A.A. Kovalev, V.V. Kotlyar, S.G. Zaskanov, D.S. Kalinkina

Samara State Aerospace University, Samara, Russia

Full text of article: Russian language.

Abstract**:**

We studied a generalization of the family of Laguerre-Gaussian (LG) laser modes with asymmetrical intensity distribution. As the asymmetrical LG beam is propagating in a homogeneous medium, the asymmetry of its main (central) bright ring reduces, while the contrast of the rest rings increases. The number of bright rings coincides with that of a standard (symmetrical) LG mode. Using the expansion of the complex amplitude into the angular spectrum of plane waves, we calculated analytically the power of the asymmetrical LG beams and projection of their orbital angular momentum (OAM) on the optical axis. It is found that the normalized OAM (OAM per photon) is completely determined by the topological charge and the ratios between the shifts and the waist radius. We also found the conditions under which the normalized OAM coincides with the topological charge (as is the case for the optical vortices).

Keywords:

diffraction theory, optical vortices, propagation, Laguerre-Gaussian mode, orbital angular momentum, beam power, complex shift.

Citation:

Kovalev AA, Kotlyar VV, Zaskanov SG, Kalinkina DS. Laguerre-Gaussian beams with complex shift in Cartesian coordinates. Computer Optics 2016; 40(1): 5-11. DOI: 10.18287/2412-6179-2016-40-1-5-11.

References:

- Huang S, Miao Z, He C, Pang F, Li Y, Wang T. Composite vortex beams by coaxial superposition of Laguerre-Gaussian beams. Optics and Lasers in Engineering 2016; 78: 132-139.
- Plick WN, Krenn M. Physical meaning of the radial index of Laguerre-Gauss beams. Physical Review A 2015; 92(6): 063841.
- Savelyev DA, Khonina SN. Characteristics of sharp focusing of vortex Laguerre-Gaussian beams [In Russian]. Computer Optics 2015; 39(5): 654-662.
- Stilgoe AB, Nieminen TA, Rubinsztein-Dunlop H. Energy, momentum and propagation of non-paraxial high-order Gaussian beams in the presence of an aperture. Journal of Optics (United Kingdom) 2015; 17(12): 125601.
- Zhang Y, Liu X, Belic M, Zhong W, Wen F, Zhang Y. Anharmonic propagation of two-dimensional beams carrying orbital angular momentum in a harmonic potential. Optics Letters 2015; 40: 3786-3789.
- Kim DJ, Kim JW. High-power TEM00 and Laguerre–Gaussian mode generation in double resonator configuration. Applied Physics B 2015; 121(3): 401-405.
- Das BC, Bhattacharyya D, De S. Narrowing of Doppler and hyperfine line shapes of Rb - D2 transition using a Vortex beam. Chemical Physics Letters 2016; 644: 212-218.
- Allocca A, Gatto A, Tacca M, Day RA, Barsuglia M, Pillant G, Buy C, Vajente G. Higher-order Laguerre-Gauss interferometry for gravitational-wave detectors with in situ mirror defects compensation. Physical Review D 2015; 92(10): 102002.
- Sun K, Qu C, Zhang C. Spin-orbital-angular-momentum coupling in Bose-Einstein condensates. Physical Review A 2015; 91(6): 063627.
- Kravtsov YuA. Complex ray and complex caustics. Radiophysics and Quantum Electronics 1967; 10: 719-730.
- Kotlyar VV, Kovalev AA, Soifer VA. Asymmetric Bessel modes. Optics Letters 2014; 39(8): 2395-2398.
- Kovalev AA, Kotlyar VV, Porfirev AP. Shifted nondiffractive Bessel beams. Physical Review A 2015; 91(5): 053840.
- Kim HC, Lee YH. Hermite–Gaussian and Laguerre–Gaussian beams beyond the paraxial approximation. Optics Communications 1999; 169: 9-16.
- Gradshteyn IS, Ryzhik IM. Table of Integrals, Series, and Products. NY: Academic; 1965.

© 2009,Institution of Russian Academy of Sciences, Image Processing Systems Institute of RAS, Russia, 443001, Samara, Molodogvardeyskaya Street 151; E-mail: journal@computeroptics.ru; Phones: +7 (846 2) 332-56-22, Fax: +7 (846 2) 332-56-20IPSI RAS