• Photonics Research
  • Vol. 11, Issue 10, A54 (2023)
Julius Kullig1、*, Daniel Grom1、3, Sebastian Klembt2, and Jan Wiersig1
Author Affiliations
  • 1Institut für Physik, Otto-von-Guericke-Universität Magdeburg, 39106 Magdeburg, Germany
  • 2Technische Physik and Würzburg-Dresden Cluster of Excellence ct.qmat, Physikalisches Institut and Wilhelm-Conrad-Röntgen-Research Center for Complex Material Systems, Am Hubland, University of Würzburg, 97070 Würzburg, Germany
  • 3e-mail: daniel.grom@ovgu.de
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    DOI: 10.1364/PRJ.496414 Cite this Article Set citation alerts
    Julius Kullig, Daniel Grom, Sebastian Klembt, Jan Wiersig. Higher-order exceptional points in waveguide-coupled microcavities: perturbation induced frequency splitting and mode patterns[J]. Photonics Research, 2023, 11(10): A54 Copy Citation Text show less

    Abstract

    Exceptional points are degeneracies in the spectrum of non-Hermitian open systems where at least two eigenfrequencies and simultaneously the corresponding eigenstates of the Hamiltonian coalesce. Especially, the robust construction of higher-order exceptional points with more than two degenerate eigenfrequencies and eigenstates is challenging but yet worthwhile for applications. In this paper, we reconsider the formation of higher-order exceptional points through waveguide-coupled microring cavities and asymmetric backscattering. In this context, we demonstrate the influence of perturbations on the frequency splitting of the system. To generate higher-order exceptional points in a simple and robust way, a mirror-induced asymmetric backscattering approach is used. In addition to the exceptional-point enhanced sensing capabilities of such systems, also a cavity-selective sensitivity is achieved for particle sensing. The results are motivated by an effective Hamiltonian description and verified by full numerical simulations of the dielectric structure.
    H0=(ΩDDΩ),

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    HTP=(V+U(VU)ei2mϕTP(VU)ei2mϕTPV+U),

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    HTP(ϵ)ϵ(1ei2mϕTPei2mϕTP1),

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    ΔΩ=|Ω1Ω2|=2|D2+2Dϵcos(2mϕTP)+ϵ2|,

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    H0=(ΩDA0DΩ0000ΩD0ADΩ).

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    ΔΩ=maxi,j|ΩiΩj|,

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    H(1)(ϵ)=H0+HTP(1)(ϵ),

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    H(1+2)(ϵ)=H0+HTP(1)(ϵ)+HTP(2)(ϵ).

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    (Δ+n2k2)ψ(x,y)=0,

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    H0=(ΩDA000DΩ000000ΩDA00ADΩ000000ΩD+Rm000ADΩ),

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    H0=(ΩA00000ΩA00000ΩRm00000ΩA00000ΩA00000Ω),

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    H0=(ΩD000000DΩA0000000ΩD0A00A0DΩ0000000AΩD000000DΩA0000000ΩD+Rm0000A0DΩ).

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    If=18g=18cavity f|ψg(x,y)|2dxdy.

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    G(ω)=(ω1H)1,

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    R(ω)=|G21(ω)A|2.

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    G(ω)=k=12NMk1(ωΩEP)k,

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    H=H0+HTP(ϕTP=π/2),(A1)

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    M=12(11ii)(A2)

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    H˜H˜0=H˜TP=(2V002U),(A3)

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    V=12(ΩTP,1numΩ1num),U=12(ΩTP,2numΩ2num),(A4)

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    Ω=14i=14Ωinum.(B1)

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    f(χ)=i(min{σ}σ|Ωjeff(ζi,χ)Ωσ(j)num(ζi)|),(B2)

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    Julius Kullig, Daniel Grom, Sebastian Klembt, Jan Wiersig. Higher-order exceptional points in waveguide-coupled microcavities: perturbation induced frequency splitting and mode patterns[J]. Photonics Research, 2023, 11(10): A54
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