The passage-time (PT) distribution associated with the switch on of a laser with an injected signal can be used to detect weak signals. We calculate the distribution function of such a distribution. Results for the mean PT interpolate between the limit of no injected signal and a simple logarithmic law for strong signals. It has a scaling form with a single important independent parameter. The variance of the distribution is more sensitive to the presence of the injected signal than the mean. Explicit formulas for the limit of sensitivity of the detection method and for the bandwidth resolution are given.
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Balle et al. (1990) studied this question.
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