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Field Fluctuations Produced by Parametric Processes in Fibers

In this tutorial, the optical field fluctuations produced by four-wave mixing processes in fibers are studied in detail. Modulation interaction and phase conjugation amplify input signals, whereas Bragg scattering frequency converts an input signal. If the input states are coherent, the quadrature fluctuations associated with the output states have Gaussian statistics. Formulas are derived for the output quadrature means, variances, and correlations, which are valid for arbitrary pump-induced coupling and dispersion- and pump-induced mismatch coefficients. These formulas allow one to determine the output Wigner distributions, which specify the output fields completely, and the effects of the aforementioned processes on the information carried by signals. The results of this paper are relevant to communication systems and quantum-information protocols based on continuous variables.