General Phase Diagram of Multimodal Ordered and Disordered Lasers in Closed and Open Cavities

We present a unified approach to the theory of multimodal laser cavities including a variable amount of structural disorder. A general mean-field theory is studied for waves in media with variable nonlinearity and randomness. Phase diagrams are reported in terms of optical power, degree of disorder, and degree of nonlinearity, tuning between closed and open cavity scenarios. In the thermodynamic limit of infinitely many modes, the theory predicts four distinct regimes: a continuous wave behavior for low power, a standard mode-locking laser regime for high power and weak disorder, a random laser for high pumped power and large disorder, and a novel intermediate regime of phase locking occurring in the presence of disorder but below the lasing threshold.

Figure 1

Phase diagrams in the (${\mathcal{P}}^2$, $R_J$, $\alpha ={\alpha }_0$) space. For low disorder, only the SML and CW phases occur, varying pumping and degree of linearity. As disorder increases, the intermediate PLW phase arises between CW and SML. For strong disorder, RL replaces SML above the pumping threshold line. For any $R_J$, for low ${\alpha }_0$ the transition driven by $\mathcal{P}$ is continuous in the order parameters, whereas for high nonlinearity ($\alpha >{\alpha }_{\text{nl}}=0.6297$) it is discontinuous. Insets: phase diagrams in the (${\mathcal{P}}^2$, $R_J$) plane for closed ($\alpha ={\alpha }_0=1$) and open ($\alpha ={\alpha }_0=0.4$) cavities.

Figure 2

Phase diagram in ${\mathcal{P}}^2{R}_J=\beta {\epsilon }^{2}J$ vs $J_0/J=1/R_J$ for closed cavity $\alpha ={\alpha }_0=1$ for $J_0/J$ ranging from negative to positive. Inset: open cavity with $\alpha =0.7$.