Phase transition in multimode nonlinear parity-time-symmetric waveguide couplers

Parity-time-symmetric ([Image: see text]-symmetric) optical waveguide couplers offer new possibilities for fast, ultracompact, configurable, all-optical signal processing. Here, we study nonlinear properties of finite-size multimode [Image: see text]-symmetric couplers and predict the nonlinear oscillatory dynamics that can be controlled by three parameters: input light intensity, gain and loss amplitude, and input beam profile. Moreover, we show that this dynamics is driven by a [Image: see text] transition triggered by nonlinearity in these structures, and we demonstrate that with the increase of the number of dimers in the system, the transition threshold decreases and converges to the value corresponding to an infinite array. Finally, we present a variety of periodic intensity patterns that can be formed in these couplers depending on the initial excitation.