Topological Charge of Optical Vortices

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 the topological charge is preserved.

Autorentext

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 and 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 and 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.

Anton G. Nalimov, graduated from Samara State Aerospace University in February, 2003. Entered in postgraduate study in 2003 on speciality 05.13.18 Mathematical modeling and program complexes, finished it in 2006 with speciality 01.04.05 Optics. A.G. Nalimov works on Technical Cybernetics department in Samara National Research University as an associate professor, works as a scientist in Image Processing Systems Institute of the Russian Academy of Science, a branch of the Federal Scientific Research Center Crystallography and Photonics in Samara. Candidate in Physics and Mathematics, coauthor of 200 papers and 3 inventions.

Zusammenfassung

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 PoincareHopf 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.

Inhalt

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.