Statistical fluctuations in multiple four-wave mixing in a single-mode optical fiber

When two pump waves propagate through a single-mode optical fiber, sidebands are generated due to third-order (${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$) nonlinear interactions in the fiber. The transfer of energy from the pumps to the sidebands can be periodic or chaotic, depending on the detuning and power of the input waves. We experimentally examine the statistical distributions of sideband power at the output of the fiber for input power and detuning regimes that correspond to periodic and chaotic energy exchange. Fluctuations of the input pump waves are accounted for in the comparison of experimental measurements with predictions of the theoretical model. Good agreement is obtained between experimental observations and numerical computations of the statistical distributions of sideband power. Limitations of the theoretical model and the experimental procedure for testing its predictions are discussed.