• Laser & Optoelectronics Progress
  • Vol. 59, Issue 7, 0726001 (2022)
Fan Huang and Xinting Jia*
Author Affiliations
  • College of Science, Wuhan University of Technology, Wuhan , Hubei 430070, China
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    DOI: 10.3788/LOP202259.0726001 Cite this Article Set citation alerts
    Fan Huang, Xinting Jia. Spin-Orbit Coupling of Laguerre-Gaussian Beams on High-Order Poincaré Sphere in Near Field[J]. Laser & Optoelectronics Progress, 2022, 59(7): 0726001 Copy Citation Text show less

    Abstract

    The research of optical angular momentum and spin-orbit coupling under non-paraxial conditions will help people understand the phenomenon of light in sub-wavelength structures. The evanescent wave in the near field may produce strong spin-orbit coupling. In this paper, based on the angle spectrum diffraction theory and Parseval theorem, the near field evolution characteristics of propagating waves, evanescent waves and angular momentum of Laguerre-Gaussian vector vortex beams on high-order Poincaré sphere are analyzed in detail, as well as the spin-orbit coupling caused by evanescent waves. The results show that the evanescent wave action near the source plane of the beam with sub-wavelength waist width is strong, and dominates the total optical field. Moreover, the orbital angular momentum contains the contributions of both the transverse and longitudinal electric fields in the near field, and the transverse spin angular momentum in the evanescent wave is related to the transverse polarization state, furthermore there is a phenomenon of spin direction locking. The research provides a theoretical support for the study and application of vector vortex beams in sub-wavelength structures.
    ψθ,ϕ=cos π4-θLmexp-iϕ+sin π4-θRmexpiϕ
    E(x0,y0,0) =Ex(x0,y0,0)Ey(x0,y0,0)=E02ρ0w0mLnm2ρ02w02exp-ρ02w02cos(mφ0+ϕ)cos θ-isin(mφ0+ϕ)sin θsin(mφ0+ϕ)cos θ+icos(mφ0+ϕ)sin θ
    E(r)=-+Ax(p,q)ex+Ay(p,q)ey-ezγpAx(p,q)+qAy(p,q)×expik(px+qy+γz)dpdq
    Axp,q=1λ2-+Ex(x0,y0,0)exp-ik(px0+qy0)dx0dy0=i2n+2m+mπE0λ2kb2w0mw02m+2Lnmk2b2w022exp-k2b2w024×cos mϕ0+ϕcos θ-isinmϕ0+ϕsin θ,
    Ayp,q=1λ2-+Ey(x0,y0,0)exp-ik(px0+qy0)dx0dy0=i2n+2m+mπE0λ2kb2w0mw02m+2Lnmk2b2w022exp-k2b2w024×sin mϕ0+ϕcos θ+icosmϕ0+ϕsin θ,
    E(r)=i2n+3m+mE02kw02m+20+bm+1Lnmk2b2w022expikγz-k2b2w024×1-icos mφ+ϕ-θ+1+icos mφ+ϕ+θJmkρbex+1-isin mφ+ϕ-θ+1+isin mφ+ϕ+θJmkρbey+bγ1+icos mφ-φ+ϕ-θ-1-icos mφ-φ+ϕ+θJm-1kρbezdb
    E(r)=i2n+3m+mE0kw02m+20+bm+1Lnmk2b2w022expikγz-k2b2w024×cosmφ+ϕJmkρbex+sinmφ+ϕJmkρbey+bγicosmφ-φ+ϕJm-1kρbezdb
    Ipr=Epr2dxdy=π01C22-b2b1-b2db
    Iev=Eev2dxdy=π1C23b2-2bb2-1×exp-2kzb2-1db
    P=12ReE*r×Hr=14μ0ωIm×E*×E+12μ0ωImE*E
    S=12μ0ωImE*×E
    Lz=12μ0ωImr×E*Eez
    Fan Huang, Xinting Jia. Spin-Orbit Coupling of Laguerre-Gaussian Beams on High-Order Poincaré Sphere in Near Field[J]. Laser & Optoelectronics Progress, 2022, 59(7): 0726001
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