(43-6) 22 * << * >> * Russian * English * Content * All Issues

Spin angular momentum density in the tight focus of a light field with phase and polarization singularities

A.A. Kovalev1,2, V.V. Kotlyar1,2, D.S. Kalinkina2

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

 PDF, 814 kB

DOI: 10.18287/2412-6179-2019-43-6-1098-1102

Pages: 1098-1102.

Full text of article: Russian language.

For a light field with both phase and polarization singularities at its center, expressions are obtained that describe the distribution of the spin angular momentum (SAM) density in the sharp focal spot of an aplanatic system. These expressions include the radial, azimuthal, and longitudinal SAM components. As special cases, focusing of optical vortices with radial, azimuthal, and saddle polarizations is studied. Using the Bessel beam as an example, it is shown that in some areas in the focal plane the longitudinal SAM component is zero (resulting in a photonic wheel), while in others it is an order of magnitude less than the transverse component.

spin angular momentum, sharp focusing, phase singularity, polarization singularity, photonic wheel, longitudinal magnetization.

Kovalev AA, Kotlyar VV, Kalinkina DS. Spin angular momentum density in the tight focus of a light field with phase and polarization singularities. Computer Optics 2019; 43(6): 1098-1102. DOI: 10.18287/2412-6179-2019-43-6-1098-1102.

This work was supported by the Russian Science Foundation (grant 17-19-01186) in the parts “Numerical calculation of the SAM density of a narrow ring beam with polarization singularities in the vicinity of an acute focus” and “SAM density in the sharp focus of an optical vortex with radial polarization”, Russian Fundamental Fund studies (grant 18-07-01129) in the part “General expressions for the SAM density at the sharp focus of the light field with polarization and phase singularities”, and (grant 18-07-01380) in the part “The SAM density at the sharp focus of the optical vortex with az polarization ”, as well as the Ministry of Science and Higher Education of the Russian Federation in the framework of the work on the State assignment of the Federal Research Center for Crystallography and Photonics of the Russian Academy of Sciences (agreement No. 007-GZ / Ch3363 / 26) in the part“ SAM density in the sharp focus of an optical vortex with a saddle polarization ".


  1. Aiello A, Banzer P, Neugebauer M, Leuchs G. From transverse angular momentum to photonic wheels. Nat Photon 2015; 9: 789-95. DOI: 10.1038/nphoton.2015.203.
  2. Jiang Y, Li X, Gu M. Generation of sub-diffraction-limited pure longitudinal magnetization by the inverse Faraday effect by tightly focusing an azimuthally polarized vortex beam. Opt Lett 2013; 38: 2957-60. DOI: 10.1364/OL.38.002957.
  3. Bliokh KY, Bekshaev AYa, Nori F. Extraordinary momentum and spin in evanescent waves. Nat Commun 2014; 5: 3300. DOI: 10.1038/ncomms4300.
  4. Picardi MF, Bliokh KY, Rodríguez-Fortuño FJ, Alpeggiani F, Nori F. Angular momenta, helicity, and other properties of dielectric-fiber and metallic-wire modes. Optica 2018; 5: 1016-26. DOI: 10.1364/OPTICA.5.001016.
  5. Neugebauer M, Bauer T, Aiello A, Banzer P. Measuring the transverse spin density of light. Phys Rev Lett 2015; 114: 063901. DOI: 10.1103/PhysRevLett.114.063901.
  6. Bekshaev AYa. Subwavelength particles in an inhomogeneous light field: optical forces associated with the spin and orbital energy flows. J Opt 2013; 15(4): 044004. DOI: 10.1088/2040-8978/15/4/044004.
  7. Shi P, Du L, Yuan X. Structured spin angular momentum in highly focused cylindrical vector vortex beams for optical manipulation. Opt Express 2018; 26: 23449-59. DOI: 10.1364/OE.26.023449.
  8. Nieminen TA, Stilgoe AB, Heckenberg NR, Rubinsztein-Dunlop H. Angular momentum of a strongly focused Gaussian beam. J Opt A: Pure Appl Opt 2008; 10(11): 115005. DOI: 10.1088/1464-4258/10/11/115005.
  9. Cui Z, Sun J, Litchinitser NM, Han Y. Dynamical characteristics of tightly focused vortex beams with different states of polarization. J Opt 2019; 21(1): 015401. DOI: 10.1088/2040-8986/aaed91.
  10. Kotlyar VV, Stafeev SS, Kovalev AA. Sharp focusing of a light field with polarization and phase singularities of an arbitrary order. Computer Optics 2019; 43(3): 337-46. DOI: 10.18287/2412-6179-2019-43-3-337-346.
  11. Richards B, Wolf E. Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic systems. Proc R Soc London, Ser. A 1959; 253: 358-79. DOI: 10.1098/rspa.1959.0200.
  12. Chen B, Pu J. Tight focusing of elliptically polarized vortex beams. Appl Opt 2009; 48: 1288-94. DOI: 10.1364/AO.48.001288.
  13. Fu S, Gao C, Shi Y, Dai K, Zhong L, Zhang S. Generating polarization vortices by using helical beams and a Twyman Green interferometer. Opt Lett 2015; 40: 1775-8. DOI: 10.1364/OL.40.001775.
  14. Dennis MR. Topological singularities in wave fields. PhD thesis, Bristol, 2001.


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