PT-symmetric mode-locking

Parity-time ($\mathcal{PT}$) symmetry is one of the most important accomplishments in optics over the past decade. Here the concept of $\mathcal{PT}$ mode-locking (ML) of a laser is introduced, in which active phase-locking of cavity axial modes is realized by asymmetric mode coupling in a complex time crystal. $\mathcal{PT}$ ML shows a transition from single- to double-pulse emission as the $\mathcal{PT}$ symmetry breaking point is crossed. The transition can show a turbulent behavior, depending on a dimensionless modulation parameter that plays the same role as the Reynolds number in hydrodynamic flows.