Localized WavesISBN: 9780470108857
369 pages
February 2008

Localized waves—also known as nondiffractive waves—are beams and pulses capable of resisting diffraction and dispersion over long distances even in nonguiding 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 wellbalanced 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 waves

Explores the interconnections of the subject with other technologies and scientific areas

Analyzes the effect of arbitrary anisotropies on both continuouswave and pulsed nondiffracting fields

Describes the physical nature and experimental implementation of localized waves

Provides a general overview of wave localization, for example in photonic crystals, which have received increasing attention in recent years
Localized 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 freespace communications, while also serving as a requisite text for graduate students.
1.1 A General Introduction.
1.1.1 Preliminary Remarks.
1.2 A More Detailed Introduction.
1.2.1 The Localized Solutions.
1.3 A Historical (Theoretical and Experimental) Perspective.
1.3.1 Introduction.
1.3.2 Historical Recollections: Theory.
1.3.2.1 The Particular XShaped Field Associated With a Superluminal Charge.
1.3.3 A Glance at the Experimental StateOfTheArt.
References.
2. Structure of The Nondiffracting Waves And Some Interesting Applications (Michel ZamboniRached, Erasmo Recami, and Hugo E. HernándezFigueroa).
2.1 Introduction.
2.2 Spectral Structure of The Localized Waves And The Generalized Bidirectional Decomposition.
2.2.1 The Generalized Bidirectional Decomposition.
2.2.1.1 Closed Analytical Expressions Describing Some Ideal Nondiffracting Pulses.
2.2.1.2 Finite Energy Nondiffracting Pulses.
2.3 SpaceTime Focusing Of XShaped Pulses.
2.3.1 Focusing Effects By Using Ordinary XWaves.
2.4 Chirped Optical XType Pulses In Material Media.
2.4.1 An Example: Chirped Optical XTyped Pulse In Bulk Fused Silica.
2.5 Modeling The Shape Of Stationary Wave Fields: Frozen.
Waves.
2.5.1 Stationary Wave Fields With Arbitrary Longitudinal Shape In Lossless Media, Obtained By Superposing EqualFrequency Bessel Beams.
2.5.1.1 Increasing The Control On The Transverse Shape By Using HigherOrder Bessel Beams.
2.5.2 Stationary Wave Fields With Arbitrary Longitudinal Shape In Absorbing Media: Extending The Method.
2.5.2.1 Some Examples.
References.
3. Two Hybrid Spectral Representations and Their Applications To The Derivations Of Finite Energy Localized Waves And Pulsed Beams (Ioannis M. Besieris and Amr M. Shaarawi).
3.1 Introduction.
3.2 An Overview Of The Bidirectional And Superluminal.
Spectral Representations.
3.2.1 The Bidirectional Spectral Representation.
3.2.2 Superluminal Spectral Representation.
3.3 The Hybrid Spectral Representation And Its Application To.
The Derivation Of Finite Energy XShaped Localized Waves.
3.3.1 The Hybrid Spectral Representation.
3.3.2 (3+1)D Focus X Wave.
3.3.3 (3+1)D FiniteEnergy XShaped Localized Waves.
3.4 Modified Hybrid Spectral Representation And Its.
Application To The Derivation Of FiniteEnergy Pulsed Beams.
3.4.1 The Modified Hybrid Spectral Representation.
3.4.2 (3+1)D Splash Modes And Focused Pulsed Beams.
3.5 Conclusions.
References.
4. Ultrasonic Imaging With LimitedDiffraction Beams (Jianyu Lu).
4.1 INTRODUCTION.
4.2 Fundamentals Of Limited Diffraction Beams.
4.3 Applications Of Limited Diffraction Beams.
4.4 Conclusion.
References.
5. PropagationInvariant Fields: Rotationally Periodic And Anisotropic Nondiffracting Waves (Janne Salo And Ari T. Fribergÿ).
5.1 Introduction.
5.1.1 Brief Overview Of PropagationInvariant Fields.
5.1.2 Scope Of This Article.
5.2 Rotationally Periodic Waves.
5.2.1 Fourier Representation of general RPWs.
5.2.2 Special propagation symmetries.
5.2.3 Monochromatic waves.
5.2.4 Pulsed singlemode waves.
5.2.4.1 Superluminal singlemode wave.
5.2.4.2 Subluminal singlemode wave.
5.2.4.3 Luminal singlemode wave.
5.2.5 Discussion.
5.3 Nondiffracting Waves In Anisotropic
5.3.1 Representation Of Anisotropic Nondiffracting Waves.
5.3.2 Effects due to anisotropy.
5.3.3 Acoustic generation of NDWs.
5.3.4 Discussion.
5.4 CONCLUSIONS.
References.
6. BesselX Waves Propagation (Daniela Mugnai and
1.1 Introduction.
1.2 Optical Tunneling: Frustrated Total Reflection.
1.2.1 Bessel beam propagation into a layer: normal incidence.
1.2.1.1 Scalar treatment.
1.2.1.2 A vectorial approach.
1.2.2 Oblique incidence.
1.3 Free Propagation.
1.3.1 Phase, group, and signal velocity: scalar approximation.
1.3.2 Energy localization and energy velocity: a vectorial treatment.
1.3.2.1 A first approach.
1.3.2.2 Another, more rigorous, treatment of the problem.
1.4 SpaceTime And Superluminal Propagation References.
7. LinearOptical Generation Of Localized Waves (Kaido Reivelt and Peeter Saari).
7.1 Introduction.
7.2 On Definition Of LW's.
7.3 The Principle Of Optical Generation Of LW's.
7.4 Finite Energy Approximations Of LW's.
7.5 On The Physical Nature Of PropagationInvariance Of Pulsed Wave Fields.
7.6 THE EXPERIMENTS.
7.6.1 LW's in interferometric experiments.
7.6.2 Experiment on optical BesselX pulses.
7.6.2.1 Setup.
7.6.2.2 Results of the experiment.
7.6.3 Experiment on optical LW's.
7.6.3.2 Setup.
7.6.3.3 Results of the experiment.
7.7 Concluding Remarks.
References.
8. Optical WaveModes: Localized And PropagationInvariant WavePackets In Optically Transparent, Dispersive Media (Miguel A. Porras, Paolo Di Trapani, and Wei Hu).
8.1 Introduction.
8.2 Localized And Stationary WaveModes Within The Svea.
8.2.1 Dispersion Curves Within The Svea.
8.2.2 ImpulseResponse WaveModes.
8.3 Classification Of WaveModes Of Finite Bandwidth.
8.3.1 PhaseMismatchDominated Case: Pulsed Bessel Beam Type Modes.
8.3.2 GroupVelocityMismatchDominated Case: Envelope Focus Wave Modes.
8.3.3 GroupVelocityDispersionDominated Case: Envelope X And Envelope O Type Modes.
8.3.3.1 Normal Group Velocity Dispersion: Envelope X Waves.
8.3.3.2 Anomalous Group Velocity Dispersion: Envelope O Waves.
8.4 WaveModes With UltraBroad Bandwidth.
8.4.1 Classification of SEWA dispersion curves.
8.4.1.1 Distorted Xlike and Olike wavemodes.
8.4.1.2 Fishlike and singlebranch wavemodes.
8.5 About The Effective Frequency, Wave Number And Phase.
Velocity Of WaveModes.
8.6 Comparison Between Exact, Sewa And Svea WaveModes.
8.7 Conclusion.
References.
9. Nonlinear X Waves(Claudio Conti and Stefano Trillo).
9.1 Introduction.
9.2 The NLX Model.
9.3 Envelope Linear XWaves.
9.3.1 XWave Expansion And Finite Energy Solutions.
9.4 Conical Emission And XWave Instability.
9.5 The Nonlinear XWave Expansion.
9.5.1 Some Examples.
9.5.2 Proof.
9.5.3 Evidences.
9.6 Numerical Solutions For Nonlinear XWaves.
9.6.1 Bestiary Of Solutions.
9.7 Coupled XWave Theory.
9.7.1 Fundamental XWave/Fundamental Solution.
9.7.2 Splitting And Replenishment In Kerr Media As An Higher Order Solution.
9.8 A Brief Review Of Experiments.
9.8.1 Angular dispersion.
9.8.2 Nonlinear Xwaves in Quadratic media.
9.8.3 Xwaves in selffocusing of ultrashort pulses in Kerr media.
9.9 Conclusions And Developments.
References.
10. DiffractionFree SubwavelengthBeam Optics On Nanometer Scale (Sergei V. Kukhlevsky).
10.1 Introduction.
10.2 Natural Spatial And Temporal Broadening Of Light Waves.
10.3 DiffractionFree Optics In The Overwavelength Domain.
10.4 DiffractionFree SubwavelengthBeam Optics At.
Nanometer Scale.
10.5 Summary And Conclusions.
Appendix.
References.
11. SelfReconstruction Of Pulsed Optical XWaves (Ruediger Grunwald, Uwe Neumann, Uwe Griebner, Günter Steinmeyer, Gero Stibenz, Martin Bock, and Volker Kebbel).
11.1 Introduction.
11.2 SmallAngle BesselLike Waves And XPulses.
11.3 SelfReconstruction Of Pulsed BesselLike XWaves.
11.4 Nondiffracting Images.
11.5 Self Reconstruction Of Truncated Ultrabroadband BesselGauss Beams.
11.6 Concluding Remarks.
References.
12. Localization And Wannier Wave Packets In Photonic
12.1 Introduction.
12.2 Diffraction And Localization Of Monochromatic Waves In.
Photonic
12.2.1 Basic Equations.
12.2.2 Localized Waves.
12.3 SpatioTemporal Wave Localization In Photonic
12.3.1 Wannier Function Technique.
12.3.2 Undistorted Propagating Waves In 2d And 3d Photonic
12.4 Conclusions.
References.
13. Spatially Localized Vortex Structures (Zdenek Bouchal, Radek Celechovsky and Grover A. Swartslander).
13.1 Introduction.
13.2 Single And Composite Optical Vortices.
13.3 Basic Concepts Of Nondiffracting Beams.
13.4 Energetics Of Nondiffracting Vortex Beams.
13.5 Vortex Arrays And Mixed Vortex Fields.
13.6 PseudoNondiffracting Vortex Fields.
13.7 Experiments.
13.8 Applications And Perspectives.
References.
Hugo E. HernÁNdezFigueroa, PhD, is a Full Professor in the School of Electrical and Computer Engineering of the State University of Campinas (UNICAMP), Brazil. He is a Senior Member of the IEEE, an Associate Editor of the IEEE/OSA Journal of Lightwave Technology, and a Member of the Editorial Board of the IEEE Transactions on Microwave Theory and Techniques. His research interests concentrate on a wide variety of wave electromagnetics phenomena and applications mainly in photonics and microwaves.
Michel ZamboniRached, PhD, is a Professor in the Centro de Ci?ncias Naturais e Humanas, Universidade Federal do ABC, Brazil. His research interests are electromagnetic field theory, theory and applications of localized waves (in electromagnetism, acoustics, and wave mechanics), optics, optical communications, and some topics in theoretical physics.
Erasmo Recami, PhD, has been a Professor of Physics (currently at Bergamo State University, Italy) for the past forty years. His current research includes the structure of leptons, tunneling times, the application of the GR methods to strong interactions, extended SR, and, in particular, the superluminal group velocities associated with evanescent waves and with the localized solutions to Maxwell's equations.
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