Parametric Instabilities Driven by Orthogonal Pump Waves in Birefringent Fibers

The four-sideband model of parametric instabilities driven by orthogonal pump waves in birefringent fibers is developed and validated by numerical simulations. A polynomial eigenvalue equation is derived and used to determine how the spatial growth rates and frequency bandwidths of various instabilities depend on the system parameters. The maximal growth rate is associated with a group-speed matched four-sideband process (coupled modulation instability), whereas broad-bandwidth gain is associated primarily with two-sideband process (phase conjugation). This four-sideband model facilitates the design of parametric amplifiers driven by two pump waves with different frequencies and polarizations.