Non-Diffracting Waves -- Title Page -- Copyright -- Contents -- Preface -- List of Contributors -- Chapter 1 Non-Diffracting Waves: An Introduction -- 1.1 A General Introduction -- 1.1.1 A Prologue -- 1.1.2 Preliminary, and Historical, Remarks -- 1.1.3 Definition of Non-Diffracting Wave (NDW) -- 1.1.4 First Examples -- 1.1.5 Further Examples: The Non-Diffracting Solutions -- 1.2 Eliminating Any Backward Components: Totally Forward NDW Pulses -- 1.2.1 Totally Forward Ideal Superluminal NDW Pulses -- 1.3 Totally Forward, Finite-Energy NDW Pulses -- 1.3.1 A General Functional Expression for Whatever Totally-Forward NDW Pulses -- 1.4 Method for the Analytic Description of Truncated Beams -- 1.4.1 The Method -- 1.4.2 Application of the Method to a TB Beam -- 1.5 Subluminal NDWs (or Bullets) -- 1.5.1 A First Method for Constructing Physically Acceptable, Subluminal Non-Diffracting Pulses -- 1.5.2 Examples -- 1.5.3 A Second Method for Constructing Subluminal Non-Diffracting Pulses -- 1.6 ``Stationary'' Solutions with Zero-Speed Envelopes: Frozen Waves -- 1.6.1 A New Approach to the Frozen Waves -- 1.6.2 Frozen Waves in Absorbing Media -- 1.6.3 Experimental Production of the Frozen Waves -- 1.7 On the Role of Special Relativity and of Lorentz Transformations -- 1.8 Non-Axially Symmetric Solutions: The Case of Higher-Order Bessel Beams -- 1.9 An Application to Biomedical Optics: NDWs and the GLMT (Generalized Lorenz-Mie Theory) -- 1.10 Soliton-Like Solutions to the Ordinary Schroedinger Equation within Standard Quantum Mechanics (QM) -- 1.10.1 Bessel Beams as Non-Diffracting Solutions (NDS) to the Schroedinger Equation -- 1.10.2 Exact Non-Diffracting Solutions to the Schroedinger Equation -- 1.10.3 A General Exact Localized Solution -- 1.11 A Brief Mention of Further Topics -- 1.11.1 Airy and Airy-Type Waves.

1.11.2 ``Soliton-Like'' Solutions to the Einstein Equations of General Relativity and Gravitational Waves -- 1.11.3 Super-Resolution -- Acknowledgments -- References -- Chapter 2 Localized Waves: Historical and Personal Perspectives -- 2.1 The Beginnings: Focused Wave Modes -- 2.2 The Initial Surge and Nomenclature -- 2.3 Strategic Defense Initiative (SDI) Interest -- 2.4 Reflective Moments -- 2.5 Controversy and Scrutiny -- 2.6 Experiments -- 2.7 What's in a Name: Localized Waves -- 2.8 Arizona Era -- 2.9 Retrospective -- Acknowledgments -- References -- Chapter 3 Applications of Propagation Invariant Light Fields -- 3.1 Introduction -- 3.2 What Is a ``Non-Diffracting'' Light Mode? -- 3.2.1 Linearly Propagating ``Non-Diffracting'' Beams -- 3.2.2 Accelerating ``Non-Diffracting'' Beams -- 3.2.3 Self-Healing Properties and Infinite Energy -- 3.2.4 Vectorial ``Non-Diffracting'' Beams -- 3.3 Generating ``Non-Diffracting'' Light Fields -- 3.3.1 Bessel and Mathieu Beam Generation -- 3.3.2 Airy Beam Generation -- 3.4 Experimental Applications of Propagation Invariant Light Modes -- 3.4.1 Microscopy, Coherence, and Imaging -- 3.4.2 Optical Micromanipulation with Propagation Invariant Fields -- 3.4.3 Propagation Invariant Beams for Cell Nanosurgery -- 3.5 Conclusion -- Acknowledgment -- References -- Chapter 4 X-Type Waves in Ultrafast Optics -- 4.1 Introduction -- 4.2 About Physics of Superluminal and Subluminal, Accelerating and Decelerating Pulses -- 4.2.1 Remarks on Some Persistent Issues -- 4.2.1.1 Group Velocity: Plane Waves versus Three-Dimensional Waves -- 4.2.1.2 Group Velocity: Superluminal versus Subluminal Cylindrically Symmetric Wavepackets -- 4.2.1.3 Group Velocity versus Energy Transport Velocity -- 4.2.1.4 Group Velocity versus Signal Velocity.

4.2.1.5 Cherenkov Radiation versus Superluminal X-Type Waves and Causality versus Acausality -- 4.2.2 Accelerating and Decelerating Quasi-Bessel-X Pulses -- 4.2.3 ``Technology Transfer'' to Quantum Optics -- 4.3 Overview of Spatiotemporal Measurements of Localized Waves by SEA TADPOLE Technique -- 4.3.1 Spatiotemporal Measurement of Light Fields -- 4.3.2 New Results on Bessel-X Pulse -- 4.3.3 Grating-Generated Bessel Pulses -- 4.3.4 Lens-Generated Accelerating and Decelerating Quasi-Bessel-X Pulses -- 4.3.5 Boundary Diffraction Wave as a Decelerating Quasi-Bessel-X Pulse -- 4.4 Conclusion -- Acknowledgments -- References -- Chapter 5 Limited-Diffraction Beams for High-Frame-Rate Imaging -- 5.1 Introduction -- 5.2 Theory of Limited-Diffraction Beams -- 5.2.1 Generalized Solutions to Wave Equation -- 5.2.2 Bessel Beams and X Waves -- 5.2.2.1 Bessel Beams -- 5.2.2.2 X Waves -- 5.2.3 Limited-Diffraction Array Beams -- 5.3 Received Signals -- 5.3.1 Pulse-Echo Signals and Relationship with Imaging -- 5.3.2 Limited-Diffraction Array Beam Aperture Weighting and Spatial Fourier Transform of Echo Signals -- 5.3.3 Special Case for 2D Imaging -- 5.4 Imaging with Limited-Diffraction Beams -- 5.4.1 High-Frame-Rate Imaging Methods -- 5.4.1.1 Plane-Wave HFR Imaging without Steering -- 5.4.1.2 Steered Plane-Wave Imaging -- 5.4.1.3 Limited-Diffraction Array Beam Imaging -- 5.4.2 Other Imaging Methods -- 5.4.2.1 Two-Way Dynamic Focusing -- 5.4.2.2 Multiple Steered Plane Wave Imaging -- 5.5 Mapping between Fourier Domains -- 5.5.1 Mapping for Steer Plane Wave Imaging -- 5.5.2 Mapping for Limited-Diffraction-Beam Imaging -- 5.5.2.1 General Case -- 5.5.2.2 Special Case -- 5.6 High-Frame-Rate Imaging Techniques-Their Improvements and Applications.

5.6.1 Aperture Weighting with Square Functions to Simplify Imaging System -- 5.6.1.1 Applied to Transmission -- 5.6.1.2 Applied to Reception -- 5.6.2 Diverging Beams with a Planar Array Transducer to Increase Image Frame Rate -- 5.6.3 Diverging Beams with a Curved Array Transducer to Increase Image Field of View -- 5.6.4 Other Studies on Increasing Image Field of View -- 5.6.5 Coherent and Incoherent Superposition to Enhance Images and Increase Image Field of View -- 5.6.6 Nonlinear Image Processing for Speckle Reduction -- 5.6.7 Coordinate Rotation for Reduction of Computation -- 5.6.8 Reducing Number of Elements of Array Transducer -- 5.6.9 A Study of Trade-Off between Image Quality and Data\hb Densification -- 5.6.10 Masking Method for Improving Image Quality -- 5.6.11 Reducing Clutter Noise by High-Pass Filtering -- 5.6.12 Obtaining Flow or Tissue Velocity Vectors for Functional Imaging -- 5.6.13 Strain and Strain Rate Imaging to Obtain Tissue Parameters\hb or Organ Functions -- 5.6.14 High-Frame-Rate Imaging Systems -- 5.7 Conclusion -- References -- Chapter 6 Spatiotemporally Localized Null Electromagnetic Waves -- 6.1 Introduction -- 6.2 Three Classes of Progressive Solutions to the 3D Scalar Wave Equation -- 6.2.1 Luminal Localized Waves -- 6.2.1.1 Luminal -- 6.2.1.2 Modified Luminal -- 6.2.2 Superluminal Localized Waves -- 6.2.2.1 Superluminal -- 6.2.2.2 Hybrid Superluminal -- 6.2.2.3 Modified Hybrid Superluminal -- 6.2.3 Subluminal Localized Waves -- 6.3 Construction of Null Electromagnetic Localized Waves -- 6.3.1 Riemann-Silberstein Vector -- 6.3.2 Null Riemann-Silberstein Vector -- 6.3.3 The Whittaker-Bateman Method -- 6.4 Illustrative Examples of Spatiotemporally Localized Null Electromagnetic Waves -- 6.4.1 Luminal Null Electromagnetic Localized Waves -- 6.4.2 Modified Luminal Null Electromagnetic Localized Waves.

6.4.3 Superluminal Null Electromagnetic Localized Waves -- 6.4.4 Hybrid Superluminal Null Electromagnetic Localized Waves -- 6.4.5 Modified Hybrid Superluminal Null Electromagnetic Localized Waves -- 6.4.6 A Note on Subluminal Null Electromagnetic Localized Waves -- 6.5 Concluding Remarks -- References -- Chapter 7 Linearly Traveling and Accelerating Localized Wave Solutions to the Schr"odinger and Schr"odinger-Like Equations -- 7.1 Introduction -- 7.2 Linearly Traveling Localized Wave Solutions to the 3D Schr"odinger Equation -- 7.2.1 MacKinnon-Type, Infinite-Energy, Localized, Traveling Wave Solutions -- 7.2.2 Extensions to MacKinnon-Type, Infinite-Energy, Localized, Traveling Wave Solutions -- 7.2.3 Finite-Energy, Localized, Traveling Wave Solutions -- 7.3 Accelerating Localized Wave Solutions to the 3D Schr"odinger Equation -- 7.4 Linearly Traveling and Accelerating Localized Wave Solutions to Schr"odinger-Like Equations -- 7.4.1 Anomalous Dispersion -- 7.4.1.1 Linearly Traveling Localized Wave Solutions -- 7.4.1.2 Accelerating Localized Wave Solutions -- 7.4.2 Normal Dispersion -- 7.4.2.1 Linearly Traveling X-Shaped Localized Waves -- 7.4.2.2 Accelerating Localized Waves -- 7.5 Concluding Remarks -- References -- Chapter 8 Rogue X-Waves -- 8.1 Introduction -- 8.2 Ultrashort Laser Pulse Filamentation -- 8.3 The X-Wave Model -- 8.4 Rogue X-Waves -- 8.5 Conclusions -- Acknowledgments -- References -- Chapter 9 Quantum X-Waves and Applications in Nonlinear Optics -- 9.1 Introduction -- 9.2 Derivation of the Paraxial Equations -- 9.3 The X-Wave Transform and X-Wave Expansion -- 9.4 Quantization -- 9.5 Optical Parametric Amplification -- 9.6 Kerr Media -- 9.7 Conclusions -- Acknowledgments -- References -- Chapter 10 TE and TM Optical Localized Beams -- 10.1 Introduction -- 10.2 TE Optical Beams -- 10.2.1 We First Suppose krr ≤ 1.

10.2.2 We Now Suppose krr > 1.