LEADER 04142nam 22006735 450 001 9911009339303321 005 20250611130242.0 010 $a3-031-92217-4 024 7 $a10.1007/978-3-031-92217-6 035 $a(CKB)39239621700041 035 $a(MiAaPQ)EBC32151505 035 $a(Au-PeEL)EBL32151505 035 $a(DE-He213)978-3-031-92217-6 035 $a(OCoLC)1525622088 035 $a(EXLCZ)9939239621700041 100 $a20250611d2025 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aHelical Laser Beams /$fby Victor V. Kotlyar, Eugeny G. Abramochkin, Alexey A. Kovalev 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (261 pages) 311 08$a3-031-92216-6 327 $aIntroduction -- 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. 330 $aThis 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. 606 $aOptics 606 $aLasers 606 $aElectrodynamics 606 $aQuantum theory 606 $aMathematical physics 606 $aOptics and Photonics 606 $aLaser Technology 606 $aClassical Electrodynamics 606 $aQuantum Physics 606 $aTheoretical, Mathematical and Computational Physics 615 0$aOptics. 615 0$aLasers. 615 0$aElectrodynamics. 615 0$aQuantum theory. 615 0$aMathematical physics. 615 14$aOptics and Photonics. 615 24$aLaser Technology. 615 24$aClassical Electrodynamics. 615 24$aQuantum Physics. 615 24$aTheoretical, Mathematical and Computational Physics. 676 $a535 700 $aKotlyar$b Victor V$01827894 701 $aAbramochkin$b Eugeny G$01827895 701 $aKovalev$b Alexey A$01827896 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911009339303321 996 $aHelical Laser Beams$94396011 997 $aUNINA