• Photonics Research
  • Vol. 11, Issue 6, 1085 (2023)
Xiaofeng Wang1, Jiafu Wang1,2,*, Yajuan Han1, Mingbao Yan1..., Yongfeng Li1, Tonghao Liu1, Hua Ma1 and Shaobo Qu1,3,*|Show fewer author(s)
Author Affiliations
  • 1Shaanxi Key Laboratory of Artificially-Structured Functional Material and Devices, Air Force Engineering University, Xi’an 710051, China
  • 2e-mail: wangjiafu1981@126.com
  • 3e-mail: qushaobo@mail.xjtu.edu.cn
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    DOI: 10.1364/PRJ.481821 Cite this Article Set citation alerts
    Xiaofeng Wang, Jiafu Wang, Yajuan Han, Mingbao Yan, Yongfeng Li, Tonghao Liu, Hua Ma, Shaobo Qu, "Leaky cavity modes in metasurfaces: a route to low-loss wideband anomalous dispersion," Photonics Res. 11, 1085 (2023) Copy Citation Text show less

    Abstract

    Metasurfaces have provided unprecedented degrees of freedom in manipulating electromagnetic waves upon interfaces. In this work, we first explore the condition of wide operating bandwidth in the view of reflective scheme, which indicates the necessity of anomalous dispersion. To this end, the leaky cavity modes (LCMs) in the meta-atom are analyzed and can make effective permittivity inversely proportional to frequency. Here we employ the longitudinal Fabry–Perot (F-P) resonances and transverse plasmonic resonances to improve the LCMs efficiency. It is shown that the order of F-P resonance can be customized by the plasmonic modes, that is, the F-P cavity propagation phase should match the phase delay of surface currents excited on the meta-atom. The nth order F-P resonance will multiply the permittivity by a factor of n, allowing larger phase accumulation with increasing frequencies and forming nonlinear phase distribution which can be applied in weak chromatic-aberration focusing design. As a proof-of-concept, we demonstrate a planar weak chromatic-aberration focusing reflector with a thickness of λ0/9 at 16.0–21.0 GHz. This work paves a robust way to advanced functional materials with anomalous dispersion and can be extended to higher frequencies such as terahertz, infrared, and optical frequencies.
    ES=E0ejωtγz(1+r0e2γz).

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    Re(Es)=E0[e2δz+e2δz+2cos(4πz/λ)]1/2.

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    ω=c·acos[1/2(A2e2δze2δz)]/z,

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    δ=ωcμε12[tanθetanθm1+(1+tan2θe)(1+tan2θm)],

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    Δφ=4πzλ0neff.

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    φ=4nπzλ0εeff(ω),

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    η=PfocPinc=PrefPinc×PfocPref=|Rrr|2PfocPref.

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    {n=cv=λsλvεeffμeff=n.(A1)

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    φ(np,ki)=φ(0,ki)+2πfc[(np)2+F2F],(B1)

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    {j=01j!((j)φnf(j)(j)φn=0f(j))|f=0fj=ρnfρn=2πc[(np)2+F2F].(B2)

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    {(φnfφn=0f)|f=0=ρn((j)φnf(j)(j)φn=0f(j))|f=0=0,jN,j0.(B3)

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    d2xdt2+γdxdt+ω02x=qE0m.(B4)

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    d2xdt2+γdxdt+ω02x=qE0eiαm.(B5)

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    x=qE0eiα/mω02ω2+jγω.(B6)

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    χe=Nq2eiαε0m(ω02ω2+iγω).(B7)

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    Re(χe)=C[(ω02ω2)2cosα+γωsinα],C=Nq2(ω02ω2)ε0m[(ω02ω2)2+γ2ω2].(B8)

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    Re(χe)=Nq2ω02cosα/ε0m.(B9)

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    εeff=Nq2ω02(cosα+ε0m)/ε0m.(B10)

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    {φ(R,k)=2α(R)+2kdneff,α(0,π)neff=εeff=qω0(N/ε0m)2cos2(α/2)1.(B11)

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    Xiaofeng Wang, Jiafu Wang, Yajuan Han, Mingbao Yan, Yongfeng Li, Tonghao Liu, Hua Ma, Shaobo Qu, "Leaky cavity modes in metasurfaces: a route to low-loss wideband anomalous dispersion," Photonics Res. 11, 1085 (2023)
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