interstage loss, a single-stage amplifier with the loss after the amplification performs better than a two-stage amplifier. This solution however fails to represent a very important characteristic of real amplifiers that disappear when the quantum limit approximation is performed. As a matter of fact, realistic amplifiers have a noise factor greater than what is repre- sented by Equation 4.74 and, more important, the noise factor is generally bigger for ampli- fiers with a great gain. Thus, in our previous solution, if all the gain is concentrated in the first stage, also the noise factor of the first stage increases SO that the overall noise is no more the minimum possible. In order to represent this situation, let us do a very simple model of the amplification mechanism taking into account this phenomenon. In a real amplifier, the situation is much more complex, but this model allows us to concentrate on the main phenomena without the complexity of a real model of the real amplifier mechanism. We will assume that the active medium is a passive matrix with the insertion of the active molecules, exactly as happens in erbium-doped fibers. In this situation, the local unsaturated gain go can be assumed proportional to the den- sity of active molecules. Let us also image that the insertion of the active molecules some- how risks damaging locally the host matrix, thus creating microscattering locations whose density is proportional to the density of active molecules too. Thus, eliminating the density of active molecules, we can say that the number of scatter- ing imperfections is proportional to the local unsaturated gain. Once a photon is scattered by an imperfection in the matrix, it can be considered lost for the amplified radiation; thus, this phenomenon reflects in a decrease of the local gain that is proportional to the gain itself. Including this very simple model of active medium imperfection, Equation 4.63 can be rewritten as (4.81) where the effects of the scattering points on the noise can be neglected if 