Impact of pump phase modulation on the gain of fiber optical parametric amplifier

In practice, fiber optical parametric amplifiers are generally driven by a phase-modulated pump wave to avoid stimulated Brillouin back-scattering. We show both analytically and numerically that the phase modulation of the pump can induce strong parametric gain modulation and that this detrimental effect depends both on the rise-fall time of the phase modulator and on the fiber dispersion slope.