Extension for “Consistent Optical and Electrical Noise Figure”

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 is
F_e
= 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 figure
$F_{pnf}$
in direct-detection receivers has the minimum value
$F_{pnf}$
= 2 for an amplifier with high gain.
$F_{pnf}$
is 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 minimum
$F_{pnf}$
= 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. If
$F_{pnf}$
is a valid noise figure then power and gain need to be redefined and the system linearity requirement of noise figure definition must be overcome.
$F_{pnf}$
is in contradiction with physics and is incompatible with
F_e
. It is to be replaced by the correct optical noise figure
F_o,IQ
for linear transmission with two available receiver quadratures. That is observable in coherent I&Q receivers, has the minimum
F_o,IQ
= 1 and is compatible with
F_e
. In the derivation of the consistent unified noise figure
F_IQ
for all frequencies, with the limit cases
F_e
and
F_o,IQ
, thermal noise energy is needed. Its usual simplified expression
kT
is now replaced by Nyquist's correct result. This holds also in a unified homodyne noise figure
F_I
, against which H. Haus’ unified noise figure
F_fas
is 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 ideal
F_I
of a standard amplifier changes from 1 in electronics to
F_o,I
= 2 in optics.
F_o,I
is the optical homodyne noise figure.