Glassy Behavior of Light

We study the nonlinear dynamics of a multimode random laser using the methods of statistical physics of disordered systems. A replica-symmetry breaking phase transition is predicted as a function of the pump intensity. We thus show that light propagating in a random nonlinear medium displays glassy behavior; i.e., the photon gas has a multitude of metastable states and a nonvanishing complexity, corresponding to mode-locking processes in random lasers. The present work reveals the existence of new physical phenomena, and demonstrates how nonlinear optics and random lasers can be a benchmark for the modern theory of complex systems and glasses.

Figure 1

The 1rsb overlap $\overline{q}$ as a function of the reduced temperature. The full line is the stable part of the curve; the dashed line is the metastable part. Inset: the complexity $\Sigma (T)$ as a function of the temperature. It jumps discontinuously at $T_d$ where the metastable solution first appears and vanishes at $T_c$ where the glass transition takes place.