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Soviet Journal of Quantum Electronics

Fluctuation-dissipation theory of four-photon parametric frequency upconverters

Yu. N. Yashkir

Published Oct 31, 1984• 0 citations
Publisher

Abstract

Fluctuation-dissipation theory is developed for parametric noise in a four-photon frequency upcon verter of infrared signals. General analytic formulas are obtained for the parametric converter efficiency, as well as for the signal/noise ratio and the threshold sensitivity. The most important dependences of these characteristics on the parameters of the problem are analyzed and the optimal conditions for the realization of a parametric converter are determined.

DOI
10.1070/qe1984v014n10abeh006418

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Fluctuation-dissipation theory is developed for parametric noise in a four-photon frequency upcon verter of infrared signals. General analytic formulas are obtained for the parametric converter efficiency, as well as for the signal/noise ratio and the threshold sensitivity. The most important dependences of these characteristics on the parameters of the problem are analyzed and the optimal conditions for the realization of a parametric converter are determined.
A systematic analysis was made of the spectral characteristics of resonance four-photon parametric conversion of infrared radiation as a result of two-photon resonance pumping of the 3S–3D and 3S–5S transitions in sodium and the influence of these characteristics on the threshold sensitivity of a parametric conversion detector was investigated. An experimental study was made of the characteristics of the noise radiation generated as a result of hyperparametric scattering. The results obtained can be used to select the optimal parameters of high-sensitivity detectors of weak infrared signals by parametric conversion in alkali metal vapors.
Four-photon parametric up-conversion of a weak infrared signal under conditions of two-photon resonance of a constant nonmonochromatic pump field is analyzed allowing for population migration, transient response of the medium, Stark shift of the levels, and width of the pump frequency spectrum. It is found that under steady-state conversion conditions in a nonmonochromatic pump field, it is possible to achieve an average conversion efficiency differing only negligibly from the maximum conversion efficiency in a monochromatic pump field. An analysis is made of the influence of optically induced relaxation on the average conversion efficiency in the transient regime. Numerical estimates are made of the transition parameters for an alkali metal vapor in a frequency-degenerate pump field exciting a two-photon transition.
In this paper the quantum noise properties of phase-insensitive and phase-sensitive parametric processes are studied. Formulas for the field-quadrature and photon-number means and variances are derived, for processes that involve arbitrary numbers of modes. These quantities determine the signal-to-noise ratios associated with the direct and homo-dyne detection of optical signals. The consequences of the aforementioned formulas are described for frequency conversion, amplification, monitoring, and transmission through sequences of attenuators and amplifiers.
A theoretical analysis is made of the process of parametric up-conversion of the frequency of an infrared signal involving two-photon resonance of a pump field whose spectrum is considerably wider than the widths of the atomic transition lines. It is shown that the maximum steady-state efficiency of conversion in a wideband field is only slightly different from the maximum efficiency of conversion in a regular and monochromatic field. A dynamic improvement in the conversion efficiency is possible under transient interaction conditions.
We develop for the first time a quantum theory of simultaneous amplification and frequency up-conversion of optical images in two coupled three-wave processes. The theory developed takes into account the diffraction effect and the difference of the group velocities of the interacting waves. Due to the degenerate parametric process involved in the nonlinear optical interactions, the up-conversion also possesses phase sensitivity. As a result, the statistical characteristics of the amplified image and the converted one depend on the phase relation between the signal and the pump waves. It is shown that at the output of the nonlinear crystal the signal-to-noise ratios for the amplified image and the converted one may be same as those for the initial image, i.e. transformation of the optical image may be 'noiseless'.