Energy backflow in a focal spot of the cylindrical vector beam
Stafeev S.S., Nalimov A.G., Kotlyar V.V.

 

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

 PDF

Abstract:
Using Richards-Wolf formulae it is shown that a tightly focused azimuthally-radially polarized m-th order laser beam with an arbitrary apodization function produces a reverse energy flow in the focal plane (m=2). If m=3, the reverse energy flow on the axis is equal to zero, increasing in the axis vicinity as the square of the distance to the axis. The azimuthally-radially polarized beam of the m-th order is an example of a polarization vortex. Previously, the reverse energy flow in the focus was obtained only for circularly polarized vortex beams with the topological charge m. Using the FDTD method and the Richards-Wolf formulae, we show numerically that in the focus of a zone plate such laser beams produce regions where the Poynting vector is opposite to the direction of the beam propagation.

Keywords:
Richards-Wolf formulae, FDTD-method, polarization vortex, energy backflow.

Citation:
Stafeev SS, Nalimov AG, Kotlyar VV. Energy backflow in a focal spot of the cylindrical vector beam. Computer Optics 2018; 42(5): 744-750. DOI: 10.18287/2412-6179-2018-42-5-744-750.

References:

  1. Zhan Q. Cylindrical vector beams: from mathematical concepts to applications. Adv Opt Photon 2009; 1(1): 1-57. DOI: 10.1364/AOP.1.000001.
  2. Xiaoqiang Z, Ruishan C, Anting W. Focusing properties of cylindrical vector vortex beams. Opt Commun 2018; 414: 10-15. DOI: 10.1016/j.optcom.2017.12.076.
  3. Han Y, Chen L, Liu YG, Wang Z, Zhang H, Yang K, Chou KC. Orbital angular momentum transition of light using a cylindrical vector beam. Opt Lett 2018; 43(9): 2146-2149. DOI: 10.1364/OL.43.002146.
  4. Matsusaka S, Kozawa Y, Sato S. Micro-hole drilling by tightly focused vector beams. Opt Lett 2018; 43(7): 1542-1545. DOI: 10.1364/OL.43.001542.
  5. Rashid M, Maragò OM, Jones PH. Focusing of high order cylindrical vector beams. J Opt A: Pure Appl Opt 2009; 11(6): 065204. DOI: 10.1088/1464-4258/11/6/065204.
  6. Li Y, Zhu Z, Wang X, Gong L, Wang M, Nie S. Propagation evolution of an off-axis high-order cylindrical vector beam. J Opt Soc Am A 2014; 31(11): 2356-2361. DOI: 10.1364/JOSAA.31.002356.
  7. Qi J, Wang W, Zhang H, Pan B, Deng H, Yang J, Shi B, Shan H, Zhang L, Wang H. Multiple-slit diffraction of high-polarization-order cylindrical vector beams. Proc SPIE 2017; 10339: 1033927. DOI: 10.1117/12.2271191.
  8. Wang X-L, Ding J, Ni W-J, Guo C-S, Wang H-T. Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement. Opt Lett 2007; 32(24): 3549-3551. DOI: 10.1364/OL.32.003549.
  9. Chen H, Hao J, Zhang BF, Xu J, Ding J, Wang HT. Generation of vector beam with space-variant distribution of both polarization and phase. Opt Lett 2011; 36(16): 3179-3181. DOI: 10.1364/OL.36.003179.
  10. Liu Y, Ke Y, Zhou J, Liu Y, Luo H, Wen S, Fan D. Generation of perfect vortex and vector beams based on Pancharatnam-Berry phase elements. Sci Rep 2017; 7: 44096. DOI: 10.1038/srep44096.
  11. Sukhov S, Dogariu A. On the concept of “tractor beams”. Opt Lett 2010; 35(22): 3847-3849. DOI: 10.1364/OL.35.003847.
  12. Richards B, Wolf E. Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 1959; 253(1274): 358-379. DOI: 10.1098/rspa.1959.0200.
  13. Kotlyar VV, Nalimov AG. A vector optical vortex generated and focused using a metalens. Computer Оptics 2017; 41(5): 645-654. DOI: 10.18287/2412-6179-2017-41-5-645-654.
  14. Stafeev SS, Nalimov AG. Longitudinal component of the Poynting vector of a tightly focused optical vortex with circular polarization. Computer Optics 2018; 42(2): 190-196. DOI: 10.18287/2412-6179-2018-42-2-190-196.
  15. Kovalev A, Kotlyar V, Nalimov A. Energy density and energy flux in the focus of an optical vortex: reverse flux of light energy. Opt Lett 2018; 43(12): 2921-2924. DOI: 10.1364/OL.43.002921.
  16. Monteiro PB, Neto PAM, Nussenzveig HM. Angular momentum of focused beams: Beyond the paraxial approximation. Phys Rev A 2009; 79(3): 033830. DOI: 10.1103/PhysRevA.79.033830.
  17. Rondón-Ojeda I, Soto-Eguibar F. Properties of the Poynting vector for invariant beams: Negative propa-gation in Weber beams. Wave Motion 2018; 78: 176-184. DOI: 10.1016/j.wavemoti.2018.02.003.
  18. Davidson N, Bokor N. High-numerical-aperture focusing of radially polarized doughnut beams with a parabolic mirror and a flat diffractive lens. Opt Lett 2004; 29(12): 1318-1320. DOI: 10.1364/OL.29.001318.
  19. Stafeev SS, Nalimov AG, Kotlyar MV, Gibson D, Song S, O’Faolain L, Kotlyar VV. Microlens-aided focusing of linearly and azimuthally polarized laser light. Opt Express 2016; 24(26): 29800-29813. DOI: 10.1364/OE.24.029800.
© 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