Noise Statistics in Fiber Optical Parametric Amplifiers

In this paper, we show both theoretically and experimentally that the probability density function of the intensity of an amplified signal by parametric amplifiers subject to a pump with excess noise is highly asymmetric. This is due to the nonlinear relationship between the optical pump power and the parametric gain. Because of this, the relationship between the noise figure (NF) and the bit error rate (BER) is modified, compared with that predicted by the chi
²
theory, which is an effect that is notable at large NFs and low BERs. The difference in predicted BER can be of several orders of magnitudes between the correct theory and the chi
²
approximation in single-stage parametric amplifiers. We also show that in the limit of many cascaded parametric amplifiers, the statistics of the noise of an amplified optical signal approaches chi
²
. Furthermore, the BER of a parametric amplifier is generally lower compared with erbium-doped fiber amplifiers for the same NF values if we assume quantum-limited amplification