On the theory of a two-photon quantum amplifier

P. Lambropoulos

A theory of a quantum amplifier based on two-photon transitions is presented. The model consists of an assemblage of atoms interacting with a single mode of the light field via two-photon absorption and emission. The treatment is quantum mechanical, and the emphasis is on the photon-statistical aspects of the problem. Difference-differential equations for the density matrix of the field mode are derived. The equations are solved for a special case. Differential equations for the expectation vaues of the number of photons and of the field amplitudes, and for their higher statistical moments, are also obtained. Approximate solutions for the average number of photons are found, and the effect of the amplification process on the statistical fluctuations of the number of photons and the field amplitudes is discussed. The results of this study suggest that such an amplifier does not have the coherence properties of a laser amplifier because it tends to increase the statistical fluctuations of the field.

Ou M

Bernard Calvas, Paul Urquhart

A model is presented for erbium-doped fiber amplifiers that operate by an upconversion process in which two pump photons at ~800 nm are absorbed and can provide an inverted population and hence the ability to amplify signal photons at ~850 nm. The most important spectroscopic features of the amplifier are identified and used to formulate a theory that predicts how the amplifier gain varies with fiber length and doping density, as well as with launched pump and signal powers. The limitation that amplified spontaneous emission imposes on the gain is investigated, and useful approximate formulas are derived in the limit where amplified spontaneous emission is negligible.

Wang Zhi Cheng, Hermann Haken

L. Sáinz de los Terreros, Francisco Javier Bermejo

Lorenzo M. Narducci, Lambros G. Johnson, E. J. Seibert +2 more