Gaussian-wave theory of sub-Poissonian light generation by means of travelling-wave parametric deamplification

A Gaussian wave theory is developed to analyse the sub-Poissonian light generated by means of a travelling-wave optical parametric deamplification. The Gaussian spatial profile of the pump beam limits the observable Fano factor to -3 dB (0.5). Gain-induced diffraction of the signal beam and classical fluctuations of the pump-signal relative phase cause further degradation. The theory is compared with our recent experimental results, and excellent agreement is found after the effect of non-ideal photoelectron efficiency is taken into account.