• Photonics Research
  • Vol. 11, Issue 7, 1162 (2023)
Xinmin Fu1、†, Jie Yang1、2、†, Jiafu Wang1、2、3、*, Yajuan Han1、4、*, Chang Ding1, Tianshuo Qiu1, Bingyue Qu2, Lei Li1, Yongfeng Li1, and Shaobo Qu1
Author Affiliations
  • 1Shaanxi Key Laboratory of Artificially-Structured Functional Materials and Devices, Air Force Engineering University, Xi’an 710051, China
  • 2School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an 710049, China
  • 3e-mail: wangjiafu1981@126.com
  • 4e-mail: mshyj_mail@126.com
  • show less
    DOI: 10.1364/PRJ.473698 Cite this Article Set citation alerts
    Xinmin Fu, Jie Yang, Jiafu Wang, Yajuan Han, Chang Ding, Tianshuo Qiu, Bingyue Qu, Lei Li, Yongfeng Li, Shaobo Qu. Completely spin-decoupled geometric phase of a metasurface[J]. Photonics Research, 2023, 11(7): 1162 Copy Citation Text show less

    Abstract

    Metasurfaces have provided an unprecedented degree of freedom (DOF) in the manipulation of electromagnetic waves. A geometric phase can be readily obtained by rotating the meta-atoms of a metasurface. Nevertheless, such geometric phases are usually spin-coupled, with the same magnitude but opposite signs for left- and right-handed circularly polarized (LCP and RCP) waves. To achieve independent control of LCP and RCP waves, it is crucial to obtain spin-decoupled geometric phases. In this paper, we propose to obtain completely spin-decoupled geometric phases by engineering the surface current paths on meta-atoms. Based on the rotational Doppler effect, the rotation manner is first analyzed, and it is found that the generation of a geometric phase lies in the rotation of the surface current paths on meta-atoms. Since the induced surface current paths under the LCP and RCP waves always start oppositely and are mirror-symmetrical with each other, it is natural that the geometric phases have the same magnitude and opposite signs when the meta-atoms are rotated. To obtain spin-decoupled geometric phases, the induced surface current under one spin should be rotated by one angle while the current under the other spin is rotated by a different angles. In this way, LCP and RCP waves can acquire different geometric phase changes. Proof-of-principle prototypes were designed, fabricated, and measured. Both the simulation and experiment results verify spin-decoupled geometric phases. This work provides a robust means to obtain a spin-dependent geometric phase and can be readily extended to higher frequency bands such as the terahertz, IR, and optical regimes.
    φ=Δωdt=σΩzdt,

    View in Article

    φ=2στχ=2δχ,

    View in Article

    {φR=2(β140)+2α,40°β1220°φL=2α,0°α180°,

    View in Article

    |LPθ=[cosθsinθ]=22{12[1i]eiθ+12[1i]eiθ}=22(eiθ|L+eiθ|R),

    View in Article

    {B=0E=ρε0×E=Bt×B=μ0(ε0Et+J).(A1)

    View in Article

    {t=tr=r=F=F.(A2)

    View in Article

    {ρ=ρJ=Jρυ.(A3)

    View in Article

    F=ρE=F=ρ(E+υ×B).(A4)

    View in Article

    E=E+υ×B.(A5)

    View in Article

    B=B.(A6)

    View in Article

    dAdt=(dAdt)+Ω×A.(A7)

    View in Article

    dAdt=At+υA.(A8)

    View in Article

    (dAdt)=(At).(A9)

    View in Article

    At=(At)+Ω×A(υ)A.(A10)

    View in Article

    Ω×A=Ω×(A)r=(A)(Ω×r)=(A)υ,(A11)

    View in Article

    ×(υ×A)=(A)υ(υ)A+(A)υ(υ)A=Ω×A+υ(A)(υ)A.(A12)

    View in Article

    At+(A)υ=(At)+×(υ×A).(A13)

    View in Article

    B=0,(A14)

    View in Article

    E=(E+υ×B)=ρε0+2ΩBυ(×B).(A15)

    View in Article

    Bt=(Bt)+×(υ×B)=Bt+×(υ×B),(A16)

    View in Article

    Et+ρυε0=(Et)+×(υ×E)=(Eυ×B)t+×[υ×(Eυ×B)]=Etυ×Bt+×[υ×(Eυ×B)].(A17)

    View in Article

    ×E=×(E+υ×B)=Bt+×(υ×B)=Bt,(A18)

    View in Article

    ×B=×B=μ0(ε0Et+J)=μ0ε0[(Et)ρυε0+×(υ×E)]+μ0J=μ0ε0{(Eυ×B)t+×[υ×(Eυ×B)]}+μ0J=μ0J+μ0ε0(Et)μ0ε0υ×Bt+μ0ε0×[υ×(Eυ×B)]μ0J+μ0ε0(Et)μ0ε0υ×Bt+μ0ε0×(υ×E).(A19)

    View in Article

    {B=0E=2ΩBυ(×B)×E=Bt×B=μ0ε0(Et)μ0ε0υ×Bt+μ0ε0(υ×E).(A20)

    View in Article

    2Eμε2Et2+2μεt[(υ)EΩ×E]2(ΩB)=0.(A21)

    View in Article

    (υ)E=υxEx+υyEy+υzEz0,(A22)

    View in Article

    2(ΩB)=2(ΩxBx)xx^+2(ΩyBy)yy^+2(ΩzBz)zz^0,(A23)

    View in Article

    Ω×E=(ΩyEzΩzEy)x^+(ΩzExΩxEz)y^+(ΩxEyΩyEx)z^ΩzEyx^+ΩzExy^=Ωz(z^×E)(A24)

    View in Article

    2Eμε2Et2+2μεt[Ωz(z^^×E)]=0.(A25)

    View in Article

    {E=EL+EREL=ELx^+iy^2=Ex+iEy2x^+iy^2ER=ERx^iy^2=ExiEy2x^iy^2.(A26)

    View in Article

    2Eσ+ω02Eσc2+2ωσΩzc2Eσ=0,(A27)

    View in Article

    2Eσ+(ω0+σΩzc)2Eσ=0.(A28)

    View in Article

    ω=ω0+σΩz.(A29)

    View in Article

    φ=(ωω0)dt=σΩzdt.(A30)

    View in Article

    Xinmin Fu, Jie Yang, Jiafu Wang, Yajuan Han, Chang Ding, Tianshuo Qiu, Bingyue Qu, Lei Li, Yongfeng Li, Shaobo Qu. Completely spin-decoupled geometric phase of a metasurface[J]. Photonics Research, 2023, 11(7): 1162
    Download Citation