Discusses 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 Presents a single approach based on the M. Berry formula Describes the topological competition between different optical vortices in a superposition Demonstrates the stability of the topological charge to random phase distortions and insensitivity to amplitude distortions Contains many numerical examples, which clearly show how the phase of optical vortices changes during propagation in free space and the topological charge is preserved

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).

Readers will learn in which ways light can be "confined" within a subwavelength region smaller than half a wavelength. Strictly within the focal spot, all degrees of freedom of light interact and manifest themselves in a dramatic way. The size and shape of the focal spot and the magnitude of side-lobes depend on the polarization state alongside phase and amplitude distributions of a light beam. Readers will learn techniques in which inhomogeneously (i.e., azimuthally and radially) polarized optical beams can be focused. In sharp focus, exotic phenomena can occur, including the negative propagation of light and a toroidal optical flow. Throughout the book, the numerical simulation is performed using the rigorous solution of Maxwell's equations based on a Finite-Difference Time-Domain (FDTD) approach, which makes the results of modeling highly reliable. The photonic components, including optical metasurfaces, discussed in the book have been implemented using state-of-the-art techniques of electron beam writing and reactive ion-beam etching of microrelief. Two chapters are concerned with photonics hot spots, which deal with the control of light by means of optical metasurfaces and the generation of an energy backflow in the region of sharp focus of a laser beam. Another hot topic is diffractive polarization converters implemented as subwavelength diffraction gratings to convert polarization of light. By way of illustration, such converters are shown to perform linear-to-radial or linear-to-azimuthal polarization conversion. The book describes advanced photonic components fabricated by the authors to perform sharp focusing of light, including binary zone plates, binary axicons, a planar photonic crystal lens, diffraction polarization converters, and metalenses. This book is a must-have for individuals and institutions studying cutting edge optics.