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Introduction to Singular Correlation Optics
Editor(s): Oleg V. Angelsky
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Book Description

This book mainly concerns the experimental aspects of a rapidly developing area of modern photonics, i.e., the singular optics of partially coherent, partially polarized, and polychromatic light fields. This topic gives rise to both new concepts and experimental tools for laboratory investigation, and considerably extends the possibilities for implementing the singular optics paradigm in solving diverse practical problems ranging from nanoscience to astrophysics.

Book Details

Date Published: 22 January 2019
Pages: 252
ISBN: 9781510622098
Volume: PM295

Table of Contents
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Table of Contents


1 Introduction: From Coherent Singular Optics to Correlation Optics
Oleg V. Angelsky, Steen Grüner Hanson, and Peter V. Polyanskii
1.1 Classical (Coherent) Singular Optics: Applying Solid State Physics to Optics—Wavefront Dislocations
1.2 Problems of Scalar Coherent Singular Optics: Light Fields with Phase Singularities—Control and Diagnostics of their       Parameters
1.3 From Optical Vortices to Coherent Polarization Singularities: Sign Principle of Vector Singular Optics
1.4 Polychromatic Singular Optics
1.5 Forerunners of Correlation Singular Optics
1.6 Organization of the Book

2 Edge Diffraction/Dislocation Wave
Peter V. Polyanskii
2.1 The Concept of the Edge Diffraction Wave
2.2 The Physical Reality and Peculiarities of the Edge Diffraction Wave
2.3 Relevant Studies
2.4 Edge Diffraction for Diagnostics of Phase Singularities in Coherent Optical Fields
2.5 Conclusions on Diffraction Diagnostics of Phase Singularities

3 Spatial Correlation Phase Singularities in Partially Coherent Light Fields
Peter V. Polyanskii and Christina V. Felde
3.1 Methodological Remarks
3.2 Light Beams with a Separable Phase of the Spatial Coherency Function
3.3 Diffraction Diagnostics of the Azimuthal Dependence of a Phase of the Spatial Coherency Function in Combined      Vortex Beams
3.4 Young's Diagnostics of the Ring Singularities of the Complex Degree of Coherency in Combined Vortex Beams
3.5 Feasibility of Implementing Partially Coherent Singular-Optical Traps
3.6 Diffraction Analysis of Edge Dislocations in Combined Beams Assembled from Uncorrelated Hermite–Gaussian Modes

4 Vector Singularities in Partially Polarized Light Fields
Peter V. Polyanskii and Christina V. Felde
4.1 From Completely Coherent to Partially Coherent (Correlation) Singular Optics of Vector Light Fields
4.2 Complex Degree of Polarization
4.3 Representation of U and P Singularities in Stokes Space
4.4 Distribution of the Degree of Polarization in the Vicinities of U and P Singularities in Real Space
4.5 Experimental Determination of U and P Singularity Locations and Reconstruction of the Vector Skeleton of the               Combined Beams

5 Phase Singularities in Polychromatic (White Light) Fields
Oleg V. Angelsky, Peter P. Maksimyak, Peter V. Polyanskii, and Steen Grüner Hanson
5.1 Diffraction Diagnostics of Isolated Polychromatic Vortices and Vortices in Polychromatic Speckle Fields
5.2 Angular Momentum of Temporally Incoherent (Quasi-monochromatic) Optical Fields
5.3 Phase Singularities of the Complex Transmission Coefficient of Moderately Rough Surfaces
5.4 Interferometric and Chromascopic Techniques for Studying Phase Singularities in Polychromatic Light Fields

6 Optics Contamination
Oleg V. Angelsky, Claudia Yu. Zenkova, Steen Grüner Hanson, Bin Guo, and Zhebo Chen
6.1 Initial Approaches to Crystal Singular Optics
6.2 Peculiarities of Propagation of Optical Beams Through Anisotropic Crystals
6.3 Formation of Fine Structure of Optical Singularities in Anisotropic Media with Dichroism and Absorption
6.4 Formation of Optical Quadrupoles in Optical Beams Inclined to the Optic Axis
6.5 Formation of White-Light Vortices in Crystal Singular Optics
6.6 Propagation of Optical Beams in Biaxial Crystals
6.7 Anisotropic Crystals as a Medium for Generating Optical Vortices
6.8 Use of Anisotropic Media for Transforming Singular Beam Polarization

7 Applications of Correlation Singular Optics
Oleg V. Angelsky, Peter P. Maksimyak, Claudia Yu. Zenkova, Steen Grüner Hanson, Bin Guo, and Zhebo Chen
7.1 Introduction
7.2 Use of Phase Singularities of Scalar Optical Speckle Fields for Diagnostics of Rough Surfaces with Large      Inhomogeneities
     7.2.1 Computer simulation of rough surfaces and computing the scattered field
     7.2.2 Phase dislocation lines in an optical field
     7.2.3 Determining the localization of amplitude zeros in a monochromatic field
     7.2.4 Dependence of the number of amplitude zeros in a field scattered by rough surfaces on the interval of              inhomegeneity heights
7.3 Optical Correlation Diagnostics of Strongly Rough Surfaces
     7.3.1 Determining the longitudinal coherence function
     7.3.2 Reconstruction of a rough-surface relief
7.4 Optical Tweezers Based on a Biaxial Crystal
     7.4.1 Generation of phase singularities in polychromatic light
     7.4.2 Formation of optical flows in biaxial crystals
7.5 Optical Vortex Coronagraphy
7.6 Approaches to Optical Vortex Metrology
7.7 Applications of Vortex Optical Beams in Microscopy
     7.7.1 Stimulated emission depletion (STED) microscopy
     7.7.2 Spiral phase contrast imaging
7.8 Looking Ahead
     7.8.1 What will happen in the future?
     7.8.2 The impact of modern technologies
     7.8.3 Fundamentals



Singular optics is among the actively developing and promising areas of modern photonics whose numerous and diverse applications—ranging from microscopy to astrophysics—emerged at the beginning of the third millennium.1 Originating from the depth-of-wave concept,2 singular optics was initially developed within the coherent approximation. Namely, its origins mainly focused on phase singularities (phase indeterminicity) of the complex amplitude of a completely coherent, monochromatic field aexp(iφ). These phase singularities are associated with the field elements (points, lines, and surfaces) where the field amplitude equals zero. The structure-forming role of the set of such elements (i.e., the singular skeleton) is of great importance, as is the set of polarization singularities of EM fields with inhomogeneous polarization,3 such as the elements where the azimuth of polarization or the angle of ellipticity is indeterminate. The location and characteristics of phase singularities (referred to also as amplitude zeros) together with the corresponding sign principles governing formation of the nets of singularities as holistic systems provide the basis for understanding important regularities of the field formation and lay the foundation for key applications of the singular-optics approach.

The mentioned tendency for light fields to be incompletely coherent substantiates the establishment of a distinct domain of singular optics called correlation singular optics, i.e., singular optics of partially coherent, partially polarized, and polychromating light fields, taking into account the definition of correlation optics introduced in the 2007 SPIE Press monograph Optical Correlation Techniques and Applications.5 As is seen it the title, Introduction to Singular Correlation Optics, this new book is devoted solely to the domain of singular optics.

Considerable attention has recently been paid to both the fundamentals6 and the applications7 of singular optics, including the correlation optics domain of this R&D area. The majority of relevant monographs and reviews deal with the theoretical aspects of singular optics approaches, while experimental techniques intrinsic to this field are disseminated among numerous special papers. A distinct feature of this book lies in the authors' endeavors to collect at least some original experimental approaches that will be instructive for understanding and mastering the topic. Taking into account the rapidly increasing maturity of the area of interest, one can expect that the information represented in the book (being an introduction to the topic rather than a summary of its current developments) will be applicable and relevant into the foreseeable future. The book will certainly be a useful complement to modern theoretical textbooks on the subject.

Finally, I would like to thank one of the authors of this monograph, Prof. Peter Polyanskii, who irrevocably left us a few weeks before the publication of this monograph. Prof. Polyanskii was a leader in the field of modern optics who has gained world recognition for his scientific achievements. His research efforts in holographic associative memory, the conception of edge diffraction of Jung–Rubinovich, and singular optics of partially coherent and partially polarized polychromatic optical fields are well known and repeatedly evaluated by different global scientific organizations. The importance of Prof. Polyanskii's scientific results in optics is invaluable to each of us.

Oleg V. Angelsky
Chernivtsi, Ukraine
November 2018

1. M. S. Soskin and M. V. Vasnetsov, "Singular Optics," in Progress in Optics 42, E. Wolf, Ed., North Holland, Amsterdam, pp.     219–276 (2001).
2. J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. Royal Soc. Lond. A 336, 165–190 (1974).
3. J. F. Nye, Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations, Institute of Physics Publishing,     Bristol (1999).
4. M. Born and E. Wolf, Principles of Optics, Seventh Edition (expanded), Cambridge University Press, Cambridge (1999).
5. O. V. Angelsky, Ed., Optical Correlation Techniques and Applications, SPIE Press, Bellingham, Washington (2007) [doi:     10.1117/3.714999].
6. G. J. Gbur, Singular Optics, CRC Press, Boca Raton, Florida (2016).
7. H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, et al., "Roadmap on structured light," J. Opt. 19(1), 013001 (2016).

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