A three-dimensional quantum vacuum-noise/signal beamsplitter model for nonideal linear optical amplifiers

We generalize the two-dimensional vacuum-noise/signal beamsplitter model describing quantum noise properties of either ideal linear optical amplifiers or passive optical attenuators. This generalization, which couples a second orthogonal vacuum state, makes it possible to describe the general case of nonideal optical amplifiers which have incomplete inversion and background loss. We show that the amplifier operating conditions are characterized by a three-dimensional unitary vector normal to the beamsplitter plane where signal and vacuum modes mix together. A general formula for Heisenberg's minimal uncertainty in the signal field is derived. Such a model could be useful in analyzing coherent signal measurements involving laser preamplifiers. (C) 1999 Academic Press.