Polarization dependent gain in erbium-doped fiber amplifiers: computer model and approximate formulas

A computer model for polarization dependent gain (PDG) in Er-doped fiber amplifiers (EDFA) is presented. The model assumes that each erbium ion possesses an ellipsoidal gain surface and that all ion orientations are equally likely. By dividing the ions into subsets based upon orientation and computing the inversion of each subset in the presence of polarized pump and signal waves, the model predicts the dependence of the PDG induced by this polarization hole-burning (PHB) on the design of the EDFA, the signal degree and state of polarization (SOP), and the pump SOP. For moderate gain amplifiers (made from the same fiber) with the same gain peak wavelength and the same compression level, the magnitude of the PDG is nearly independent of the EDFA gain. Internal and random fiber birefringence are included to model real fibers. In fibers which cause the signal SOP to walk rapidly around the Poincare sphere, the PDG is reduced by a factor of 2/3 when compared with a linear polarization-maintained signal. Scrambled signals and partially-polarized saturating tones are also considered. Simple rules are derived for predicting the PDG of a given EDFA.