Analysis of few-mode EDFAs with complex doping profiles by theoretical models based on vector modes

Tailoring erbium doping profile is one of the important methods to equalize modal gain of few-mode optical amplifiers. For accurate analysis of these amplifiers, the vector nature of pump and signal modes should be considered in numerical models. In the vector-mode-based models (VMM), the off-centered linearly polarized (LP) modes evolve their transverse intensity patterns (TIPs) during propagation, instead of being assumed to have constant TIPs as done in the LP-mode-based scalar models. The evolved TIPs change the spatial overlaps between pump and signal modes and hence would lead to a different amplifier performance relative to the one obtained by scalar models. Based on VMM, we analyze the gain characteristics of a two-LP-mode erbium-doped fiber amplifier (2LPEDFA) with a ring-doped core and a double-ring-doped 4LPEDFA, respectively. Further, results computed by scalar models are also presented for comparison, showing that the TIP evolutions in the 2LPEDFA have negligible impact upon the modal gain and optimal doping radii. While for the 4LPEDFA, differences in both modal gain and optimal doping radii have been demonstrated between the vector- and LP-mode-based methods. Our results show that vector models are preferable to implement high-precision design of few-mode EDFAs with complex erbium doping profiles.