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).

Victor V. Kotlyar is the head of a laboratory at Image Processing Systems Institute (IPSI) of the Russian Academy of Sciences (RAS) and a professor of Computer Science department at Samara National Research University. He graduated from Kuibyshev State University (1979), received his Candidate's and Doctor's Degrees in Physics & Mathematics from Saratov State University (1988) and Moscow Central Design Institute of Unique Instrumentation of the RAS (1992). He is a co-author of 300 scientific papers, 5 books and 7 inventions. His current research interests include diffractive optics, gradient optics, nanophotonics, and optical vortices.

Alexey A. Kovalev graduated (2002) from Samara National Research University, majoring in Applied Mathematics. He received his Doctor in Physics & Maths degree in 2012. He is a senior researcher of Laser Measurements laboratory at IPSI RAS. He is a coauthor of more than 150 scientific papers. His current research interests are mathematical diffraction theory and photonic crystal devices.

Alexey P. Porfirev graduated (2010) from Samara National Research University, majoring in Applied Physics and Mathematics. He holds the Candidate's Degree in Physics and Mathematics (2013). Currently he is an assistant professor at Technical Cybernetics department of Samara National Research University and a researcher at Micro- and Nanotechnologies laboratory of the IPSI RAS. His current research interests include diffractive optics and optical manipulation.