THE STATISTICAL DISTRIBUTION OF SWITCH-ON DELAY IN SINGLE-MODE SEMICONDUCTOR-LASERS .1. EQUILIBRIUM OFF-CONDITION

The theory of stochastic processes as applied to photon emission and a bsorption events is used to calculate the distribution of delay in swi tch-on from a sub-threshold condition in directly modulated semiconduc tor lasers down to a probability of 10(-10), This involves the derivat ion of the relative probability distribution of photon number in the l aser late enough in the switch-on process such that deterministic rela tions can be applied thereafter, This distribution, assumed constant i n some treatments, is found to change only a little from its initial f orm, which is a negative binomial, From this one deduces a delay distr ibution whose width is proportional to the period of the switch-on tra nsient, relatively independently of the precise starting point, but wh ich can be narrowed by injection of additional spontaneous emission, E xperiment satisfactorily supports the theory.