First-Passage-Time Distributions in a Bistable Two-Mode Laser
The statistical properties of a two-mode laser can be described by a four-dimensional Fokker-Planck (FP) equation for the real and imaginary parts of the weakly time dependent field amplitudes.1 It has been shown in the rather special case in which the only asymmetry between the modes was in their net linear gain while there was no dispersion, that this equation can be reduced to a one-dimensional FP-equation for the intensity of one of the modes,2,3 which led to certain predictions that have been confirmed by experiment.4 A similar way of approach, that is, reducing the description of the statistical behavior of a field to the analysis of a one-dimensional FP-equation, was followed in the problem of the mean first-passage time in optical bistability.5 In the present contribution we will deal with the first-passage-time (FPT) problem in a bistable two-mode laser without making any of the above mentioned restrictions concerning the symmetry of the modes or the absence of dispersion. The method employed as well as the results obtained are applicable to a wide class of bistable lasers, including homogeneously broadened ring lasers3. single-mode lasers exhibiting polarization bistabilityb6 and single-mode lasers operating under weak external optical feedback conditions7. Moreover, they will be relevant in other contexts too, such as in optical bistability.
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