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Singular optics. (English) Zbl 1379.78001

Series in Optics and Optoelectronics. Boca Raton, FL: CRC Press (ISBN 978-1-4665-8077-0/hbk; 978-1-315-37426-0/ebook). xviii, 545 p. (2017).
This book focuses on the various forms of wavefields singularities, excluding the singularities that appear in ray optics, namely “the bright regions where many rays intersect, known as optical caustics” (Preface, p. xvii). It highlights how singular optics describes wave properties from its null regions versus the traditional optics that focuses on the shape and structure of the nonzero portions of the wavefield. The book is intended to both advanced undergraduate as well as beginning graduate students in physics and optics. A working knowledge of electromagnetic and scalar waves is somewhat essential. The book assumes familiarity of complex analysis and mathematical analysis. In detail, the book is divided into twelve chapters. Each chapter finalizes with some exercises.
Chapter 1 (Introduction: Vortices in nature) outlines the exposition of the book.
Chapter 2 (Anatomy of a vortex beam) begins by introducing the adopted approximations in the Maxwell equations for the fields, namely (1) in vacuum, (2) in the absence of sources, (3) that are monochromatic, (4) whose polarization effects can be neglected, and (5) that are paraxial. Then, the characteristics of such beams are addressed. A first list covers a number of general properties of wavefields, vortices, and other singularities. This chapter ends by deriving the Gaussian beam solutions and also the completely shape-invariant on propagation as the Hermite as the Laguerre laser modes.
Chapter 3 (Generic properties of phase singularities) offers an overview of the Young’s two- and three-pinhole experiments. The author determines the distribution of light near the central axis that runs between the pinholes to the observation screen. The mixed edge-screw dislocations (in particular, the pure edge and screw dislocations) are described and compared with crystal dislocations.
Chapter 4 (Generation and detection of optical vortices) deals with the generation of pure vortex beams and the measurement of the characteristics. This chapter begins by covering the simplest method for producing a vortex beam: to pass a pure Gaussian laser mode through an optical element known as the spiral phase plate. Next, different methods of the holographic design among some other methods are mentioned. For the detection of a vortex structure, or the topological charge of a vortex, methods of measuring and quantifying the phase of vortex beams are addressed, as the natural tool: the interferometry. This chapter ends by briefly summarizing the method of the stationary phase.
Chapter 5 (Angular momentum of light) starts by returning to the Maxwell equations in the microscopic form and deriving the appropriate conservation laws in terms of electric and magnetic fields. The decoupling of the angular momentum of light into the spin part (associated with circular polarization) and the orbital part (associated with vortex phase) is firstly derived to the paraxial beams of light and after to the specific case of Laguerre-Gaussian beams in the waist plane (\(z=0\)). For the point dipoles, the total force is decomposed into the gradient, scattering, and spin forces. This chapter finalizes with a debate over whether the wave or particle nature of light determines its momentum in matter (Abraham-Minkowski dilemma).
Chapter 6 (Applications of optical vortices) covers selected applications in optical micromanipulation, optical communications, remote sensing, and other areas.
Chapter 7 (Polarization singularities) begins by deriving the general polarization state on the Majorana sphere. Then, generic polarization singularities are identified and discussed.
Chapter 8 (Singularities of the Poynting vector) focuses on a descriptive discussion of the Poynting vector and its significance.
Chapter 9 (Coherence singularities) deals with certain partially coherent vortex beams that act like rigid rotators as well as others that act like rigid-fluid mix. The author introduces the mathematical concepts of coherence theory. Also experiments and applications are addressed.
Chapter 10 (Singularities and vortices in quantum optics) is concerned with the quantum optics. It covers the uncertaintly principle for angular momentum.
In Chapter 11 (Vortices in random wavefields), the author investigates the statistics of vortices in the random speckle wavefields, produced through the scattering of coherent laser light from a rough surface, considering both the density of vortices and their arrangement in space. The author considers the instantaneous field firstly at a single point in a speckle pattern, successively at two or more points, and after in any cross section of a speckle field.
Chapter 12 (Unusual singularities and other topological tricks) closes the book by studying nondiffractive beams as in particular the Bessel-Gauss beams. This chapter ends by discussing the interrelationships between knots, braids, linked vortices, cascades of singularities, and superoscillatory fields.
A selected list of references for further productive reading on different levels of knowledge is given.

MSC:

78-02 Research exposition (monographs, survey articles) pertaining to optics and electromagnetic theory
78A60 Lasers, masers, optical bistability, nonlinear optics
00A79 Physics
78A25 Electromagnetic theory (general)
81V80 Quantum optics
81P40 Quantum coherence, entanglement, quantum correlations
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