Abstract
The theoretical treatment of the optical frequency up-conversion process with stochastic pumping is presented. This process consists of exchange of photons between two modes of different frequencies. It is assumed that the two modes are coupled by a short memory stochastic function. Statistically averaged occupation numbers of both modes were calculated exactly by means of the theory of multiplicative stochastic processes. The obtained nonperturbative solution sums secular terms and is valid for arbitrary times. The oscillatory-damped nature of the exchange of energy between two modes and the role of partial incoherence of the pump is discussed. It is shown that stochastic coupling causes the equipartition of energy between two modes for sufficiently long times. Analogies between an up-converter and a two-level atom driven by a single mode electromagnetic field are indicated. Optical Bloch equations for an up-conversion process are derived.
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