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We report emergence of saturation and chaotic spiking of optical power in adouble ring resonator with balanced loss and gain, obeying the so-calledparity-time symmetry. We have modeled the system using a discrete-timeiterative equation known as the Ikeda Map. In the linear regime, evolution ofoptical power in the system shows power saturation behavior below the PTthreshold and exponential blow-up above the PT threshold. We found that in theunbroken PT regime, optical power saturation occurs owing to the existence ofstable stationary states, which lies on the surface of 4-dimensionalhypersphere. Inclusion of Kerr nonlinearity into our model leads to theemergence of a stable, chaotic and divergent region in the parameter basin forperiod-1 cycle. A closer inspection into the system shows us that the largestLyapunov exponent blows up in the divergent region. It is found that theexistence of high non-negative largest Lyapunov exponent causes chaotic spikingof optical power in the resonators.

Chaotic Dynamics and Optical Power Saturation in Parity-Time (PT) Symmetric Double Ring Resonator