• Photonics Research
  • Vol. 13, Issue 5, 1365 (2025)
Tian Xia1, Jia Ma1, Zhenwei Xie1,2,*, and Xiaocong Yuan1,3,*
Author Affiliations
  • 1Nanophotonics Research Centre, Institute of Microscale Optoelectronics & State Key Laboratory of Radio Frequency Heterogeneous Integration, Shenzhen University, Shenzhen 518060, China
  • 2e-mail: ayst31415926@szu.edu.cn
  • 3e-mail: xcyuan@szu.edu.cn
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    DOI: 10.1364/PRJ.541783 Cite this Article Set citation alerts
    Tian Xia, Jia Ma, Zhenwei Xie, Xiaocong Yuan, "Symmetric and asymmetric Hall effect-like splitting of optical Stokes skyrmions via a hybrid multi-zone filter," Photonics Res. 13, 1365 (2025) Copy Citation Text show less

    Abstract

    In recent years, optical skyrmions have garnered increasing attention for their ability to introduce new degrees of freedom in manipulating optical fields. While most research has focused on creating innovative optical topological states such as merons and hopfions, there has been limited exploration into their manipulation, which hinders practical applications in this field. In this study, we utilize a hybrid multi-zone filter to induce a Hall effect-like splitting of optical Stokes skyrmions (HESSs), enabling effective separation and manipulation. By manipulating the horizontal phase gradient parameter, we independently control the separation angle of skyrmions. Additionally, we demonstrate control over the topological charge parameter to achieve symmetric and asymmetric HESSs. This effect not only enhances the manipulation capabilities of optical fields but also opens up potential applications for high precision displacement measurements and preservation quantum information.
    φ=(l1θ+β1kx/f)·fMZF1+(l2θ+β2kx/f)·fMZF2,

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    fMZF1={1(i1)R/Nr(i1+α)R/N0else,

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    fMZF2=fCFfMZF1,

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    fCF={10rR0else,

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    U(ρ,ψ,z)=ifλ0α02πB(θ,φ)T(θ)P(θ,φ)exp{ik[ρsinθcos(φψ)+zcosθ]}sinθdθdφ.

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    P(θ,φ)=[1+cos2φ(cosθ1)sinφcosφ(cosθ1)sinθcosφ]a(θ,φ)+[sinφcosφ(cosθ1)1+sin2φ(cosθ1)sinθsinφ]b(θ,φ),

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    E=B(θ,φ)exp(ilφ)[cos(mφ+π2)sin(mφ+π2)].

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    Ex=ilm12ei(lφmφπ2)(I0,lm+ei2φI2,lm+2)+il+m12ei(lφ+mφ+π2)(I0,l+m+ei2φI2,l+m2),Ey=ilm2ei(lφmφπ2)(I0,lmei2φI2,lm+2)+il+m2ei(lφ+mφ+π2)(I0,l+m+ei2φI2,l+m2),Ez=ilmei(lφmφπ2)(eiφI1,lm+1)il+mei(lφ+mφ+π2)(eiφI1,l+m1).

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    EL=12(Ex+iEy),ER=12(ExiEy),S3=|EL|2|ER|2=12(|I0,l+m+I2,lm+2|2|I0,lm+I2,l+m2|2),

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    I0,ν=(πfλ)0αsinθcos1/2θ(1+cosθ)×A(θ)eikzcosθJν(x)dθ,I1,ν=(πfλ)0αsin2θcos1/2  θA(θ)eikzcosθJν(x)dθ,I2,ν=(πfλ)0αsinθcos1/2θ(1cosθ)×A(θ)eikzcosθJν(x)dθ.

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    n=14πM·(Mx×My)dxdy,

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    AP=ei(φ+φ){ei(φ+π2)[1i]+ei(φπ2)[1i]}=(eiφ·eiφ){ei(φ+π2)[1i]+ei(φπ2)[1i]}=(SP1·SP1)AP,(D1)

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    SP1AP=eiφ{ei(φ+π2)[1i]+ei(φπ2)[1i]}=ei(2φ+π2)[1i]+eiπ2[1i]=|2,1+|0,1,(D2)

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    SP1AP=eiφ{ei(φ+π2)[1i]+ei(φπ2)[1i]}=eiπ2[1i]+ei(2φπ2)[1i]=|0,1+|2,1.(D3)

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    Tian Xia, Jia Ma, Zhenwei Xie, Xiaocong Yuan, "Symmetric and asymmetric Hall effect-like splitting of optical Stokes skyrmions via a hybrid multi-zone filter," Photonics Res. 13, 1365 (2025)
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