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Off-axis elliptic Gaussian beams with an intrinsic orbital angular momentum
A.A. Kovalev 1,2, V.V. Kotlyar 1,2, D.S. Kalinkina 2, A.G. Nalimov 1,2

1 IPSI RAS – Branch of the FSRC "Crystallography and Photonics" RAS,
443001, Samara, Russia, Molodogvardeyskaya 151,
2 Samara National Research University, 443086, Samara, Russia, Moskovskoye Shosse 34

 PDF, 1399 kB

DOI: 10.18287/2412-6179-CO-916

Pages: 809-817.

Full text of article: Russian language.

Abstract:
We discuss paraxial light beams composed of decentered Gaussian beams, with their phase selected in a special way so that their superposition is invariant as it propagates in free space, retaining its cross-section shape. By solving a system of five nonlinear equations, a superposition is constructed that forms an invariant off-axis elliptic Gaussian beam. An expression is obtained for the orbital angular momentum of this beam. It is shown that it consists of two components. The first of them is equal to the moment relative to the center of the beam and increases with increasing ellipticity. The second one quadratically depends on the distance from the center of mass to the optical axis (an analogue of Steiner's theorem). It is shown that the orientation of the ellipse in the transverse plane does not affect the normalized orbital angular momentum.

Keywords:
light beam with non-uniform elliptical polarization, topological charge, intrinsic orbital angular momentum.

Citation:
Kovalev AA, Kotlyar VV, Kalinkina DS, Nalimov AG. Off-axis elliptic Gaussian beams with an intrinsic orbital angular momentum. Computer Optics 2021; 45(6): 809-817. DOI: 10.18287/2412-6179-CO-916.

Acknowledgements:
The work was partly funded by the Russian Foundation for Basic Research under grant #18-29-20003 (Section "Invariant propagation of off-axis Gaussian beams"), the Russian Science Foundation grant #18-19-00595 (Section "Structurally-stable elliptical Gaussian beams"), and the RF Ministry of Science and Higher Education within a state contract with the "Crystallography and Photonics" Research Center of the RAS (Section "Energy and orbital angular momentum").

References:
  1. Durnin J, Miceli JJ Jr, Eberly JH. Diffraction-free beams. Phys Rev Lett 1987; 58(15): 1499-1501.
  2. Gutiérrez-Vega J, Iturbe-Castillo M, Chávez-Cerda S. Alternative formulation for invariant optical fields: Mathieu beams. Opt Lett 2000; 25: 1493-1495..
  3. Bandres M, Gutiérrez-Vega J, Chávez-Cerda S. Parabolic nondiffracting optical wave fields. Opt Lett 2004; 29: 44-46.
  4. Siegman AE. Lasers. University Science; 1986.
  5. Indebetouw G. Optical vortices and their propagation. J Mod Opt 1993; 40(1): 73-87.
  6. Abramochkin EG, Volostnikov VG. Generalized Gaussian beams. J Opt A–Pure Appl Op 2004; 6(5): S157-S161.
  7. Kotlyar VV, Kovalev AA, Porfirev AP. Vortex Hermite–Gaussian laser beams. Opt Lett 2015; 40(5): 701-704. DOI: 10.1364/OL.40.000701.
  8. Abramochkin EG, Volostnikov VG. Modern optics of Gaussian beams [In Russian]. Moscow: "Fismatlit" Publisher; 2010. ISBN: 978-5-9221-1216-1.
  9. Liu X, Pu J. Investigation on the scintillation reduction of elliptical vortex beams propagating in atmospheric turbulence. Opt Express 2011; 19(27): 26444-26450.
  10. Andrews LC, Phillips RL. Laser beam propagation through random media. Bellingham, Washington: SPIE Press; 1998.
  11. Zhang X, Xia T, Cheng S, Tao S. Free-space information transfer using the elliptic vortex beam with fractional topological charge. Opt Commun 2019; 431: 238-244.
  12. Wu K, Huai Y, Zhao T, Jin Y. Propagation of partially coherent four-petal elliptic Gaussian vortex beams in atmospheric turbulence. Opt Express 2018; 26(23): 30061-30075.
  13. Skidanov RV, Rykov MA. The modification of laser beam for optimization of optical trap force characteristics. Computer Optics 2013; 37(4): 431-435. DOI: 10.18287/0134-2452-2013-37-4-431-435.
  14. Belousov DA, Dostovalov AV, Korolkov VP, Mikerin SL. A microscope image processing method for analyzing TLIPSS structures. Computer Optics 2019; 43(6): 936-945. DOI: 10.18287/2412-6179-2019-43-6-936-945.
  15. Dostovalov AV, Okotrub KA, Bronnikov KA, Terentyev VS, Korolkov VP, Babin SA. Influence of femtosecond laser pulse repetition rate on thermochemical laser-induced periodic surface structures formation by focused astigmatic Gaussian beam. Laser Phys Lett 2019; 16(2): 026003.
  16. Dostovalov AV, Derrien TJY, Lizunov SA, Přeučil F, Okotrub KA, Mocek T, Korolkov VP, Babin SA, Bulgakova NM. LIPSS on thin metallic films: New insights from multiplicity of laser-excited electromagnetic modes and efficiency of metal oxidation. Appl Surf Sci 2019; 491: 650-658.
  17. Goodman JW. Introduction to Fourier optics. 2nd ed. New York: McGraw-Hill; 1996.
  18. Cai Y, Lin Q. Decentered elliptical Gaussian beam. Appl Opt 2002; 41: 4336-4340.
  19. Kotlyar VV, Kovalev AA, Porfirev AP. Vortex astigmatic Fourier-invariant Gaussian beams. Opt Express 2019; 27(2): 657-666. DOI: 10.1364/OE.27.000657.
  20. Kotlyar VV, Kovalev AA, Porfirev AP. Astigmatic laser beams with a large orbital angular momentum. Opt Express 2018; 26(1): 141-156. DOI: 10.1364/OE.26.000141.
  21. Berry MV, Jeffrey MR, Mansuripur M. Orbital and spin angular momentum in conical diffraction. J Opt A–Pure Appl Op 2005; 7: 685-690.
  22. Bullen PS. Handbook of means and their inequalities. Ch III. Dordrecht, Netherlands: Kluwer; 2003: 175-265.
  23. Backlund MP, Lew MD, Backer AS, Sahl SJ, Grover G, Agrawal A, Piestun R, Moerner WE. The double-helix point spread function enables precise and accurate measurement of 3D single-molecule localization and orientation. Proc SPIE 2013; 8590: 85900.
  24. Zannotti A, Denz C, Alonso MA, Dennis MR. Shaping caustics into propagation-invariant light. Nat Commun 2020; 11: 3597.
  25. Izdebskaya Y, Shvedov V, Volyar A. Symmetric array of off-axis singular beams: spiral beams and their critical points. J Opt Soc Am A 2008; 25(1): 171-181.

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