• Photonics Research
  • Vol. 10, Issue 1, 41 (2022)
Caifu Fan1, Xi Shi2、4、*, Feng Wu3, Yunhui Li1, Haitao Jiang1, Yong Sun1、5、*, and Hong Chen1
Author Affiliations
  • 1MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
  • 2Department of Physics, Shanghai Normal University, Shanghai 200234, China
  • 3School of Optoelectronic Engineering, Guangdong Polytechnic Normal University, Guangzhou 510665, China
  • 4e-mail: xishi@shnu.edu.cn
  • 5e-mail: yongsun@tongji.edu.cn
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    DOI: 10.1364/PRJ.441278 Cite this Article Set citation alerts
    Caifu Fan, Xi Shi, Feng Wu, Yunhui Li, Haitao Jiang, Yong Sun, Hong Chen. Photonic topological transition in dimerized chains with the joint modulation of near-field and far-field couplings[J]. Photonics Research, 2022, 10(1): 41 Copy Citation Text show less

    Abstract

    Topological systems containing near-field or far-field couplings between unit cells have been widely investigated in quantum and classic systems. Their band structures are well explained with theories based on tight-binding or multiple scattering formalism. However, characteristics of the topology of the bulk bands based on the joint modulation of near-field and far-field couplings are rarely studied. Such hybrid systems are hardly realized in real systems and cannot be described by neither tight-binding nor multiple scattering theories. Here, we propose a hybrid-coupling photonic topological insulator based on a quasi-1D dimerized chain with the coexistence of near-field coupling within the unit cell and far-field coupling among all sites. Both theoretical and experimental results show that topological transition is realized by introducing near-field coupling for given far-field coupling conditions. In addition to closing and reopening the bandgap, the change in near-field coupling modulates the effective mass of photonics in the upper band from positive to negative, leading to an indirect bandgap, which cannot be achieved in conventional dimerized chains with either far-field or near-field coupling only.
    a˜˙n=(iω0γ)a˜n+Cb˜n+iγeikL(1Δ)/2S˜L++iγeikL(1+Δ)/2S˜R+,

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    b˜˙n=(iω0γ)b˜n+Ca˜n+iγeikL(1+Δ)/2S˜L++iγeikL(1Δ)/2S˜R+,

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    (SLSR)=(trrt)(SR+SL+).

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    (SL+SL)=(1trRtrLtt2rLrRt)(SRSR+)=T(SRSR+).

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    t=eikL+[iγeikL(1+Δ)/2an+iγeikL(1Δ)/2bn]/SL+,

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    r=[iγeikL(1Δ)/2an+iγeikL(1+Δ)/2bn]/SL+.

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    |S(eiqL00eiqL)|=0,

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    θnZak=π/Lπ/L[iL/2L/2dxε(x)un,q*(x)qun,q(x)]dq,

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    sgn[arg(rn)]=(1)n(1)pexp(im=1nθmZak),

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    (En+1Hn+1)=M(EnHn),(A1)

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    M=PTP1,(A2)

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    En+1Hn+1=EnHn=Z.(A3)

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    Z=M11M22±(M11M22)2+4M21M122M21.(A4)

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    r=ZZ0Z+Z0.(A5)

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    t1=[cos(nkL)i2(Z+1Z)sin(nkL)]eikL,(B1)

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    rt=i2(Z1Z)sin(nkL).(B2)

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    Z=±(1+r)2t2(1r)2t2.(B3)

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    Im(n)=±Im{arccos{12t[1(r2t2)]}kL},(B4)

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    Re(n)=±Re{arccos{12t[1(r2t2)]}kL}+2πmkL,(B5)

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    a˜˙1=(iω0γΓ)a˜1+iγeikL/2S˜L+,(C1)

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    r1=iγeikL/2a1/SL+.(C2)

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    Caifu Fan, Xi Shi, Feng Wu, Yunhui Li, Haitao Jiang, Yong Sun, Hong Chen. Photonic topological transition in dimerized chains with the joint modulation of near-field and far-field couplings[J]. Photonics Research, 2022, 10(1): 41
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