相關主題
商品描述
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.
商品描述(中文翻譯)
本書討論了螺旋 Ince-Gaussian 光束，這些光束以 Hermite-Gaussian 模式的展開形式呈現，並為其獲得了軌道角動量的解析表達式。在標量光學中，光被描述為一個複數振幅，這是一個三個笛卡爾坐標的複數函數。這個函數必須是標量旁軸 Helmholtz 方程的解，這與量子力學中的薛丁格方程是等價的。已知的這個方程的精確解析解不多，只有幾十個特殊函數形式的解。每個這樣的解都可以與某種激光光束相關聯，例如 Bessel、Laguerre-Gaussian 或 Hermite-Gaussian 光束。每個這樣的 Helmholtz 方程的解析解都能在建模之前充分描述光束的所有特徵。可以找到在腰部任何距離的強度分佈、相位分佈、總光束功率及其其他特性。因此，尋找描述新激光光束的新解析解，包括具有軌道角動量和拓撲電荷的螺旋（漩渦）光束，是非常重要的。本書描述了作者在 2023-2024 年獲得的新螺旋光束。這些是廣義不對稱的 Laguerre-Gaussian 和 Hermite-Gaussian 光束、雙重和方形的 Bessel-Gaussian 和 Laguerre-Gaussian 光束，以及幾種類型的 Bessel-Bessel-Gaussian 光束。每個這樣的新 Helmholtz 旁軸方程的解析解都是對光學的重要貢獻。本書對於在光學、光子學、激光物理、光信息技術和光學儀器領域工作的廣泛科學家和工程師都具有興趣。它對於應用數學和物理、應用數學和資訊學、光學專業的學士和碩士生，以及專攻這些領域的研究生也將是有用的。
作者簡介
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.
作者簡介(中文翻譯)
Victor V. Kotlyar 是俄羅斯國家研究中心「庫爾恰托夫研究所」影像處理系統研究所的實驗室負責人，以及薩馬拉國立研究大學的計算機科學教授。他於1979年在薩馬拉國立大學獲得物理與數學碩士學位，1988年在薩拉托夫國立大學獲得博士學位，1992年在俄羅斯科學院莫斯科中央獨特儀器設計研究所獲得科學博士學位。他是400篇科學論文、10本書籍和7項發明的共同作者。
Evgeniy G. Abramochkin 於1984年畢業於庫伊比雪夫國立大學，獲得數學物理學位。2006年獲得物理與數學科學博士，現任俄羅斯科學院列別傑夫物理研究所薩馬拉分所的首席研究員。他的科學著作清單包括約60篇文章。其研究興趣與複雜分析、特殊函數理論及數學物理方程有關。
Alexey A. Kovalev 於2002年畢業於薩馬拉國立研究大學，主修應用數學。他於2012年獲得物理與數學博士學位。現任俄羅斯國家研究中心「庫爾恰托夫研究所」激光測量實驗室的高級研究員，以及薩馬拉國立研究大學的計算機科學副教授。他是超過270篇科學論文和4本書籍的共同作者。其研究興趣包括數學衍射理論和光學漩渦。
