Output Photon Number Distribution of Erbium-Doped Fiber Amplifiers

Abstract

Erbium-doped fiber amplifiers (EDFA) are gaining increasing importance in the lightwave communications arena due mainly to their low insertion loss and easy manufacturability. Consequently there is significant motivation in obtaining the photon number distribution at the output of an EDFA taking finite bandwith and line shape of the signal lasers into account. In this paper the photon number distribution at the output of an EDFA resulting from an input wave packet having an arbitrary photon number distribution is evaluated. Previously the output photon number distribution was derived [1] for input fields having Poisson photon number distributions, i.e. for coherent sate input fields. Our treatment is more general in the sense that the input field can be in an arbitrary quantum sate. This generality will enable researchers to evaluate EDFA photon number distributions resulting from non-monochromatic incident fields [for example laser sources with phase and/or intensity noise] simply by using the appropriate input photon number distributions in the equations that will be derived below [see for example [2] for several photon number distributions corresponding to various laser line shapes].