Mean switching time of bistable two-mode lasers

Mean switching time of a two-mode laser is calculated in two different approaches: the first-passage-time treatment by the generalized Kramers method and the lifetime approach by the two-dimensional WKB method. In both cases, the most probable path is generally curved. Numerical study in the WKB calculation reveals that the general curved most probable path can be replaced with high accuracy by the path specified by the minimum potential for many cases of practical interest, that is, when the mode-coupling constant 3/4 is within the range 1<3/4<5. Thus, we are able to carry out calculations of the mean switching time that are accurate (within the framework of the WKB approximation) throughout the entire range, above threshold, of the pump parameter a. Compared with the analytical formula which is valid only for large a, our result yields perfect agreement in the large-a limit, but shows that the previously used formula consistently overestimates the mean switching time when a is not large where the experiments are performed.