Nonlinearly induced PT transition in photonic systems

We study the effect of nonlinearity on systems with periodic parity-time (PT) symmetry, and show that nonlinearity can transform the system from broken to full PT symmetry and vice versa. Furthermore, we show that even when the nonlinearity is insufficient to induce a transition from broken to full PT symmetry, still, the wave functions neither decay nor diverge, despite the fact that the system has a complex eigenvalue spectrum. Rather, the amplitudes of the wavefunctions oscillate around the transition point. Our results apply to a wide variety of systems in optics and beyond.