Optical Hall Effect in the Sharp Focus of Laser Light

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

Introduction.- 1. Spin Hall effect at the focus for light with linear polarization.- 2. Spin Hall effect at the focus for light with circular polarization.- 3. Focusing of cylindrical vector beams and their modifications.- 4. Cylindrical fractional-order and double-index vector laser beams.- 5. Sharp focusing of modified cylindrical vector laser beams.- 6. Poincare beams at the tight focus.- 7. Hall effect in paraxial laser beams.- Conclusion.- References.

Victor V. Kotlyar is the head of the Laboratory at the Image Processing Systems Institute, National Research Center «Kurchatov Institute» and a professor of Computer Science at Samara National Research University. He obtained his M.S., Ph.D., and Dr.Sc. degrees in Physics and Mathematics from Samara State University (1979), Saratov State University (1988), and the Moscow Central Design Institute of Unique Instrumentation, Russian Academy of Sciences (1992), respectively. He is a member of SPIE and OSA and has co-authored 400 scientific papers, 7 books, and 7 inventions. His current research interests include diffractive optics, gradient optics, nanophotonics, and optical vortices.

Alexey A. Kovalev graduated from Samara National Research University in 2002 with a major in Applied Mathematics and earned his Doctorate in Physics and Mathematics in 2012. He is a senior researcher at the Laser Measurements Laboratory at the Image Processing Systems Institute, National Research Center «Kurchatov Institute». He has co-authored over 270 scientific papers and is particularly interested in mathematical diffraction theory, photonic crystal devices, and optical vortices.

Anton G. Nalimov completed his undergraduate studies at Samara National Research University in February 2003 and pursued postgraduate studies in "Mathematical Modeling and Program Complexes," earning his degree in Optics in 2006. He serves as an associate professor in the Technical Cybernetics department at Samara National Research University and works as a scientist at the Image Processing Systems Institute, National Research Center «Kurchatov Institute».