersive optical bistability 117
11.3 Optical bistability in two-level systems: the general case 120
11.4 Functionalities of optically bistable systems 123
12 Modal equations for the ring cavity. The single-mode model 126
12.1 Transformation of coordinates and transformation
of variables. Modal equations 127
12.2 Introduction of the low-transmission approximation 131
12.3 The single-mode model 132
12.4 Stationary solutions of the single-mode model 134
IX
Contents
13 Single-and two-mode models 135
13.1 A laser with an injected signal 13 5
13.2 A laser with a saturable absorber 139
13.3 The cubic model for dispersive optical bistability 142
13.4 A model for the degenerate optical parametric oscillator (and harmonic
generation in a cavity) and its stationary solutions 144
14 Nonlinear dynamics in Fabry-Perot cavities 150
14.1 Modal equations for the Fabry-Perot cavity 151
14.2 The single-mode model for the Fabry-Perot cavity. Spatial hole-burning 156
14.3 A more convenient set of modal equations 159
14.4 Again the ring cavity: simplified forms of the models 163
14.5 The case of an atomic sample of length much shorter than the
wavelength: difference-differential equations 165
15 Inhomogeneous broadening 170
15.1 Multimode dynamical equations 170
15.2 The single-mode model. The stationary state for the laser.
Spectral hole-burning 172
16 The semiconductor laser 177
16.1 Some elements of semiconductor physics 177
16.2 The p-n junction 179
16.3 The double heterojunction. Optical confinement 180
16.4 Band structure 182
16.5 Dynamical equations 184
16.6 Vertical-cavity surface-emitting lasers 190
17 Lasers without inversion and the effects of atomic coherence 192
17.1 Model equations 192
17.2 Coherent population trapping 194
17.3 Electromagnetically induced transparency 196
17.4 Amplification without inversion 199
17.5 Lasing without inversion 202
Part II Dynamical phenomena, instabilities, chaos 205
Introduction to Part II 207
18 Some general aspects in nonlinear dissipative dynamical systems 209
18.1 Stationary solutions and their stability 210
18.2 Attractors and repellers; bistability and multistability 212
18.3 Other kinds of attractors: limit cycles, tori, strange attractors;
deterministic chaos; generalized multistability 213
18.4 Transitions induced by the variation of a control parameter 214
Contents
19 Special limits in the single-mode model 219
19 Л Classification of lasers 219
19.2 Adiabatic elimination of the atomic variables (the good-cavity limit) 220
19.3 Adiabatic elimination of the atomic polarization: the single-mode
rate-equation model 225
19.4 Adiabatic elimination of the electric field (the bad-cavity limit) 232
20 The linear-stability analysis of the Maxwell-Bloch equations 233
20.1 Coupled multimodal equations for field and atomic variables.
Single-mode and multimode instabilities 234
20.2 Multimode instabilities and their features 238
20.3 Single-mode instabilities and their features 241
20.4 The general connection between single-mode and multimode instabilities 244
20.5 The resonant case, amplitude and phase instabilities 244
21 Adiabatic elimination in the complete Maxwell-Bloch equations 247
21.1 The rate-equation approximation 247
21.2 Adiabatic elimination of the atomic polarization and comparison with the
rate-equation approximation 248
21.3 Adiabatic elimination of the atomic variables 249
22 Dynamical aspects in the laser 252
22.1 Linear-stability analysis of the trivial stationary solution
in the standard laser 252
22.2 Linear-stability analysis of the trivial stationary solution in the laser
without inversion 254
22.3 Class-C lasers: the analogy with the Lorenz model and optical chaos 255
22.4 The resonant single-mode laser instability 257
22.5 The multimode amplitude instability 261
22.6 The multimode phase instability 265
22.7 An ultrathin medium: the multimode amplitude instability in the
Fabry-Perot laser 269
23 Single-mode and multimode operation in inhomogeneously broadened lasers 275
23.1 Multimode and single-mode instabilities 276
23.2 Mode-locking 285
24 Dynamical aspects in optical bistability 288
24.1 Critical slowing down 288
24.2 Multimode instabilities in optical bistability 291
24.3 Single-mode instabilities in optical bistability 300
25 Self-pulsing in other optical systems 306
25.1 A laser with an injected signal. Frequency locking and
coexisting attractors 306
xi
Contents
25.2 A laser with a saturable absorber. Repetitive passive ^-switching 309
25.3 A degenerate optical parametric oscillator, period doubling
and chaos 313
Part III Transverse optical patterns 317
Introduction to Part III 319
26 Gaussian beams and modes of cavities with spherical mirrors 323
26.1 Gaussian-shaped beams 324
26.2 Higher-order modes 327
26.3 Gaussian modes in a cavity with spherical mirrors. The case of
Fabry-Perot cavities 332
26.4 The ABCD matrix method 334
26.5 Gaussian modes in a cavity with spherical mirrors. The case
of ring cavities 336
26.6 Mode frequencies 337
27 General features about optical pattern formation in planar cavities 342
27.1 Dynamical models with diffraction 342
27.2 Systems with translational symmetry. The mechanisms for
pattern formation 345
27.3 Pattern formation in optical parametric oscillators 353
27.4 Systems with a single feedback mirror 356
27.5 The analogy with hydrodynamics. Vortices and other defects 359
28 The Lugiato-Lefever model 363
28.1 Modulational instability and the patterns arising from it 364
28.2 The temporal version of the LL model and its application
perspectives 370
29 Spatial patterns in cavities with spherical mirrors 378
29.1 Modal equations and the single-longitudinal-mode model 379
29.2 The single-mode Gaussian model 382
29.3 The multimodal transverse regime and cooperative frequency
locking in the laser 384
29.4 Laser patterns from frequency-degenerate families of modes.
Spontaneous breaking of the cylindrical symmetry.
Phase-singularity crystals 388
30 Cavity solitons 393
30.1 Localized structures in optics 394
30.2 Generation and control of cavity solitons 398
30.3 Cavity solitons in semiconductor microresonators 402
30.4 The “cavity-soliton laser” 409
XÜ
Contents
Appendix A The Routh-Hurwitz stability criterion 412
Appendix B Calculation of the oscillatory instability boundary 413
B.l The cubic case 413
B.2 The quartic case 414
B.3 The quintic case 414
Appendix C Coefficients of the characteristic equation (20.20) 415
Appendix D Derivation of equations (20.27) and (20.28) 416
Appendix E Coefficients of equations (20.60) and (20.61) 417
Appendix F The exact boundary of the Risken-Nummedal-Graham-Haken instability 418
Appendix G Nonlinear analysis of the roll solution 419
References 425
Index 447
|
| any_adam_object | 1 |
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| discipline | Physik Elektrotechnik / Elektronik / Nachrichtentechnik |
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| id | DE-604.BV042555635 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T17:14:16Z |
| institution | BVB |
| isbn | 9781107062672 1107062675 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027989436 |
| oclc_num | 915660473 |
| open_access_boolean | |
| owner | DE-703 DE-11 |
| owner_facet | DE-703 DE-11 |
| physical | XIV, 454 S. graph. Darst. |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spellingShingle | Lugiato, Luigi Prati, Franco Brambilla, Massimo Nonlinear optical systems Laser (DE-588)4034610-9 gnd Nichtlineare Optik (DE-588)4042096-6 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Quantenelektronik (DE-588)4137298-0 gnd |
| subject_GND | (DE-588)4034610-9 (DE-588)4042096-6 (DE-588)4126142-2 (DE-588)4137298-0 |
| title | Nonlinear optical systems |
| title_auth | Nonlinear optical systems |
| title_exact_search | Nonlinear optical systems |
| title_full | Nonlinear optical systems Luigi Lugiato ; Franco Prati ; Massimo Brambilla |
| title_fullStr | Nonlinear optical systems Luigi Lugiato ; Franco Prati ; Massimo Brambilla |
| title_full_unstemmed | Nonlinear optical systems Luigi Lugiato ; Franco Prati ; Massimo Brambilla |
| title_short | Nonlinear optical systems |
| title_sort | nonlinear optical systems |
| topic | Laser (DE-588)4034610-9 gnd Nichtlineare Optik (DE-588)4042096-6 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Quantenelektronik (DE-588)4137298-0 gnd |
| topic_facet | Laser Nichtlineare Optik Nichtlineares dynamisches System Quantenelektronik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027989436&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027989436&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT lugiatoluigi nonlinearopticalsystems AT pratifranco nonlinearopticalsystems AT brambillamassimo nonlinearopticalsystems |