Contents
Contributors
Preface

1. Multilayer Mirrors for Attosecond Pulses

1.1. Introduction
1.1.1. Attosecond Pulses (Isolated and Pulse Trains)
1.1.2. HHG as Major/Only Attosecond Pulse Source
1.1.3. What Is It Good for? The Applications
1.2. Reflective Optics in the EUV/Soft X-Ray Range
1.2.1. Interaction of Radiation with Matter
1.2.2. Single Interface Reflectance (and Transmission)
1.2.3. Multilayer Mirrors
1.2.3.1. Principal of Multilayer Mirrors
1.2.3.2. Periodic and Aperiodic Multilayer Systems
1.2.3.3. Imperfect Interfaces
1.3. Simulations of Multilayer Systems - Their Theoretical Optical Performance
1.4. Fabrication of Multilayer Coatings
1.5. Achieved Results and Examples for Attosecond Multilayer Mirrors
1.5.1. A Normal Incidence Broadband 30-60 eV Mirror
1.5.2. Short Pulses in the 60 100 eV Range
1.5.3. Above the Silicon L-Edge in the 100 eV – 150 eV Photon Range
1.5.3.1. Attosecond Dispersion Control by Multilayer Mirrors above 100 eV
1.5.3.2. Chromium/Scandium Multilayer Mirror for Attosecond Pulses at 145 eV
1.5.4. Multilayer Mirrors for Attosecond Pulses in the Water Window Soft X-Ray Range
1.5.4.1. Aperiodic Multilayer Mirrors
1.6. Metrology and Application
1.6.1. Streaking Measurements
1.6.2. Transient Absorption Measurements
1.6.3. The RABBITT Technique
1.7. Outlook
1.7.1. The Way Toward Ever Shorter Pulses - Approaching the Atomic Unit of Time
1.7.2. Multilayer Mirrors for HHG Photon Energies up to the keV Spectral Range
1.8. Conclusions
Acknowledgements
References

2. Moiré Effect in 3D Structures

2.1. Introduction
2.2. Moiré Effect around Us
2.3. Plain Coplanar Case
2.3.1. Projected Mesh
2.3.2. Moiré Wavevector
2.3.3. Spectral Trajectories
2.4. Moiré in Regular 3D Bodies
2.4.1. Parallelepiped (Parallel Planes)
2.4.2. Prism (Wedge)
2.4.3. Cylinder
2.5. Interesting Moiré Issues
2.5.1. Moiré Statistics
2.5.2. Moiré Lens
2.5.3. Square and Octagon
2.6. Conclusion
References

3. Numerical Method for Diffraction by Multilayered Dielectric Gratings Using Scattering Factors

3.1. Introduction
3.2. Matrix Eigenvalues Method
3.3. Application of Shadow Theory to All Regions
3.3.1. In the Case of Uniform Regions
3.3.2. In the Case of Periodic Regions
3.4. An Excitation Source and Boundary Conditions
3.5. Diffraction Efficiencies and Optical Theorem
3.6. Analysis of Low Grazing Scattering by Dielectric Gratings
3.7. Analysis of Eigenvalues Degeneracy in the Middle Region
3.8. Conclusions
References

4. An Alternative Model of the Spatial Light Intensity Distribution

4.1. Introduction
4.2. Motivation and Related Previous Work
4.3. Mathematical Model
4.4. Experiment – a Comparison of Two Error Measures
4.4.1. The Algorithms Used in Previous Studies
4.4.2. The Algorithms IF-RMS and IF-MAX
4.4.3. Setup
4.4.4. Results
4.5. Conclusion
References

5. Optical Beams in Linear and Nonlinear Media

5.1. Introduction
5.2. Nonparaxial Beams in Linear Media
5.2.1. Nonparaxial Radially Polarized Beams
5.2.2. Nonparaxial Elegant Hermite-Laguerre Gaussian Beams
5.2.3. Nonparaxial Pearcey Gaussian Beams
5.2.4. Nonparaxial Parabolic Rotational Coordinate Beams
5.3. Paraxial Beams in Nonlocal Nonlinear Media
5.3.1. Ince-Gaussian Breathers and Solitons
5.3.2. Complex Variable Function Breathers and Solitons
5.4. Conclusions
Acknowledgements
References

6. Incoherently Coupled Soliton Families in Photorefractive Media

6.1. Introduction
6.2. Theoretical Model
6.2.1. Dynamical Evolution Equation for Soliton families in Centrosymmetric Photorefractive Material
6.2.2. Modulation Instability
6.2.3. Dynamical Evolution Equation for Soliton Pairs in aPyroelectric Photorefractive Material
6.3. Discussion
6.3.1. Coupled Solitons in Centrosymmetric Photorefractive Material
6.3.1.1. Dark-Dark Soliton Pair
6.3.1.2. Bright-Bright Soliton Pair
6.3.1.3. Grey-Grey Soliton Pair
6.3.1.4.2N-Component Dark Solitons
6.3.1.5.2N-Component Bright Solitons
6.3.1.6. N Component Grey Solitons
6.3.1.7. Modulation Instability
6.3.2. Coupled Solitons in Pyroelectric Photorefractive Materials
6.3.2.1. Bright Soliton Pair
6.3.2.2. Dark Soliton Pair
6.3.2.3. Grey Soliton Pair
6.3.3. Bright-Dark Soliton Pair
6.3.4. Observation of Separate Components of Incoherently Coupled Solitons
6.4. Conclusions
Acknowledgement
References

7. Vectorial Complex Ray Model for Light Scattering of Nonspherical Particles

7.1. Introduction
7.2. Fundamentals of Geometrical Optics
7.2.1. Snell Laws and Fresnel Formulas
7.2.2. Light Scattering by a Sphere and a Circular Cylinder
7.2.2.1. Deviation of Rays on Particle Surface
7.2.2.2. Amplitudes of Reflected and Refracted Rays
7.2.2.3. Phases of Rays
7.2.2.4. Scattering of an Infinite Circular Cylinder
7.2.2.5. Scattering of a Sphere
7.2.3. Comparison of Scattering Diagrams with Lorenz - Mie Theory
7.3. Vectorial Complex Ray Model
7.3.1. Snell Law and Fresnel Formulas in Vector Form
7.3.2. Wave Front Equation
7.3.3. Amplitude and Phase of a Ray
7.3.3.1. Amplitude
7.3.3.2. Phase
7.3.4. Simple Applications of the Wave Front Equation
7.3.4.1. Image Formation by a Plane Diopter
7.3.4.2. Image Formation by a Spherical Diopter
7.3.4.3. Divergence Factor of a Circular Cylinder
7.3.4.4. Divergence Factor of a Sphere
7.4. Applications of VCRM in Light Scattering
7.4.1. Revisit of Airy Theory in Term of VCRM
7.4.2. Scattering by an Elliptical Cylinder
7.4.3. Scattering of the Plane Wave by an Ellipsoidal Particle
7.4.4. Software VCRMEll2D
7.4.5. Hyperbolic Umbilic Foci of an Oblate Particle and Experimental Validation
7.4.6. Dependence of Two Rainbow Intensity Ratio on the Aspect Ratio of a Prolate Particle
7.5. Conclusions
Acknowledgements
References

8. Magneto-Optical Effects Arising from Coupling of Magnetic and Dielectric Properties for Colloidal Particle System

8.1. Introduction
8.2. Theoretical Framework
8.2.1. Origin of Magneto-Optical Effects for Colloidal Particle System
8.2.2. Magneto-Dielectric Properties of Crystals and Colloids
8.2.3. Magneto-Optical Birefringence and Dichroism in Colloids
8.3. Experiment Description and Results
8.3.1. Sample Description
8.3.2. The Optical Experiments and Results
8.3.2.1. The Optical Effect of Light Beam Perpendicular to Magnetic Field
8.3.2.2. The Optical Effect of Light Beam Parallel to Magnetic Field
8.4. Conclusions
Acknowledgement
References

9. General Overview of Coherent X-Ray Diffraction Imaging and Ptychography and Their Developments and Applications

9.1. Coherent X-Ray Diffraction Imaging
9.1.1. Overview and Introduction
9.1.2. Bragg CXDI
9.2. Ptychography
9.2.1. Overview and Introduction
9.2.2. Forward Ptychography
9.2.3. Bragg Ptychography
9.2.3.1. Bragg Ptychography on Single Crystals
9.2.3.2. Bragg Ptychography on Thin Film Phase Domains
9.2.4. Partial Coherence and Multimodes in CXDI Diffraction Imaging
9.2.4.1. Transverse Partial Coherence
9.2.4.2. Longitudinal Partial Coherence
9.2.5. Resolution Limit and Inverse 4^th Power Law (Flux and Resolution)
9.3. Future Developments Aspects of Single-Shot Coherent Diffraction Imaging
9.3.1. Diffract-and-Destroy Serial Femtosecond Nanocrystallography in 4^th Generation Free Electron Laser Facilities
9.3.2. Single-Shot Coherent Modulation Imaging (CMI) for Materials Sciences Application
9.4. Conclusion and Future Outlooks
Acknowledgements
References

10. The Optical Anderson Localization in Three-Dimensional Percolation System

10.1. Introduction
10.2. Basic Equations
10.3. Lasing in Percolating System with Incorporated Emitters
10.3.1. The Case of Small Time
10.3.2. Numerical 3D Simulations
10.4. Condition of Optical Localization in Percolating System
10.5. Inverse Participation Ratio
10.6. Localization for Large Time
10.7. Discussion
10.8. Conclusions
References

11. A Highly Directional Supercontinuum in the Visible upon Filamentation in Air

11.1. Introduction
11.2. Experimental Setup and Research Methods
11.3. Experimental Results and Discussion
11.4. Conclusion
References

12. Study of Third-Harmonic Generation at Interfaces Taking into Account the Contribution of Self-Focusing Effect

12.1. Introduction
12.2. Basic Theory of Nonlinear Polarization and Nonlinear Refractive Index
12.3. THG under Influence of SF Effect
12.4. THG at Optical Glasses Interfaces
12.4.1. Experiments
12.4.2. Results and Discussion
12.5. THG at the Interfaces of a Cuvette Filled with Organic Solvents
12.5.1. Experiments
12.5.2. Results and Discussion
12.6. THG at Organic Solvents Interfaces as a Function of Pulse Duration
12.6.1. Result and Discussion
12.7. Conclusions
Acknowledgements
References

13. Transformations and Evolution of Phase Singularities in Diffracted Optical Vortices

13.1. Introduction
13.2. Experimental Setup
13.3. Description of the Diffraction Model
13.3.1. General Principles of the Singular Skeleton Analysis
13.3.2. Description of the Incident OV Beams
13.3.3. Migration of Singularities in the Diffracted OV Beams: Experimental Data Compared with Theory
13.4. Mathematical Model of the Singular Skeleton Evolution in Diffracted OV Beams
13.4.1. Asymptotic Analytical Model
13.4.2. Refined Analytical Model
13.5. Theoretical Study of the OV Migration: LG Beams
13.5.1. OV Displacements: Incident Beam with Plane Wavefront
13.5.2. OV Displacements: Incident Beam with Spherical Wavefront
13.5.3. Incident LG Beam with the Second-Order OV
13.6. Discontinuities of the OV Trajectories and Topological Reactions
in the Diffracted OV Beams
13.6.1. The ‘Jump’ Description: Kummer Beams
13.6.2. Discontinuities in the Laguerre-Gaussian Beams’ Diffraction
13.7. OV Jumps in the z-Dependent Singular Skeleton Evolution
13.7.1. Kummer Beams
13.7.2. Laguerre-Gaussian Beams
13.7.3. 3D Trajectories and the Nature of Discontinuities
13.8. Conclusion
Acknowledgements
References
Appendix

14. Wavefront Reconstruction with Rotational Fields

14.1. Introduction
14.2. Theoretical Framework
14.2.1. Two-Dimensional Signal Processing
14.2.2. Tree Structure and Two-Dimensional Quadrature Mirror Filters
14.2.3. Wavelets in Tree Structure and Factoring Wavelets
14.2.4. Relationship of Wavelets to Shack-Hartmann Measurements
14.3. Phase Reconstruction Algorithm
14.3.1. Iteration for Level 1
14.3.2. Iteration for Level 2
14.3.3. Further Iterations
14.3.4. Setting the Mean and Waffle Values
14.3.5. Synthesis Section
14.4. Rotational Phase Fields
14.4.1. Continuous Vector Fields
14.4.2. Discrete Vector Fields
14.5. Conclusion
References
Appendix. Further Proof Details
A. High-Order Wavelet Simplification Proof
B. Iteration for Level k
C. Branch Point Boundary Condition Proof

15. Fresnel Nearfield Space-Grating Optics in the Human Retina Explains Human Color and Dimlight Vision

15.1. The Gap in the Physics of Colors
15.2. Human Color and Dimlight Vision
15.3. What a Space Grating Optical Explanation of Vision Ought to be Able to Achieve
15.4. The Development of the Cortical Retina to Become a Three-Layered Cell Body Grating
15.5. The Layered Processing of Information in the Cortical Visual Centers
15.6. The Calculation of the Achievements of the ONL Space Grating of the Retina
15.7. The Space Grating Optical Explanation of the Purkinje-Shift: RG(B) in Dimlight Vision
15.8. The Space Grating Chromatic Adaptivity in Daylight Vision
15.9. The Aperture Angle of the Light Cones of the Diffracted Light
15.10. The Retinal Space Grating Becomes a ‘Living Crystal’
15.11. The Individual and the Whole: The Relativization of Color of the Local on to the Color of the Global
15.12. Summary and Outlook
References

16. Characteristics of Unbalanced Mach-Zehnder Interferometers in Metal/Insulator/Metal Plasmonic Waveguides

16.1. Introduction
16.2. Design and Analysis of the Unbalanced MZI
16.3. Fabrication and Experimental Results in Straight MIM PWGs
16.4. Fabrication and Experimental Results in MZI Based on MIM PWGs
16.5. Conclusion
References

17. Stable Solitons of Higher Order Cubic Quintic Nonlinear Schrödinger Equation with a PT-Symmetric Potential

17.1. Introduction
17.2. PT-Symmetric Optical Lattices
17.3. Numerical Solution of Higher Order (1+1)D CQNLS Equation
17.4. Linear Stability Analysis via Linear Spectrum
17.5. Nonlinear Stability Analysis
17.6. Cubic Nonlinear Schrödinger Equation with Fourth Order Dispersion
17.7. Cubic Quintic Nonlinear Schrödinger Equation with Fourth Order Dispersion
17.8. Conclusion
References

Index