• Photonics Research
  • Vol. 9, Issue 7, 1280 (2021)
Yao Duan, Xingwang Zhang, Yimin Ding, and Xingjie Ni*
Author Affiliations
  • Department of Electrical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
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    DOI: 10.1364/PRJ.417296 Cite this Article Set citation alerts
    Yao Duan, Xingwang Zhang, Yimin Ding, Xingjie Ni, "Single-cavity bi-color laser enabled by optical anti-parity-time symmetry," Photonics Res. 9, 1280 (2021) Copy Citation Text show less

    Abstract

    The exploration of quantum inspired symmetries in optical systems has spawned promising physics and provided fertile ground for developing devices exhibiting exotic functionalities. Founded on the anti-parity–time (APT) symmetry that is enabled by both spatial and temporal interplay between gain and loss, we demonstrate theoretically and numerically bi-color lasing in a single micro-ring resonator with spatiotemporal modulation along its azimuthal direction. In contrast to conventional multi-mode lasers that have mixed-frequency output, our laser exhibits stable, demultiplexed, tunable bi-color emission at different output ports. Our APT-symmetry-based laser may point out a new route for realizing compact on-chip coherent multi-color light sources.
    H^(t)Ψ(t)=idΨ(t)dt,

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    Ψ(t)=(a1a2)eiωt,H^(t)=(ω0iκmeiωmtiκmeiωmtω0).

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    H^=(ωm/2iκmiκmωm/2).

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    ω1,2=±ωm24κm2,

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    Ψ1=(1iΔωκm),Ψ2=(1iκmΔω),

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    Δϵm(t,ϕ)=ω0m2ω0m22iΓmωω2cos(ωmtLmϕ)Δϵ.(A1)

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    ϵeff(ϕ,t)=Δϵmn=1Ncos(ωmtLmϕn)rect(ϕϕnΔϕ),(D1)

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    ϵeff(ϕ,t)=Δϵmk=(1)k(N1)sinc(Lm+kNN)cos[ωmt(Lm+kN)ϕ],(D2)

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    Δϵeff=Δϵmsinc(2lN).(D3)

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    da1dt=(iω01τ)a1+iκmeiωmta2+μ1s+1,(E1)

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    da2dt=(iω01τ)a2+iκmeiωmta2+μ2s+2.(E2)

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    s1=eiϕ1(s+1μ1*a1),(E3)

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    s2=eiϕ2(s+2μ2*a2),(E4)

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    T21(ω)=|s2s+1|2=|1+i(ωsωm)|μ|2(ωmωs)ωs+κm2|2,(E5)

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    T12(ω)=|s1s+2|2=|1+i(ωs+ωm)|μ|2(ωm+ωs)ωs+κm2|2,(E6)

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    Yao Duan, Xingwang Zhang, Yimin Ding, Xingjie Ni, "Single-cavity bi-color laser enabled by optical anti-parity-time symmetry," Photonics Res. 9, 1280 (2021)
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