1st Edition

Topological Charge of Optical Vortices

    320 Pages 196 B/W Illustrations
    by CRC Press

    320 Pages 196 B/W Illustrations
    by CRC Press

    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.

    1. Topological charge of superposition of vortices. Conservation of topological charge. 2. Evolution of an optical vortex with an initial fractional topological charge. 3. Topological charge superposition of only two Laguerre-Gaussian or Bessel-Gaussian beams with different parameters. 4. Optical vortex beams with an infinite topological charge. 5. Transformation of an edge dislocation of a wavefront into an optical vortex. 6. Fourier-invariant and structurally stable optical vortex beams. 7. Topological charge of polarization singularities. 8. Conclusion.


    Victor V. Kotlyar is Head of the Laboratory at Image Processing Systems Institute of the Russian Academy of Science, a branch of the Federal Scientific Research Center "Crystallography and Photonics", and Professor of Computer Science at Samara National Research University, Russia. He earned his MS, PhD, and DrSc degrees in Physics and Mathematics from Samara State University (1979), Saratov State University (1988), and Moscow Central Design Institute of Unique Instrumentation, the Russian Academy of Sciences (1992). He is a SPIE- and OSA-member. He is coauthor of 400 scientific papers, 7 books, and 7 inventions. His current interests are diffractive optics, gradient optics, nanophotonics, and optical vortices.

    Alexey A. Kovalev graduated in 2002 from Samara National Research University, Russia, majoring in Applied Mathematics. He earned his PhD in Physics and Maths in 2012. He is senior researcher of Laser Measurements at the Image Processing Systems Institute of the Russian Academy of Science, a branch of the Federal Scientific Research Center "Crystallography and Photonics". He is a co-author of more than 270 scientific papers. His research interests are mathematical diffraction theory, photonic crystal devices, and optical vortices.

    Anton G. Nalimov graduated from Samara State Aerospace University, Russia, in February 2003. He entered postgraduate study in 2003 with a focus on the specialty 05.13.18 "Mathematical Modeling and Program Complexes". He finished it in 2006 with the specialty 01.04.05 "Optics". Nalimov works in the Technical Cybernetics department at Samara National Research University as an associate professor, and also works as a scientist in the Image Processing Systems Institute of the Russian Academy of Science, a branch of the Federal Scientific Research Center "Crystallography and Photonics" in Samara. He is a PhD candidate in Physics and Mathematics, co-author of 200 papers and 3 inventions.