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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. In scalar optics, light is described by a complex amplitude, a complex function of three Cartesian coordinates. This function must be a solution to the scalar paraxial Helmholtz equation, which is equivalent to the Schrödinger equation in quantum mechanics. There are not many known exact analytical solutions of this equation in the form of special functions, only a few dozen. Each such solution can be associated with a certain laser beam, for example, a Bessel, Laguerre-Gaussian or Hermite-Gaussian beam. Each such analytical solution of the Helmholtz equation allows one to fully describe all the features of the light beam before modeling. Find the intensity distribution at any distance from the waist, phase distribution, total beam power and its other characteristics. Therefore, the search for new analytical solutions describing new laser beams, including helical (vortex) beams, which have orbital angular momentum and topological charge, is relevant. This book describes new helical beams that the authors obtained in 2023-2024. These are generalized asymmetric Laguerre-Gaussian and Hermite-Gaussian beams, double and square Bessel-Gaussian and Laguerre-Gaussian beams, and several types of Bessel-Bessel-Gaussian beams. Each such new analytical solution of the Helmholtz paraxial equation is a significant contribution to optics. The book is of interest to a wide range of scientists and engineers working in the field of optics, photonics, laser physics, opto-information technologies and optical instrumentation. It can also be useful for bachelors and masters in the specialties applied mathematics and physics, applied mathematics and informatics, optics and graduate students specializing in these areas.
List of contents
Introduction.- 1.Asymmetric laser beams.- 2.Ince-Gaussian beams.- 3.New type of Laguerre-Gaussian beams.- 4.New type of Bessel-Gaussian beams.- 5.Superposition of helical laser beams.- 6.Orbital angular momentum of helical laser beams.- Conclusion.
About the author
Victor V. Kotlyar is the head of the Laboratory at Image Processing Systems Institute of the National Research Center "Kurchatov Institute" and professor of Computer Science at Samara National Research University. He received his M.S., Ph.D. and Dr.Sc. 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 co-author of 400 scientific papers, 10 books and 7 inventions.
Evgeniy G. Abramochkin graduated from Kuibyshev State University in 1984 with a degree in Mathematical Physics. Doctor of Physical and Mathematical Sciences (2006), works as a leading researcher at the Samara branch of the Lebedev Physical Institute of the Russian Academy of Sciences. The list of scientific works includes about 60 articles. Scientific interests are related to complex analysis, theory of special functions and equations of mathematical physics.
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 Image Processing Systems Institute of the National Research Center "Kurchatov Institute" and Associate Professor of Computer Science at Samara National Research University He is a co-author of more than 270 scientific papers and 4 book. His research interests are mathematical diffraction theory and optical vortices.
