Con­sist­ent op­tic­al and elec­tric­al noise fig­ure

 |  Optical Communication and High-Frequency Engineering

The noise figure is the factor by which the signal-to-noise ratio is degraded from input to output of a device. The optimum noise figure of an electrical amplifier is Fe=1 and the optimum traditional noise figure of an optical amplifier is Fpnf=2. This irresolvable conflict is due to the fact that an electrical receiver receives in-phase and quadrature parts of an electric carrier while a direct-detection photoreceiver detects only power but not phase of an optical carrier. In line with this, Fe measurement requires electrical powers, proportional to squared amplitudes (voltages), while Fpnf measurement requires squares and variances of photocurrents, proportional to 4th powers of amplitudes (fields). Unifying Fe and Fpnf for all frequencies is impossible.

Optical amplifiers cause Gaussian field noise. Photodetection causes shot noise. Coherent optical receivers are linear sensors of optical fields. The sensitivity is not degraded if an ideal coherent I&Q receiver gets an ideal optical preamplifier, while Fpnf=2 suggests degradation. Coherent I&Q or heterodyne receivers have two quadratures, and electrical output powers proportional to squared amplitudes (fields). This way one has the same metric in electrical and optical domain. One gets an optical I&Q noise figure Fo,IQ. For large amplifier gain it equals Fpnf/2. In an ideal amplifier, Fo,IQ=1. For true optical homodyne receivers and for optical direct detection receivers with Gaussian approximation Fo,IQ can be converted into Fpnf and vice versa.

It is derived: Fe and the I&Q optical noise figure Fo,IQ are limit cases of one consistent unified noise figure for all frequencies. It is valid and applicable in electrical, thermal and optical domain.

Strictly speaking: When noise figure is given as a number and not in dB then in reality the noise factor (= SNR quotient) is meant. "noise figure" = (10 dB) * log10("noise factor").

Open access:

Combined presentation

Follow-up publication

Original publication

Video 29.11.2022

Support material presentation