Consistent Optical and Electrical Noise Figure

Abstract

The optimum noise figure of an electrical amplifier is <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F_e</i> = 1 and the optimum traditional noise figure of an optical amplifier is <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F_pnf</i> = 2. This irresolvable conflict is due to the fact that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F_e</i> measurement requires electrical powers, proportional to squared amplitudes (voltages), while <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F_pnf</i> measurement requires squares and variances of photocurrents, proportional to 4th powers of amplitudes (fields). In line with this an electrical receiver can receive I&Q parts of an electric carrier while a direct-detection photoreceiver can detect only power and not phase of an optical carrier. Optical amplifiers cause Gaussian field noise. Photodetection causes shot noise. Spontaneous-spontaneous beat noise in direct detection is taken into account by negative binomial or chi-squared photoelectron distributions, without errors of a Gaussian approximation. Coherent receivers linearly sense the Gaussian field noise. The sensitivity of an ideal coherent I&Q receiver is not degraded if it gets an ideal optical preamplifier, while the corresponding <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F_pnf</i> = 2 suggests degradation. Coherent I&Q or heterodyne receivers have electrical output powers proportional to squared amplitudes (fields). This way one has the same metric in electrical and optical domain. One gets an optical noise figure <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F_o</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">,</sub> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">_IQ</i> . For large amplifier gain it is <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F_pnf</i> /2. In an ideal amplifier, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F_o</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">,</sub> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">_IQ</i> = 1. For true optical homodyne receivers and for direct detection receivers with Gaussian approximation it can be converted into <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F_pnf</i> and vice versa. Phase-sensitive amplifiers are also covered. With <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F_e</i> and the I&Q optical noise figure <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F_o</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">,</sub> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">_IQ</i> a consistent unified noise figure is derived, valid and usable in electrical and optical domain.