Influence of Kerr nonlinearity on PT-transition in coupled fibre lasers

This work investigates a concept of coupled fiber lasers exhibiting PT-symmetry and a PT-transition between PTsymmetric and PT-broken lasing states. We consider a system operated via Raman gain comprising two fiber loops (ring cavities) connected to each other by means of two fiber couplers with adjustable phase shift between them. By changing the phase shift or/and amplification (loss) in fiber loops, one can switch between generation regimes, realizing either PTsymmetric or PT-broken solution. In the PT-symmetric lasing regime, equal powers are generated in both cavities despite only active one is pumped. We make theoretical and numerical description of the proposed coupled fiber lasers starting with the simple discrete matrix model taking into account coupling, phase delays, gain (which is assumed to be saturated), losses and nonlinear phase shift. We show how the PT-transition is affected by self-phase modulation inside the fiber cavity and investigate requirements that should be met in order to observe PT-transition experimentally despite Kerr effect that violates exact symmetry conditions. In particular, we show that PT-transition may be observable only near lasing threshold. Further on we adopt more sophisticated model based on Nonlinear Schrödinger equation for PT fiber laser. Taking into account quasi-CW polychromatic radiation with typical spectral bandwidth of fiber Raman lasers, chromatic dispersion and Kerr nonlinearity, we demonstrate both PT-symmetric and PT-broken lasing in a fiber laser.