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Soviet Journal of Quantum Electronics

Investigation of the statistical characteristics of spontaneous noise in parametric frequency converters

I. N. Matveev, S M Pshenichnikov, A F Umnov

Published Nov 30, 1980• 0 citations
Publisher

Abstract

An experimental investigation was made of the statistical characteristics of spontaneous parametric luminescence generated in the course of parametric frequency up-conversion. It was found that the laws governing the amplitude distribution and the distribution of photocounts of parametric luminescence were nearly of the Poisson type.
DOI
10.1070/qe1980v010n11abeh010390

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The variance and average value of photocounts (counts of electrons emitted by the cathode of a photodetector) are calculated allowing for the existence of the following sources of noise in a frequency converter: fluctuations of the pump intensity, conversion of background radiation, thermal fluctuations of fields in the converter crystal, spontaneous generation of the difference frequency, and illumination of the photodetector with the pump radiation transmitted by filters. A function representing the distribution of photocounts is obtained for short time intervals allowing for fluctuations of the pumping intensity in the case of conversion of a random Gaussian signal.
A two-step nonlinear optical interaction consisting of (i) a spontaneous frequency down-conversion process coupled with (ii) a frequency up-conversion process is treated quantum mechanically in the experimentally observed case of simultaneous collinear phase matching of both processes. The temporal behavior of the output signals is found to depend on which process, (i) or (ii), predominates. The nature of the photon statistics for each of the output modes is found to be "super-Poisson," regardless of which process, (i) or (ii), is dominant, and the zero-point fluctuations characteristic of parametric amplification are exhibited.
The parametric approximation is used in a statistical analysis of the frequency conversion of an optical field by a noncentrosymmetric crystal which couples an input wave of frequency 0 < ω < ωL/2 to output waves of frequency ω+nωL(n = 0, ±1, ±2, ...; ωL is the pump frequency). An expression is obtained for the characteristic function of the output field which is described in terms of a matrix of the coupling coefficients in the case of Gaussian (displaced) statistics of the input field with independent modes. The mutual statistics of the output waves with n ≥ 0 and n' < 0 is not Gaussian but corresponds, in the lowest approximation with respect to the pump wave and in the absence of the input field, to a spontaneous (direct or cascade) decay of pump photons into photon pairs. The intensity of the radiation represented by the n ≥ 0 modes is equal to the intensity of the radiation emerging from a classical converter which receives one photon in each mode with n' < 0. The special case of three interacting modes with n = −1, 0, 1 (upconverter or light modulator) is considered in detail. The noise intensities and correlations between the numbers of photons in two and three modes are found for this case, and the spatial-temporal correlation function of the fields of the Stokes (n' = −1) and anti-Stokes (n = 1) frequencies is determined.