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We analytically find an approximate Bloch-Messiah reduction of a noncollinearparametric amplifier pumped with a focused monochromatic beam. We consider typeI phase matching. The results are obtained using a perturbative expansion andscaled to a high gain regime. They allow a straightforward maximization of thesignal gain and minimization of the parametric fluorescence noise. We find thefundamental mode of the amplifier, which is an elliptic Gaussian defining theoptimal seed beam shape. We conclude that the output of the amplifier should bestripped of higher order modes, which are approximately Hermite-Gaussian beams.Alternatively, the pump waist can be adjusted such that the amount of noiseproduced in the higher order modes is minimized.

Noise reduction in 3D noncollinear parametric amplifier