Spin density of tightly focused hybrid-order Poincaré beams

doi:10.3969/j.issn.1000-5641.201922012

Abstract

Abstract: Research on spin of Poincaré beams not only has practical engineering applications, but is also important for understanding the nature of light. In this paper, we study the spin density of the tightly focused hybrid-order Poincaré beams (TFPB) and find that it has both longitudinal and transverse components. Unlike tightly focused full Poincaré beams whose longitudinal spin density is on average zero, the total longitudinal spin density of tightly focused hybrid-order Poincaré beams is not zero. The spin density of TFPB has rich controllable spatial patterns; in particular, the longitudinal spin density can be either a ring shape or a regular polygon. These features can be used to separate chiral particles or to manipulate dynamics of ultracold spinot gases.

Key words: hybrid-order Poincaré beams, tightly focused, spin density

CLC Number:

O436.1

SUN Hong, DONG Guangjiong. Spin density of tightly focused hybrid-order Poincaré beams[J]. Journal of East China Normal University(Natural Science), 2020, 2020(2): 70-75.

References

[1] POINCARÉ H. Leçons sur la théorie mathématique de la lumière. Théorie mathématique de la lumière. II, Nouvellesétudes sur la diffraction, théorie de la dispersion de Helmholtz:Leçons professées pendant le premier semestre 1891-1892[R].[S.l.]: LAMOTTE M, HURMUZESCU D, 1892.
[2] BORN M, WOLF E. Principles of Optics[M]. 6th ed. New York:Pergamon Press, 1980.
[3] HOLBOURN A H S. Angular momentum of circularly polarised light[J]. Nature, 1936, 137(3453):31. DOI:10.1038/137031a0.
[4] YAO A M, PADGETT M J. Orbital angular momentum:Origins, behavior and applications[J]. Advances in Optics and Photonics, 2011, 3(2):161-204. DOI:10.1364/AOP.3.000161.
[5] MILIONE G, SZTUL H I, NOLAN D A, et al. Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light[J]. Physical Review Letters, 2011, 107(5):053601. DOI:10.1103/PhysRevLett.107.053601.
[6] YI X N, LIU Y C, LING X H, et al. Hybrid-order Poincaré sphere[J]. Physical Review A, 2015, 91(2):023801. DOI:10.1103/PhysRevA.91.023801.
[7] GU M. Advanced Optical Imaging Theory[M]. Heidelberg:Springer, 2006.
[8] WOLF E. Electromagnetic diffraction in optical systems-I. An integral representation of the image field[J]. Proceedings of the Royal Society A, 1959, 253(1274):349-357. DOI:10.1098/rspa.1959.0199.
[9] RICHARDS B, WOLF E. Electromagnetic diffraction in optical systems, II. Structure of the image field in an aplanatic system[J]. Proceedings of the Royal Society A, 1959, 253(1274):358-379. DOI:10.1098/rspa.1959.0200.
[10] EHMKE T, NITZSCHE T H, KNEBL A, et al. Molecular orientation sensitive second harmonic microscopy by radially and azimuthally polarized light[J]. Biomedical Optics Express, 2014, 5(7):2231-2246. DOI:10.1364/BOE.5.002231.
[11] BEKSHAEV A Y. Corrigendum:Subwavelength particles in an inhomogeneous light field:optical forces associated with the spin and orbital energy flows[J]. Journal of Optics, 2016, 18(2):029501. DOI:10.1088/2040-8978/18/2/029501.
[12] DAI X B, LI Y Q, LIU L H. Tight focusing properties of hybrid-order Poincaré sphere beams[J]. Optics Communications, 2018, 426:46-53. DOI:10.1016/j.optcom.2018.05.017.
[13] LERMAN G, STERN L, LEVY U. Generation and tight focusing of hybridly polarized vector beams[J]. Optics Express, 2010, 18(26):27650-7. DOI:10.1364/OE.18.027650.
[14] CHEN R, AGARWAL K, SHEPPARD C J, et al. Imaging using cylindrical vector beams in a high-numerical-aperture microscopy system[J]. Optics Letters, 2013, 38(16):3111-3114. DOI:10.1364/OL.38.003111.
[15] JESACHER A, FÜRHAPTER S, BERNET S, et al. Size selective trapping with optical "cogwheel" tweezers[J]. Optics Express, 2004, 12(17):4129-4135. DOI:10.1364/OPEX.12.004129.
[16] HNATOVSKY C, SHVEDOV V, KROLIKOWSKI W, et al. Revealing local field structure of focused ultrashort pulses[J]. Physical Review Letters, 2011, 106(12):123901. DOI:10.1103/PhysRevLett.106.123901.
[17] ALLEN L, BEIJERSBERGEN M W, SPREEUW R J C, et al. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes[J]. Physical Review A, 1992, 45(11):8185. DOI:10.1103/PhysRevA.45.8185.
[18] ALLEN L, PADGETT M J, BABIKER M. IV The orbital angular momentum of light[J]. Progress in Optics, 1999, 39(C):291-372. DOI:10.1016/S0079-6638(08)70391-3.
[19] ZHAO Y, EDGAR J S, JEFFRIES G D, MCGLOIN D, & CHIU D T. Spin-to-orbital angular momentum conversion in a strongly focused optical beam[J]. Physical Review Letters, 2007, 99(7):073901. DOI:10.1103/PhysRevLett.99.073901.
[20] BEKSHAEV A Y, SOSKIN M S, VASNETSOV M V. Transformation of higher-order optical vortices upon focusing by an astigmatic lens[J]. Optics Communications, 2004, 241(4/5/6):237-247. DOI:10.1016/j.optcom.2004.07.023.
[21] AIELLO A, BANZER P, NEUGEBAUER M, et al. From transverse angular momentum to photonic wheels[J]. Nature Photonics, 2015, 9(12):789-795. DOI:10.1038/nphoton.2015.203.
[22] ZHU W, SHVEDOV V, SHE W, et al. Transverse spin angular momentum of tightly focused full Poincaré beams[J]. Optics express, 2015, 23(26):34029-34041. DOI:10.1364/OE.23.034029.
[23] BRADSHAW D S, ANDREWS D L. Chiral discrimination in optical trapping and manipulation[J]. New Journal of Physics, 2014, 16(10):103021. DOI:10.1088/1367-2630/16/10/103021.
[24] LE KIEN F, SCHNEEWEISS P, RAUSCHENBEUTEL A. Dynamical polarizability of atoms in arbitrary light fields:General theory and application to cesium[J]. The European Physical Journal D, 2013, 67 Article number:92. DOI:10.1140/epjd/e2013-30729-x.
[25] DING K, NG J, ZHOU L, et al. Realization of optical pulling forces using chirality[J]. Physical Review A, 2014, 89(6):063825. DOI:10.1103/PhysRevA.89.063825.
[26] WEYRAUCH M, RAKOV M V. Dimerization in ultracold spinor gases with Zeeman splitting[J]. Physical Review B, 2017, 96:134404. DOI:10.1103/PhysRevB.96.134404.