(48-4) 04 * << * >> * Russian * English * Content * All Issues

Ince-Gaussian laser beams as superposition of Hermite-Gaussian or Laguerre-Gaussian beams
E.G. Abramochkin 12, V.V. Kotlyar 2,3, A.A. Kovalev 2,3

1 Lebedev Physical Institute,
443011, Samara, Russia, Novo-Sadovaya 221;
2 Image Processing Systems Institute, NRC "Kurchatov Institute",
443001, Samara, Russia, Molodogvardeyskaya 151;
3 Samara National Research University, 443086, Samara, Russia, Moskovskoye Shosse 34

 PDF, 2020 kB

DOI: 10.18287/2412-6179-CO-1466

Pages: 501-510.

Abstract:
We obtain explicit analytic expressions for the Ince-Gaussian (IG) beams for several first indices p = 3, 4, 5, 6. Earlier, explicit expressions have been derived for amplitudes of the IG beams with p = 0, 1, 2 and without regard for the ellipticity parameter. Here, we give expressions for the amplitudes of 24 IG beams written as superpositions of the Laguerre-Gaussian (LG) or Hermite-Gaussian (HG) beams, with the superposition coefficients explicitly depending on the ellipticity parameter. Simultaneously expressing the IG modes both via the LG and HG modes allows easily obtaining the IG modes in the extreme cases when the ellipticity parameter is zero or infinite. Explicit dependence of the obtained expressions for the IG modes on the ellipticity allows the intensity pattern at the beam cross-section to be varied by continuously varying the parameter value. For the first time, intensity distributions are obtained for the IG beams with negative ellipticity parameter.

Keywords:
Ince-Gaussian beams, Laguerre-Gaussian beams, Hermite-Gaussian beams, elliptic beams, characteristic equation.

Citation:
Abramochkin EG, Kotlyar VV, Kovalev AA. Ince-Gaussian laser beams as superposition of Hermite-Gaussian or Laguerre-Gaussian beams. Computer Optics 2024; 48(4): 501-510. DOI: 10.18287/2412-6179-CO-1466.

Acknowledgements:
This work was financially supported by the Russian Science Foundation (Project No. 22-12-00137, theory and numerical simulation). This work was also performed within the State assignment of NRC "Kurchatov Institute" (Introduction and Conclusion).

References:
  1. Arscott FM. Periodic differential equations. Oxford: Pergamon; 1964.
  2. Arscott FM. XXI–The Whittaker-Hill equation and the wave equation in paraboloidal coordinates. Proc R Soc Edinb Sect A 1967; 67(4): 265-276. DOI: 10.1017/S008045410000813X.
  3. Miller W Jr. Symmetry and separation of variables. London: Addison-Wesley Pub Comp; 1977. ISBN: 978-0-521-17739-9.
  4. Bandres MA, Gutiérrez-Vega JC. Ince–Gaussian beams. Opt Lett 2004; 29(2): 144-146. DOI: 10.1364/OL.29.000144.
  5. Bandres MA, Gutiérrez-Vega JC. Ince–Gaussian modes of the paraxial wave equation and stable resonators. J Opt Soc Am A 2004; 21(5): 873-880. DOI: 10.1364/JOSAA.21.000873.
  6. Bandres MA. Elegant Ince–Gaussian beams. Opt Lett 2004; 29(15): 1724-1726. DOI: 10.1364/OL.29.001724.
  7. Singh SK, Haginaka H, Jackin BJ, Kinashi K, Tsutsumi N, Sakai W. Generation of Ince-Gaussian beams using azocarbazole polymer CGH. J Imaging 2022; 8(5): 144. DOI: 10.3390/jimaging8050144.
  8. Li Y, Hu XB, Perez-Garcia B, Zhao B, Gao W, Zhu ZH, Rosales-Guzmán C. Classically entangled Ince–Gaussian modes. Appl Phys Lett 2020; 116(22): 221105. DOI: 10.1063/5.0011142.
  9. Baghdasaryan B, Fritzsche S. Enhanced entanglement from Ince-Gaussian pump beams in spontaneous parametric down-conversion. Phys Rev A 2020; 102(5): 052412. DOI: 10.1103/physreva.102.052412.
  10. Krenn M, Fickler R, Huber M, Lapkiewicz R, Plick W, Ramelow S, Zeilinger A. Entangled singularity patterns of photons in Ince-Gauss modes. Phys Rev A 2013; 87: 012326. DOI: 10.1103/PhysRevA.87.012326.
  11. Plick WN, Krenn M, Fickler E, Ramelow S, Zeilinger A. Quantum orbital angular momentum of elliptically symmetric light. Phys Rev A 2013; 87: 033806. DOI: 10.1103/PhysRevA.87.033806.
  12. Yang HR, Wu HJ, Gao W, Rosales-Guzmán C, Zhu ZH. Parametric upconversion of Ince–Gaussian modes. Opt Lett 2020; 45: 3034-3037. DOI: 10.1364/OL.393146.
  13. Bai ZY, Deng DM, Guo Q. Elegant Ince-Gaussian beams in a quadratic-index medium. Chinese Physics B 2011; 20(9): 094202. DOI: 10.1088/1674-1056/20/9/094202.
  14. Xu YQ, Zhou GQ. Propagation of Ince-Gaussian beams in uniaxial crystals orthogonal to the optical axis. Eur Phys J D 2012; 66: 59. DOI: 10.1140/epjd/e2012-20603-x.
  15. Robertson E, Pires DG, Dai K, Free J, Kimmel K, Litchinitser N, Miller JK, Johnson EG. Constant-envelope modulation of Ince-Gaussian beams for high bandwidth underwater wireless optical communications. J Lightwave Techn 2023; 41(16): 5209-5216. DOI: 10.1109/JLT.2023.3252466.
  16. Bayraktar M. Scintillation performance of Ince-Gaussian beam in atmospheric turbulence. Preprint. 2023. DOI: 10.21203/rs.3.rs-1779023/v1.
  17. Siegman AE. Lasers. Mill Valley, CA: University Science Books, 1986. ISBN: 0-935702-11-3.
  18. Ince EL. A linear differential equation with periodic coefficients. Proc London Math Soc 1923; 23(2): 56-74. DOI: 10.1112/plms/s2-23.1.56.
  19. Dubrovskii VM. Equations of degree four [In Russian]. Uspekhi Matematicheskikh Nauk 1973; 28(4): 212.

© 2009, IPSI RAS
151, Molodogvardeiskaya str., Samara, 443001, Russia; E-mail: journal@computeroptics.ru ; Tel: +7 (846) 242-41-24 (Executive secretary), +7 (846) 332-56-22 (Issuing editor), Fax: +7 (846) 332-56-20