The quantum theory of noise in a chain of gain–loss elements is reviewed. A new derivation is given of the characteristic function of the photon-number distribution at the output of a long amplifier chain. The results of the quantum theory are compared with those of the semiclassical theory, and it is shown that in most practical cases the semiclassical theory gives an excellent approximation of the full quantum result. It is shown that transparency sets a fundamental limit on the maximum distance over which a signal can be transmitted and hence on the maximum spacing between regenerative stations. An analytic estimate of this limit is given.
© 2000 Optical Society of America
Antonio Mecozzi, "Quantum and semiclassical theory of noise in optical transmission lines employing in-line erbium amplifiers," J. Opt. Soc. Am. B 17, 607-617 (2000)