Alexey A. Kovalev

This book discusses helical Ince-Gaussian beams, which are presented as expansions in Hermite-Gaussian modes, and analytical expressions for the orbital angular momentum are obtained for them.

This book explores the optical Hall effect in the sharp focus of laser light. It builds upon the established theory of Richards-Wolf (1959), providing numerous real-world examples that illustrate both spin and orbital Hall effects near the focal point. Within the focal zone, distinct regions of left and right circular polarization emerge, showcasing the orbital Hall effect. This effect becomes apparent when localized areas within the focal plane experience transverse energy flow, rotating either clockwise or counterclockwise. The spin Hall effect, a fundamental occurrence, is demonstrated when a linearly polarized Gaussian beam is concentrated. Furthermore, the book reveals spin and orbital Hall effects in light fields with nonuniform linear polarization, where the polarization direction varies within the beam cross section. While the optical or photonic Hall effect has been recognized since 2004, a comprehensive monograph detailing its focal dynamics has been lacking until now. Drawing from the cohesive theoretical framework of the Richards-Wolf theory, this book offers specific examples and results from computer modeling. It equips readers with analytical relations for calculating energy and spin fluxes near a sharp focus across various initial light vector fields. Designed for a diverse audience, including scientists, engineers, and students in optics and photonics, this book serves as a valuable resource. It caters to undergraduate and graduate students in applied mathematics, physics, informatics, and optics, and can also benefit researchers and professionals in the field. Moreover, the book holds potential as a foundational text for advanced graduate courses

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.

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 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.

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).