Abstract
Parity-time () symmetric systems have two distinguished phases, e.g., one with real-energy eigenvalues and the other with complex-conjugate eigenvalues. To enter one phase from the other, it is believed that the system must pass through an exceptional point, which is a non-Hermitian degenerate point with coalesced eigenvalues and eigenvectors. Here we reveal an anomalous transition that takes place away from an exceptional point in a nonlinear system: as the nonlinearity increases, the original linear system evolves along two distinct -symmetric trajectories, each of which can have an exceptional point. However, the two trajectories collide and vanish away from these exceptional points, after which the system is left with a -broken phase. We first illustrate this phenomenon using a coupled-mode theory and then exemplify it using paraxial wave propagation in a transverse periodic potential.
- Received 17 February 2016
DOI:https://doi.org/10.1103/PhysRevA.94.013837
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