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Circular polarization before and after the sharp focus for linearly polarized light
S.S. Stafeev 1,2, V.D. Zaitsev 1,2, V.V. Kotlyar 1,2

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, 1237 kB

DOI: 10.18287/2412-6179-CO-1070

Pages: 381-387.

Full text of article: Russian language.

Abstract:
We consider sharp focusing of a linearly polarized light beam. Using the Richards-Wolf formalism, we show that before and after the focal plane there are cross-section regions in which the polarization is circular (elliptical). When passing through the focal plane, the direction of rotation of the polarization vector is reversed. If before the focus the light is left-hand circular polarized at a definite region of the beam cross-section, then exactly at the focus the polarization becomes linear at this cross-section region, before becoming right circular polarized after the focus at this region. This effect allows linearly polarized light to be used to rotate weakly absorbing dielectric microparticles around their center of mass.

Keywords:
linear and circular polarization, sharp focusing, Richards-Wolf formulas, Stokes vector, spin angular momentum.

Citation:
Stafeev SS, Zaitsev VD, Kotlyar VV. Circular polarization before and after the sharp focus for linearly polarized light. Computer Optics 2022; 46(3): 381-387. DOI: 10.18287/2412-6179-CO-1070.

Acknowledgements:
This work was partly funded by the Russian Science Foundation under project No. 18-19-00595 (Section "Theoretical background"), grant to Samara University for the implementation of the strategic academic leadership program "Priority-2030  (Section "Numerical simulation by Richards-Wolf formulae"), and the RF Ministry of Science and Higher Education within the government project of the FSRC "Crystallography and Photonics" RAS (Section “Numerical simulation by a FDTD-method”).

References:

  1. Richards B, Wolf E. Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system. Proc R Soc A 1959; 253(1274): 358-379. DOI: 10.1098/rspa.1959.0200.
  2. Yuan GH, Wei SB, Yuan X-C. Nondiffracting transversally polarized beam. Opt Lett 2011; 36(17): 3479-3481. DOI: 10.1364/OL.36.003479.
  3. Ping C, Liang Ch, Wang F, Cai Y. Radially polarized multi-Gaussian Schell-model beam and its tight focusing properties. Opt Express 2017: 25(26): 32475-32490. DOI: 10.1364/OE.25.032475.
  4. Grosjean T, Gauthier I. Longitudinally polarized electric and magnetic optical nano-needles of ultra high lengths. Opt Commun 2013; 294: 333-337. DOI: 10.1016/j.optcom.2012.12.032.
  5. Wang H, Shi L, Lukyanchuk B, Sheppard, C, Chong CT. Creation of a needle of longitudinally polarized light in vacuum using binary optics. Nat Photonics 2008; 2(8): 501-505. DOI: 10.1038/nphoton.2008.127.
  6. Lin J, Chen R, Jin P, Cada M, Ma Y. Generation of longitudinally polarized optical chain by 4π focusing system. Opt Commun 2015; 340: 69-73. DOI: 10.1016/j.optcom.2014.11.095.
  7. Zhuang, J, Zhang L, Deng D. Tight-focusing properties of linearly polarized circular Airy Gaussian vortex beam. Opt Lett 2020; 45(2): 296. DOI: 10.1364/OL.45.000296.
  8. Lyu Y, Man Z, Zhao R, Meng P, Zhang W, Ge X, Fu S. Hybrid polarization induced transverse energy flow. Opt Commun 2021; 485: 126704. DOI: 10.1016/j.optcom.2020.126704.
  9. Li H, Wang C, Tang M, Li X. Controlled negative energy flow in the focus of a radial polarized optical beam. Opt Express 2020; 28(13): 18607-18615. DOI: 10.1364/OE.391398.
  10. Kotlyar VV, Stafeev SS, Nalimov AG. Energy backflow in the focus of a light beam with phase or polarization singularity. Phys Rev A 2019; 99(3): 033840. DOI: 10.1103/PhysRevA.99.033840.
  11. Bomzon Z, Gu M, Shamir J. Angular momentum and geometrical phases in tight-focused circularly polarized plane waves. Appl Phys Lett 2006; 89(24): 241104. DOI: 10.1063/1.2402909.
  12. Aiello A, Banzer P, Neugebauer M, Leuchs G. From transverse angular momentum to photonic wheels. Nat Photonics 2015; 9(12): 789-795. DOI: 10.1038/nphoton.2015.203.
  13. Li M, Cai Y, Yan S, Liang Y, Zhang P, Yao B. Orbit-induced localized spin angular momentum in strong focusing of optical vectorial vortex beams. Phys Rev A 2018; 97(5): 053842. DOI: 10.1103/PhysRevA.97.053842.
  14. Zhao Y, Edgar JS, Jeffries GDM, McGloin D, Chiu DT. Spin-to-orbital angular momentum conversion in a strongly focused optical beam. Phys Rev Lett 2007; 99(7): 073901. DOI: 10.1103/PhysRevLett.99.073901.
  15. Gross H, Singer W, Totzeck M. Handbook of optical systems; Vol 2. Wiley-VCH; 2005. ISBN: 978-3-527-40378-3.
  16. Golovashkin DL, Kazanskiy NL. Mesh Domain Decomposition in the Finite-Difference Solution of Maxwell’s Equations. Optical Memory & Neural Networks (Information Optics) 2009; 18(3). 203-211. DOI: 10.3103/S1060992X09030102.

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