• Photonics Research
  • Vol. 6, Issue 4, A18 (2018)
Sergey V. Smirnov1、*, Maxim O. Makarenko1, Sergey V. Suchkov2, Dmitry Churkin1, and Andrey A. Sukhorukov2
Author Affiliations
  • 1Novosibirsk State University, 2 Pirogova Street, Novosibirsk 630090, Russia
  • 2Nonlinear Physics Centre, Research School of Physics and Engineering, Australian National University, Canberra, ACT 2601, Australia
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    DOI: 10.1364/PRJ.6.000A18 Cite this Article Set citation alerts
    Sergey V. Smirnov, Maxim O. Makarenko, Sergey V. Suchkov, Dmitry Churkin, Andrey A. Sukhorukov. Bistable lasing in parity-time symmetric coupled fiber rings[J]. Photonics Research, 2018, 6(4): A18 Copy Citation Text show less

    Abstract

    We propose a parity-time (PT) symmetric fiber laser composed of two coupled ring cavities with gains and losses, which operates both in PT-symmetric and symmetry-broken regimes depending on the static phase shifts. We perform analytical and numerical analysis by the transfer matrix method taking into account gain saturation and predict laser bistability in the PT-symmetric regime in contrast to a symmetry-broken single-mode operation. In the PT-broken regime, the generation power counterintuitively increases with an increase of the cavity losses.
    L=(eg1/200eg2/2)(0110)(1/2i/2i/21/2)(eiφ100eiφ2)(1/2i/2i/21/2)(eg1/200eg2/2),(1)

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    L=ieg˜+iφ˜(eΔg/2cos(Δφ2)sin(Δφ2)sin(Δφ2)eΔg/2cos(Δφ2)),(2)

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    PTeg˜iφ˜L=eg˜iφ˜LPT.(3)

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    P=(0110),(4)

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    PL(g1,g2,φ1,φ2)P1=L(g2,g1,φ2,φ1).(5)

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    TL=(L*)1T.(6)

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    μ±=ieg˜+iφ˜μ˜±,μ˜±=1/μ˜=cosh(Δg/2)cos(Δφ/2)±cosh2(Δg/2)cos2(Δφ/2)1(7)

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    (u1u2)=(exp(iν±/2)exp(iν±/2)),(8)

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    ν±=ilog[μ˜±eΔg/2cos(Δφ2)sin(Δφ2)].(9)

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    ΔgPT=2cosh1[1cos(Δφ/2)],(10)

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    ν+=ν,(11)

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    cos(Δφ/2)<1/cosh(|g2|),(12)

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    cos(Δφ/2)>1/cosh(|g2|)(13)

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    g1=g01+P˜1gh,(14)

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    J=Im(u1u2*)=|u1u2|sin[arg(u1)arg(u2)].(15)

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    Je2g˜J.(16)

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    sign(J)=sign{sin[arg(u1)arg(u2)]}=const.(17)

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    0<arg(u1)arg(u2)<π,π<arg(u1)arg(u2)<0.(18)

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    Sergey V. Smirnov, Maxim O. Makarenko, Sergey V. Suchkov, Dmitry Churkin, Andrey A. Sukhorukov. Bistable lasing in parity-time symmetric coupled fiber rings[J]. Photonics Research, 2018, 6(4): A18
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