The first book on Localized Waves—a subject of phenomenal worldwide research with important applications from secure communications to medicineLocalized waves—also known as non-diffractive waves—are beams and pulses capable of resisting diffraction and dispersion over long distances even in non-guiding media. Predicted to exist in the early 1970s and obtained theoretically and experimentally as solutions to the wave equations starting in 1992, localized waves now garner intense worldwide research with applications in all fields where a role is played by a wave equation, from electromagnetism to acoustics and quantum physics. In the electromagnetics areas, they are paving the way, for instance, to ubiquitous secure communications in the range of millimeter waves, terahertz frequencies, and optics. At last, the localized waves with an envelope at rest are expected to have important applications especially in medicine.Localized Waves brings together the world's most productive researchers in the field to offer a well-balanced presentation of theory and experiments in this new and exciting subject. Composed of thirteen chapters, this dynamic volume:Presents a thorough review of the theoretical foundation and historical aspects of localized wavesExplores the interconnections of the subject with other technologies and scientific areasAnalyzes the effect of arbitrary anisotropies on both continuous-wave and pulsed non-diffracting fieldsDescribes the physical nature and experimental implementation of localized wavesProvides a general overview of wave localization, for example in photonic crystals, which have received increasing attention in recent yearsLocalized Waves is the first book to cover this emerging topic, making it an indispensable resource in particular for researchers in electromagnetics, acoustics, fundamental physics, and free-space communications, while also serving as a requisite text for graduate students.
Author(s): Hugo E. Hernandez-Figueroa, Michel Zamboni-Rached, Erasmo Recami
Edition: 1
Year: 2008
Language: English
Pages: 369
Localized Waves......Page 4
Contents......Page 8
CONTRIBUTORS......Page 16
PREFACE......Page 18
Acknowledgments......Page 21
1 Localized Waves: A Historical and Scientific Introduction......Page 22
1.1 General Introduction......Page 23
1.2 More Detailed Information......Page 28
1.2.1 Localized Solutions......Page 30
Appendix: Theoretical and Experimental History......Page 37
Historical Recollections: Theory......Page 39
X-Shaped Field Associated with a Superluminal Charge......Page 42
A Glance at the Experimental State of the Art......Page 45
References......Page 55
2.1 Introduction......Page 64
2.2 Spectral Structure of Localized Waves......Page 65
2.2.1 Generalized Bidirectional Decomposition......Page 67
2.3 Space–Time Focusing of X-Shaped Pulses......Page 75
2.3.1 Focusing Effects Using Ordinary X-Waves......Page 76
2.4 Chirped Optical X-Type Pulses in Material Media......Page 78
2.4.1 Example: Chirped Optical X-Type Pulse in Bulk Fused Silica......Page 83
2.5.1 Stationary Wave Fields with Arbitrary Longitudinal Shape in Lossless Media Obtained by Superposing Equal-Frequency Bessel Beams......Page 84
2.5.2 Stationary Wave Fields with Arbitrary Longitudinal Shape in Absorbing Media: Extending the Method......Page 91
References......Page 97
3.1 Introduction......Page 100
3.2 Overview of Bidirectional and Superluminal Spectral Representations......Page 101
3.2.1 Bidirectional Spectral Representation......Page 102
3.2.2 Superluminal Spectral Representation......Page 104
3.3.1 Hybrid Spectral Representation......Page 105
3.3.2 (3 + 1)-Dimensional Focus X-Wave......Page 106
3.3.3 (3 + 1)-Dimensional Finite-Energy X-Shaped Localized Waves......Page 107
3.4.2 (3 + 1)-Dimensional Splash Modes and Focused Pulsed Beams......Page 110
References......Page 114
4.1 Introduction......Page 118
4.2.1 Bessel Beams......Page 120
4.2.4 X-Waves......Page 122
4.2.5 Obtaining Limited-Diffraction Beams with Variable Transformation......Page 123
4.2.6 Limited-Diffraction Solutions to the Klein–Gordon Equation......Page 124
4.2.7 Limited-Diffraction Solutions to the Schrödinger Equation......Page 127
4.2.8 Electromagnetic X-Waves......Page 129
4.2.9 Limited-Diffraction Beams in Confined Spaces......Page 130
4.2.10 X-Wave Transformation......Page 135
4.2.13 Computation with Limited-Diffraction Beams......Page 136
4.3.4 Two-Way Dynamic Focusing......Page 137
4.4 Conclusions......Page 138
References......Page 139
5.1 Introduction......Page 150
5.1.1 Brief Overview of Propagation-Invariant Fields......Page 151
5.1.2 Scope of This Chapter......Page 154
5.2 Rotationally Periodic Waves......Page 155
5.2.2 Special Propagation Symmetries......Page 156
5.2.3 Monochromatic Waves......Page 157
5.2.4 Pulsed Single-Mode Waves......Page 159
5.3 Nondiffracting Waves in Anisotropic Crystals......Page 163
5.3.1 Representation of Anisotropic Nondiffracting Waves......Page 164
5.3.2 Effects Due to Anisotropy......Page 167
5.3.3 Acoustic Generation of NDWs......Page 169
5.3.4 Discussion......Page 170
5.4 Conclusions......Page 171
References......Page 172
6.1 Introduction......Page 180
6.2.1 Bessel Beam Propagation into a Layer: Normal Incidence......Page 181
6.2.2 Oblique Incidence......Page 185
6.3.1 Phase, Group, and Signal Velocity: Scalar Approximation......Page 190
6.3.2 Energy Localization and Energy Velocity: A Vectorial Treatment......Page 193
6.4 Space–Time and Superluminal Propagation......Page 201
References......Page 202
7.1 Introduction......Page 206
7.2 Definition of Localized Waves......Page 207
7.3 The Principle of Optical Generation of LWs......Page 212
7.4 Finite-Energy Approximations of LWs......Page 214
7.5 Physical Nature of Propagation Invariance of Pulsed Wave Fields......Page 216
7.6.1 LWs in Interferometric Experiments......Page 219
7.6.2 Experiment on Optical Bessel X-Pulses......Page 221
7.6.3 Experiment on Optical LWs......Page 224
7.7 Conclusions......Page 232
References......Page 234
8.1 Introduction......Page 238
8.2 Localized and Stationarity Wave Modes Within the SVEA......Page 240
8.2.1 Dispersion Curves Within the SVEA......Page 242
8.2.2 Impulse-Response Wave Modes......Page 243
8.3 Classification of Wave Modes of Finite Bandwidth......Page 245
8.3.1 Phase-Mismatch-Dominated Case: Pulsed Bessel Beam Modes......Page 247
8.3.2 Group-Velocity-Mismatch-Dominated Case: Envelope Focus Wave Modes......Page 248
8.3.3 Group-Velocity-Dispersion-Dominated Case: Envelope X- and Envelope O-Modes......Page 250
8.4 Wave Modes with Ultrabroad Bandwidth......Page 252
8.4.1 Classification of SEWA Dispersion Curves......Page 254
8.5 About the Effective Frequency, Wave Number, and Phase Velocity of Wave Modes......Page 257
8.6 Comparison Between Exact, SEWA, and SVEA Wave Modes......Page 259
References......Page 261
9.1 Introduction......Page 264
9.2 NLX Model......Page 266
9.3 Envelope Linear X-Waves......Page 268
9.3.1 X-Wave Expansion and Finite-Energy Solutions......Page 271
9.4 Conical Emission and X-Wave Instability......Page 273
9.5.1 Some Examples......Page 276
9.5.2 Proof......Page 277
9.6 Numerical Solutions for Nonlinear X-Waves......Page 278
9.6.1 Bestiary of Solutions......Page 280
9.7 Coupled X-Wave Theory......Page 283
9.7.2 Splitting and Replenishment in Kerr Media as a Higher-Order Soliton......Page 285
9.8.2 Nonlinear X-Waves in Quadratic Media......Page 286
9.9 Conclusions......Page 287
References......Page 288
10.1 Introduction......Page 294
10.2 Natural Spatial and Temporal Broadening of Light Waves......Page 296
10.3 Diffraction-Free Optics in the Overwavelength Domain......Page 302
10.4 Diffraction-Free Subwavelength-Beam Optics on a Nanometer Scale......Page 307
Appendix......Page 313
References......Page 314
11.1 Introduction......Page 320
11.2 Small-Angle Bessel-Like Waves and X-Pulses......Page 321
11.3 Self-Reconstruction of Pulsed Bessel-Like X-Waves......Page 324
11.4 Nondiffracting Images......Page 327
11.5 Self-Reconstruction of Truncated Ultrabroadband Bessel–Gauss Beams......Page 328
11.6 Conclusions......Page 331
References......Page 332
12.1 Introduction......Page 336
12.2.1 Basic Equations......Page 338
12.2.2 Localized Waves......Page 340
12.3 Spatiotemporal Wave Localization in Photonic Crystals......Page 345
12.3.1 Wannier Function Technique......Page 346
12.3.2 Undistorted Propagating Waves in Two- and Three-Dimensional Photonic Crystals......Page 350
12.4 Conclusions......Page 355
References......Page 356
13.1 Introduction......Page 360
13.2 Single and Composite Optical Vortices......Page 363
13.3 Basic Concept of Nondiffracting Beams......Page 367
13.4 Energetics of Nondiffracting Vortex Beams......Page 371
13.5 Vortex Arrays and Mixed Vortex Fields......Page 373
13.6 Pseudo-nondiffracting Vortex Fields......Page 375
13.7.1 Fourier Methods......Page 378
13.7.2 Spatial Light Modulation......Page 379
13.8 Applications and Perspectives......Page 382
References......Page 384
INDEX......Page 388
