Statistical parity-time-symmetric lasing in an optical fibre network

Parity-time (PT)-symmetry in optics is a condition whereby the real and imaginary parts of the refractive index across a photonic structure are deliberately balanced. This balance can lead to interesting optical phenomena, such as unidirectional invisibility, loss-induced lasing, single-mode lasing from multimode resonators, and non-reciprocal effects in conjunction with nonlinearities. Because PT-symmetry has been thought of as fragile, experimental realisations to date have been usually restricted to on-chip micro-devices. Here, we demonstrate that certain features of PT-symmetry are sufficiently robust to survive the statistical fluctuations associated with a macroscopic optical cavity. We examine the lasing dynamics in optical fibre-based coupled cavities more than a kilometre in length with balanced gain and loss. Although fluctuations can detune the cavity by more than the free spectral range, the behaviour of the lasing threshold and the laser power is that expected from a PT-stable system. Furthermore, we observe a statistical symmetry breaking upon varying the cavity loss.