The correlation functions of the intensity fluctuations are calculated by use of a linearization procedure for the equations of motion which include the coupling of the counter-rotating travelling waves of the ring laser in the cases of Doppler broadening, of homogeneous broadening with a self-induced population-inversion grating, and in intermediate cases. Depending on the strength of the mode competition various stable stationary solutions exist for the amplitudes. The transition between these stable states shows phenomena closely resembling phase transitions such as critical fluctuations, critical slowing down, etc. In particular, when the system passes from the state where both modes are above threshold to the state where one mode is below threshold, the negative cross-correlation of the fluctuations also becomes critical. In the case of the transient behaviour of the ring laser in the unstable region the time development of the amplitudes and the correlation functions are described in a short-time approximation.
展开▼
