Estimation of the spatial bandwidth of an optical parametric amplifier with plane-wave pump

Abstract

We analyze the spatial-frequency dependence of the gain of phase-insensitive and phase-sensitive optical parametric amplifiers with plane-wave pumping. We discuss the dependence of their spatial bandwidths on pump power and crystal length, L, and observe that the well-known (k s/L)1/2 approximation of spatial bandwidth is not very accurate (here k s is the signal beam's wavevector magnitude). We derive an alternative approximation that is highly accurate at large gains and moderately accurate at low gains. The differences between the phase-insensitive and phase-sensitive amplifier bandwidths are shown to be insignificant for gains above several dB. Maximum phase-sensitive gain and bandwidth are realized by imposing an optimum phase profile onto the input signal's spatial spectrum, which has nearly parabolic shape with added series of π/2 phase discontinuities at spatial frequencies outside the main bandwidth of the amplifier. We show that, apart from the discontinuities, such a profile can be closely approximated by placing the image plane into the middle of the nonlinear crystal (converging input beam). The phase discontinuities contribute an additional narrow component to the point-spread function of the phase-sensitive amplifier.