This book is devoted to the consideration of unusual laser beams – vortex or singular beams. It contains many numerical examples, which clearly show how the phase of optical vortices changes during propagation in free space, and that the topological charge is preserved. Topological Charge of Optical Vortices shows that the topological charge of an optical vortex is equal to the number of screw dislocations or the number of phase singularities in the beam cross-section. A single approach is used for the entire book: based on M. Berry’s formula. It is shown that phase singularities during beam propagation can be displaced to infinity at a speed greater than the speed of light. The uniqueness of the book is that the calculation of the topological charge for scalar light fields is extended to vector fields and is used to calculate the Poincare–Hopf singularity index for vector fields with inhomogeneous linear polarization with V-points and for the singularity index of vector fields with inhomogeneous elliptical polarization with C-points and C- lines. The book is written for opticians, and graduate students interested in an interesting section of optics – singular optics. It will also be of interest to scientists and researchers who are interested in modern optics. In order to understand the content of the book, it is enough to know paraxial optics (Fourier optics) and be able to calculate integrals.

New possibilities have recently emerged for producing optical beams with complex and intricate structures, and for the non-contact optical manipulation of matter. Structured Light and Its Applications fully describes the electromagnetic theory, optical properties, methods and applications associated with this new technology. Detailed discussions are given of unique beam characteristics, such as optical vortices and other wavefront structures, the associated phase properties and photonic aspects, along with applications ranging from cold atom manipulation to optically driven micromachines. Features include: Comprehensive and authoritative treatments of the latest research in this area of nanophotonics, written by the leading researchers Accounts of numerous microfluidics, nanofabrication, quantum informatics and optical manipulation applications Coverage that fully spans the subject area, from fundamental theory and simulations to experimental methods and results Graduate students and established researchers in academia, national laboratories and industry will find this book an invaluable guide to the latest technologies in this rapidly developing field. Comprehensive and definitive source of the latest research in nanotechnology written by the leading people in the field From theory to applications - all is presented in detail Editor is Chair of the SPIE Nanotechnology Technical Group and is leading the way in generation and manipulation of complex beams

This book deals with theoretical bases of the modern optics division concerned with coherent light fields with singularities characterized by phase uncertainty. Singular light fields include laser vortex beams or beams that carry orbital angular momentum. Laser vortex beams that have been introduced in optics in recent years are discussed in detail. Among them, of special notice are families of asymmetric laser vortex beams that, while being devoid of radial symmetry, remain unchanged upon propagation. What makes the laser vortex beams especially interesting is the ability to preserve their structure while propagating in a scattering medium or through a turbulent atmosphere. The orbital angular momentum is an extra degree of freedom of laser vortices because beams with different topological charge can be utilized as independent channels for data transmission in wireless communications. Laser vortex beams are generated from conventional Gaussian beams using liquid crystal light modulators, which are now readily available at any optical laboratory. Provide a framework for the comparative analysis of the efficiency of different vortex beams for micromanipulation. Includes detailed illustrations, enabling the vortex structure to be easily understood even by non-experts. Presents detailed descriptions of more than a dozen most popular types of vortex laser beams. Explores how optical vortices have been used in many practical applications including conventional and quantum wireless communications, micromanipulation, optical measurements with super-resolution, spiral interferometry, microscopy, and atom cooling. Presents in a systematic and detailed form many analytical and numerical results for the propagation vortex optical beams (chiefly in the linear propagation regime).

This book deals with applications in several areas of science and technology that make use of light which carries orbital angular momentum. In most practical scenarios, the angular momentum can be decomposed into two independent contributions: the spin angular momentum and the orbital angular momentum. The orbital contribution affords a fundamentally new degree of freedom, with fascinating and wide-spread applications. Unlike spin angular momentum, which is associated with the polarization of light, the orbital angular momentum arises as a consequence of the spatial distribution of the intensity and phase of an optical field, even down to the single photon limit. Researchers have begun to appreciate its implications for our understanding of the ways in which light and matter can interact, and its practical potential in different areas of science and technology.

Discover the most recent advances in electromagnetic vortices In Electromagnetic Vortices: Wave Phenomena and Engineering Applications, a team of distinguished researchers delivers a cutting-edge treatment of electromagnetic vortex waves, including their theoretical foundation, related wave properties, and several potentially transformative applications. The book is divided into three parts. The editors first include resources that describe the generation, sorting, and manipulation of vortex waves, as well as descriptions of interesting wave behavior in the infrared and optical regimes with custom-designed nanostructures. They then discuss the generation, multiplexing, and propagation of vortex waves at the microwave and millimeter-wave frequencies. Finally, the selected contributions discuss several representative practical applications of vortex waves from a system perspective. With coverage that incorporates demonstration examples from a wide range of related sub-areas, this essential edited volume also offers: Thorough introductions to the generation of optical vortex beams and transformation optical vortex wave synthesizers Comprehensive explorations of millimeter-wave metasurfaces for high-capacity and broadband generation of vector vortex beams, as well as orbital angular momentum (OAM) detection and its observation in second harmonic generations Practical discussions of microwave SPP circuits and coding metasurfaces for vortex beam generation and OAM-based structured radio beams and their applications In-depth examinations and explorations of OAM multiplexing for wireless communications, wireless power transmission, as well as quantum communications and simulations Perfect for students of wireless communications, antenna/RF design, optical communications, and nanophotonics, Electromagnetic Vortices: Wave Phenomena and Engineering Applications is also an indispensable resource for researchers in academia, at large defense contractors, and in government labs.

The first comprehensive and authoritative coverage of the angular momentum of light, illustrating both its theoretical and applied aspects.

This book has been prompted by our des ire to share with others our apprecia tion of the harmony and beauty in a particular sphere of modern optics known as "optical phase conjugation". Practical applications of the phase conjugated wave are likely to be far-reaching. Optical phase conjugation (OPC) combines in itself aesthetic and pragmatic attractiveness, a synthesis that has made OPC a subject of general attention. The figure presents the ap proximate rate of publications (number of articles per year) on OPC in the world literature for recent years, the lower curve denoting the work carried out in the USSR. The efforts of a large unofficial international collective have yielded an impressive result. 150 100 50 1975 1980 At present, the physical pro ces ses underlying various OPC methods are quite understandable, and it is the physics of OPC to which our book is devoted. Practical and scientific applications of phase-conjugated waves, which are of no less interest, have been touched upon in short, as major achievements in this sphere are a matter of the future. Today there are two main methods of OPC: i) by backward stimulated light scattering, ii) by four-wave mixing. Naturally, much attention is given to these methods in our book which, after the introductory Chap. 1, can be divided into two almost independent parts - Chaps. 2 - 5, and Chaps. 6 - 8.