Coupling, competition, and stability of modes in random lasers

We studied analytically and numerically the complex properties of random lasing modes. Mode repulsion in frequency domain for inhomogeneously broadened gain media was confirmed by our numerical results. We constructed a coupled-mode model to explain the synchronized lasing behavior for modes whose frequency difference is less than the homogeneous gain width. The stability of coupled modes was investigated. The effective competition coefficient $C_e$ for two modes with both gain competition and field coupling is obtained analytically. In our numerical experiments, we also found the coupled oscillations of two lasing modes. From the analytical derivation, we demonstrated that such oscillations could reveal the field-coupling strength between the random modes.