Nonlinear suppression of time-reversals in PT-symmetric optical couplers

Andrey A. Sukhorukov, Zhiyong Xu, Yuri S. Kivshar

System dynamics for different initial conditions: (a)-(d) ' = /6 − /20 and (e)-(h) ' = /6 + /20. (a),(e) Trajectories in the phase plane (, '). Red open circle marks the point at z = 0, and open triangle marks the unstable stationary solution with '− = /6. (b),(f) Intensity dependencies on propagation distance in the first (dotted line) and second (dashed) waveguides, solid line show the sum of individual intensities. (c),(g) and (d),(h) show the intensity and phase evolution along the propagation direction. For all the plots,  = 0.5 and I(z = 0) = 2.2.We reveal a generic connection between the effect of time-reversals and nonlinear wave dynamics in systems with parity-time (PT) symmetry, considering a symmetric optical coupler with balanced gain and loss where these effects can be readily observed experimentally. We show that for intensities below a threshold level, the amplitudes oscillate between the waveguides, and the effects of gain and loss are exactly compensated after each period due to {periodic time-reversals}. For intensities above a threshold level, nonlinearity suppresses periodic time-reversals leading to the symmetry breaking and a sharp beam switching to the waveguide with gain. Another nontrivial consequence of linear PT-symmetry is that the threshold intensity remains the same when the input intensities at waveguides with loss and gain are exchanged.
Optics (physics.optics)

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