Explicit analytic efficiency equation for saturated counter-pumped fiber amplifiers: Application to cladding-pumped erbium-doped fiber amplifiers

Abstract

We derive and assess an explicit analytic expression for the power conversion efficiency (PCE) of high-power continuous-wave optical fiber amplifiers with counter-propagating pump and signal in the presence of quenching, excited-state absorption, and background loss. The expression is uniquely simple to evaluate. A crucial assumption is that the level populations and thus the gain do not depend on the signal and pump powers separately, but rather on their ratio. In the ideal, “balanced”, case, this ratio remains constant throughout the amplifier, which is possible when the signal gain is equal to the operating pump depletion. This is achieved for certain (balanced) combinations of fiber length and input signal and pump power. With these assumptions, the PCE depends only on the spectroscopy and cross-sectional geometry of the gain fiber, but not depend on the absolute power.

We use the equations to calculate and optimize the balanced PCE of homogeneously broadened cladding-pumped Er³⁺-doped fiber amplifiers based on phosphorus-rich silica fibers. Cases which fulfill as well as deviate from the ideal balanced assumptions are considered. The resulting PCE agrees well with that of well-established numerical simulations in most investigated cases, but agreement gets worse at large deviations from the ideal assumptions. The calculations are sufficiently fast for optimized curves to be updated real-time when parameters (e.g., describing quenching) are changed.

We believe that our approach is valid for a range of realistic systems, including, for example, Yb-doped and Tm-doped fiber amplifiers as well as inhomogeneously broadened systems. We also discuss criteria for the expression's validity and provide tests which are straightforward to evaluate in the balanced case. Validation in more general, “unbalanced” cases, is more difficult and may in many cases require comparisons to iterative numerical simulations.