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Optica Acta International Journal of Optics

Canonical Extension of a Problem in Parametric Frequency Up-conversion with Stochastic Pumping

S. K. Srinivasan, S. Udayabaskaran

Published Dec 1, 1979• 9 citations
Publisher

Abstract

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.

DOI
10.1080/713819941

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Journal of Physics Conference Series•Apr 1, 2006•2 citations
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 consequences of the deviation from ideal coherence of the driving (pump) field in nonlinear processes are examined. A detailed treatment of the processes of parametric amplification and frequency upconversion is presented. The treatment utilizes two different approximation methods to suit the two different physical situations considered. For slow phase variations of the pump field an adiabatic approach is useful, whereas in the treatment of fast phase variations (the nonadiabatic case) an equation describing the time evolution of thePrepresentation is found to be a good starting point. In this latter case, a closed hierarchy of equations for the moments of the photon number distribution in the signal (or idler) mode is found. In particular, we find that the efficiencies of both the amplification and the upconversion processes are reduced as a result of pump incoherence, the reduction becoming more severe in the highly incoherent case. For the frequency converter, the very nature of the process is modified as compared to the ideal case, and this modification is again of particular significance for the highly incoherent pump. Second-order moments are explicitly calculated and some of the statistical properties of the output signals are examined.
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.