Nonlinear dynamics of multiple four-wave mixing processes in a single-mode fiber

Multiple four-wave mixing processes in an optical fiber are investigated both theoretically and experimentally. The propagation equations for the complex amplitudes of two pump waves (angular frequencies ${\mathrm{\omega }}_1$ and ${\mathrm{\omega }}_2$) and four sidebands (${\mathrm{\omega }}_3$=2${\mathrm{\omega }}_1$-${\mathrm{\omega }}_2$, ${\mathrm{\omega }}_4$=2${\mathrm{\omega }}_2$-${\mathrm{\omega }}_1$, ${\mathrm{\omega }}_5$=2${\mathrm{\omega }}_3$-${\mathrm{\omega }}_1$, and ${\mathrm{\omega }}_6$=2${\mathrm{\omega }}_4$-${\mathrm{\omega }}_2$) are derived. These six waves interact through seven partially degenerate and nondegenerate four-wave mixing processes. Conservation relations for the wave amplitudes are obtained. Numerical integration of these equations reveals both periodic and chaotic energy exchange between the pump waves and sidebands. Predictions from the model are tested directly by experimental measurements on a single-mode optical fiber.