Photonics Research, 2018, 6 (4): 04000A18, Published Online: Aug. 1, 2018
Bistable lasing in parity-time symmetric coupled fiber rings 
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Fig. 1. Schematic of the proposed PT-symmetric fiber-ring laser, composed of two coupled fiber-ring cavities with gain and losses. The coupling between cavities is controlled by means of phase shifts φ 1 φ 2
Fig. 2. (a) Ratio of two linear mode eigenvalues, | μ + / μ − | arg ( u 1 / u 2 ) μ + = Re ( ν + ) | μ + | | μ − | g 2 = − 0.7 Δ φ = 1.5 Δ φ = 1 | μ | = 1
Fig. 3. (a) Stationary regimes of laser operation with nonlinear gain saturation: no lasing (white background), pair of PT-symmetric laser modes (grey shading), or one mode in PT-broken regime (yellow shading). (b), (c) Characteristic mode amplification versus power for points A and B marked in (a) corresponding to different lasing regimes. Solid circles mark stable and the open circle marks unstable regimes with balanced gain and loss (zero mode amplification). Background shading marks PT-symmetric and broken regimes. Saturable gain parameter g h = 0.23
Fig. 4. Power dependencies in stationary lasing regimes. (a) A ratio of power generated in passive and active cavities, P 2 / P 1 Δ φ = 1.5
Fig. 5. (a) Dependence of generated power P 1 Δ φ g 2 g 1 = 1.0 | g 2 |
Fig. 6. Dynamical properties of a PT-symmetric fiber laser. (a) Two trapping regions shown with shading according to Eq. (18 ), shown in the plane of relative phases and powers in two fiber cavities. Laser dynamics is confined to one region according to the initial conditions. Solid and dashed lines indicate possible stationary lasing states: PT-symmetric—vertical lines at P 2 / P 1 = 1 { 0 , ± π } g 1 = 2.3 g 2 = − 0.7 Δ φ = 2.95
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): 04000A18.
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