Extension for “Consistent Optical and Electrical Noise Figure”
R. Noé · Journal of Lightwave Technology · 2024
This extends a published paper. Noise figure from optical down toward electrical domain is described and related issues are touched upon. The minimum noise figure of an electrical amplifier isFe= 1. It is the SNR degradation factor in a linear transmission with two available receiver quadratures, i.e. one mode. E. Desurvire's traditional optical noise figureFpnfin direct-detection receivers has the minimum valueFpnf= 2 for an amplifier with high gain.Fpnfis not the SNR degradation factor in a transmission with two available receiver quadratures. The photodetector acts like an extra squaring power meter inserted before a power meter. It does not fulfill the linearity condition. Other than transmissive devices it suppresses one signal degree-of-freedom. The latter is the reason for the minimumFpnf= 2 instead of value 1. Optical amplifiers such as EDFAs cannot be held responsible for this, given that these are exact equivalents of electrical amplifiers. In the electrical domain there is intrinsic thermal source noise. But in the optical domain there is intrinsic detection shot noise which means that the number of quadratures matters. IfFpnfis a valid noise figure then power and gain need to be redefined and the system linearity requirement of noise figure definition must be overcome.Fpnfis in contradiction with physics and is incompatible withFe. It is to be replaced by the correct optical noise figureFo,IQfor linear transmission with two available receiver quadratures. That is observable in coherent I&Q receivers, has the minimumFo,IQ= 1 and is compatible withFe. In the derivation of the consistent unified noise figureFIQfor all frequencies, with the limit casesFeandFo,IQ, thermal noise energy is needed. Its usual simplified expressionkTis now replaced by Nyquist's correct result. This holds also in a unified homodyne noise figureFI, against which H. Haus' unified noise figureFfasis discussed. When there is no I&Q power splitting and one degree-of-freedom is suppressed, relative strength of detection noise is halved, thereby doubling the SNR degradation introduced by an EDFA. Accordingly, the idealFIof a standard amplifier changes from 1 in electronics toFo,I= 2 in optics.Fo,Iis the optical homodyne noise figure.