• Photonics Research
  • Vol. 10, Issue 4, 947 (2022)
Qiang Zhang1, Zhenwei Xie1、2、*, Peng Shi1, Hui Yang1, Hairong He1, Luping Du1、3、*, and Xiaocong Yuan1、4、*
Author Affiliations
  • 1Nanophotonics Research Center, Shenzhen Key Laboratory of Micro-Scale Optical Information Technology & Institute of Microscale Optoelectronics, Shenzhen University, Shenzhen 518060, China
  • 2e-mail: ayst3_1415926@sina.com
  • 3e-mail: lpdu@szu.edu.cn
  • 4e-mail: xcyuan@szu.edu.cn
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    DOI: 10.1364/PRJ.447311 Cite this Article Set citation alerts
    Qiang Zhang, Zhenwei Xie, Peng Shi, Hui Yang, Hairong He, Luping Du, Xiaocong Yuan. Optical topological lattices of Bloch-type skyrmion and meron topologies[J]. Photonics Research, 2022, 10(4): 947 Copy Citation Text show less

    Abstract

    Optical skyrmions, quasiparticles that are characterized by the topologically nontrivial vectorial textures of optical parameters such as the electromagnetic field, Stokes parameters, and spin angular momentum, have aroused great attention recently. New dimensions for optical information processing, transfer, and storage have become possible, and developing multiple schemes for manipulating the topological states of skyrmions, thus, is urgent. Here we propose an approach toward achieving dynamic modulation of skyrmions via changing the field symmetry and adding chirality. We demonstrate that field symmetry governs the skyrmionic transformation between skyrmions and merons, whereas material chirality modulates the twist degree of fields and spins and takes control of the Néel-type–Bloch-type skyrmionic transition. Remarkably, the enantioselective twist of skyrmions and merons results from the longitudinal spin arising from the chirality-induced splitting of the hyperboloid in the momentum space. Our investigation, therefore, acts to enrich the portfolio of optical quasiparticles. The chiral route to topological state transitions will deepen our understanding of light–matter interaction and pave the way for chiral sensing, optical tweezers, and topological phase transitions in quantum matter.
    Ez=i=13[F+1ekz+(z+d)+F1ekz(z+d)+F+2ekz+(zd)+F2ekz(zd)]×eiφi+φi+32cos(kxix+kyiy+φiφi+32),

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    Sz=ε8ω{[a1+ekz+(z+d)+a2+ekz+(zd)]2+[a1kekz(z+d)+a2ekz(zd)]2}Sz0,

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    Sz0=cos(krx)+cos(3kry)+cos(12krx+32kry)+cos(12krx32kry)+cos(32krx+32kry)+cos(32krx32kry).

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    Sz=ε8ω[cos(krx+kry)+cos(krxkry)]×{[a1+ekz+(z+d)+a2+ekz+(zd)]2+[a1ekz(z+d)+a2ekz(zd)]2}.

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    F+x1=1kr2(kxkz++ikyk+)F+1eikz+(z+d)eiφ1eikxx+ikyy+1kr2(kxkz++ikyk+)F+2eikz+(zd)eiφ1eikxx+ikyy,F+y1=1kr2(ikxk++kykz+)F+1eikz+(z+d)eiφ1eikxx+ikyy+1kr2(ikxk+kykz+)F+2eikz+(zd)eiφ1eikxx+ikyy,F+z1=F+1eikz+(z+d)eiφ1eikxx+ikyy+F+2eikz+(zd)eiφ1eikxx+ikyy.(A1)

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    Fx1=1kr2(kxkz+ikyk)F1eikz(z+d)eiφ1eikxx+ikyy+1kr2(kxkz+ikyk)F2eikz(zd)eiφ1eikxx+ikyy,Fy1=1kr2(ikxk++kykz)F1eikz(z+d)eiφ1eikxx+ikyy+1kr2(ikxkkykz)F2eikz(zd)eiφ1eikxx+ikyy,Fz1=F1eikz(z+d)eiφ1eikxx+ikyy+F2eikz(zd)eiφ1eikxx+ikyy.(A2)

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    Ex=1kr2i=13[F+1(kxikz+kyik+)ekz+(z+d)+F1(kxikz+kyik)ekz(z+d)+F+2(kxikz+kyik+)ekz+(zd)+F2(kxikz+kyik)ekz(zd)]×eiφi+φi+32sin(kxix+kyiy+φiφi+32),Ey=1kr2i=13[F+1(k+kxi+kyikz+)ekz+(z+d)+F1(kkxi+kyikz)ekz(z+d)+F+2(k+kxikyikz+)ekz+(zd)+F2(kkxikyikz)ekz(zd)]×eiφi+φi+32sin(kxix+kyiy+φiφi+32).(A3)

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    Ex=1kr2i=13[2F+(krsinθik+)+2F(krsinθik)]×sin(krcosθix+krrsinθiy),Ey=1kr2i=13[2F+(k+krcosθi)+2F(kkrcosθi)]×sin(krcosθix+krsinθiy).(A4)

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    F±=f±(r)exp[i(kz±zω0t+lφ)],(B1)

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    ×F±=±k±F±,2F±+k±2F±=0(B2)

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    2F±r2r2F±φφF±rr2+k±2F±r=0,(B3a)

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    2F±φ+2r2F±rφF±φr2+k±2F±φ=0,(B3b)

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    2F±z+k±2F±z=0.(B3c)

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    1rr(rf±zr)+(k±2kz±2l2r2)f±z=0,(B4)

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    f±z=a±Jl(krr)eilφeiω0teikz±z,(B5)

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    ψ(r,t)02πei[k||z+kcos(ϕ)x+ksin(ϕ)y+lϕω0t]dϕJl(kr)exp(ik||z+ilφiω0t),(B6)

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    ψ(r,t)=a+02πei[k||+z+kcos(ϕ)x+ksin(ϕ)y+lϕω0t]dϕ+a02πei[k||z+kcos(ϕ)x+ksin(ϕ)y+lϕω0t]dϕ=[a+Jl(kr)exp(ik||+z+ilφiω0t)+aJl(kr)exp(ik||z+ilφiω0t)],(B7)

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    2F±z+k±2F±z=0(C1)

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    2ΨXY±x2+2ΨXY±y2+kr2ΨXY±=0,(C2)

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    ΨXY±(x+Lx,y)=ΨXY±(x,y),ΨXY±(x,y+Ly)=ΨXY±(x,y),(C3)

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    Rz(α)ΨXY±[Rz(α)r]=eilαΨXY±(r).(C4)

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    Fy=a1ekz(z+d)1kr{kz[eiπ3cos(12krx+32kry)eiπ3cos(12krx32kry)]+13k[eiπ3cos(12krx+32kry)+eiπ3cos(12krx32kry)+2cos(krx)]}+a2ekz(zd)1kr{kz[eiπ3cos(12krx+32kry)eiπ3cos(12krx32kry)]+13k[eiπ3cos(12krx+32kry)+eiπ3cos(12krx32kry)+2cos(krx)]},(C5)

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    Sx=ε8ωkr×{[a1+2kz+e2kz+(z+d)+a12kze2kz(z+d)a2+2kz+e2kz+(zd)a22kze2kz(zd)]Sx013{[a1+ekz+(z+d)+a2+ekz+(zd)]2k+[a12kekz(z+d)+a2ekz(zd)]2k}Sy0},Sy=ε8ωkr×{{[a1+ekz+(z+d)+a2+ekz+(zd)]2k+[a12kekz(z+d)+a2ekz(zd)]2k}Sx0+13[a1+2kz+e2kz+(z+d)+a12kze2kz(z+d)a2+2kz+e2kz+(zd)a22kze2kz(zd)]Sy0},(C6)

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    Sx0=2sin(krx)+sin(12krx+32kry)+sin(12krx32kry)+sin(32krx+32kry)+sin(32krx32kry),Sy0=2sin(3kry)+sin(32krx+32kry)sin(32krx32kry)+3sin(12krx+32kry)3sin(12krx32kry).(C7)

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    F+z=[a1+ekz+(z+d)+a2+ekz+(zd)]×[isin(krx)sin(kry)],Fz=[a1ekz(z+d)+a2ekz(zd)]×[isin(krx)sin(kry)].(D1)

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    Sx,y=ε8ωkr{{sin(krx+kry)×[a1+2kz+e2kz+(z+d)+a12kze2kz(z+d)a2+2kz+e2kz+(zd)a22kze2kz(zd)]{[a1+ekz+(z+d)+a2+ekz+(zd)]2k+[a12kekz(z+d)+a2ekz(zd)]2k}}+sin(krxkry)×{±[a1+2kz+e2kz+(z+d)+a12kze2kz(z+d)a2+2kz+e2kz+(zd)a22kze2kz(zd)]+{[a1+ekz+(z+d)+a2+ekz+(zd)]2k+[a12kekz(z+d)+a2ekz(zd)]2k}}},(D2)

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    Qiang Zhang, Zhenwei Xie, Peng Shi, Hui Yang, Hairong He, Luping Du, Xiaocong Yuan. Optical topological lattices of Bloch-type skyrmion and meron topologies[J]. Photonics Research, 2022, 10(4): 947
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