Re-entrant parity-time phase transitions in locally coupled ring resonators

Abstract

We investigate two parity-time-symmetric ring resonators coupled over a finite angular region described by a super-Gaussian profile. In the linear regime, analytical spectra are obtained in the homogeneous-coupling and fixed-amplitude narrow-contact limits, while the finite-width problem is treated numerically. Local coupling introduces nonzero spatial Fourier components that mix angular harmonics and lift the degeneracy of counterpropagating modes, resolving each excited doublet into parity-dependent branches. Collisions among these branches generate multiple exceptional-point boundaries and disconnected broken-PT domains. The resulting phase diagrams exhibit re-entrant unbroken-broken-unbroken transitions when the gain-loss strength, coupling width, or peak coupling amplitude is varied. The numerical spectra continuously recover both analytical limits. In the nonlinear regime, selected ground and excited linear modes are used as seeds for adiabatic propagation into finite-amplitude Kerr waveforms that remain dynamically persistent over the simulated observation interval for finite ranges of nonlinear strength. These results show that the spatial profile of inter-resonator coupling provides a geometric means of controlling multimode PT transitions and selecting dynamically accessible nonlinear waveforms in coupled-ring systems.