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Journal of Physics A Mathematical and General

Photon statistics of optical frequency up-conversion with stochastic pumping

S Kryszewski, Jacek Chrostowski

Published Dec 1, 1977• 12 citations
Publisher

Abstract

The frequency up-conversion process with stochastic coupling function is considered. It is shown that the total photon number increases with time. The antibunching effect (g (2) <1) is predicted regardless of the mean photon numbers available in the process.
DOI
10.1088/0305-4470/10/12/011

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A canonical model for the frequency up-conversion process with stochastic coupling function is proposed. Based on it the first-order coherence functions, the time dependence of the mean photon numbers and the second-order coherence functions are found and compared with the corresponding results already available in the literature. It is shown that the total photon number, as a function of time, has a turning point. The antibunching effect is predicted regardless of the mean photon numbers available in the process.
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.
The photon statistics of quadratic parametric two-mode processes are derived starting from the results of the first part of this paper. A general theory is presented and particular processes are discussed. Assuming the initial field to be coherent, fluctuations of the pumping field are taken into account. The effects of antibunching and anticorrelation of photons on the photon distribution, its factorial moments, fluctuations in modes and their correlations for the amplification process are demonstrated and their dependence on levels of pumping field fluctuations is shown.
We develop quantum theory of process of the parametric optical image amplification at high-frequency pumping which is accompanied by up - conversion one. Such interactions can be implemented by two coupled three-frequency optical processes. The theory developed takes into account the diffraction effect and the difference of group velocities of interacting waves. The expressions for mean photon numbers and noise figures of the interacting waves are obtained and the dependence of these parameters on the interaction length are examined.