CLOSED-FORM EXPRESSIONS FOR THE GAIN IN 3-LEVEL AND 4-LEVEL LASER FIBERS

Exact and approximate theoretical models of the small-signal single-pass gain in single-mode three-level laser fibers are presented, relevant to the behavior of rare-earth-doped (in particular Er3+) silica-based fibers. These models account for the effects of both the pump and signal-mode structures and pump excited-state absorption (ESA), the latter being present for some pump wavelengths in Erdoped silica fibers. By relying on the modal overlap integral formalism introduced earlier for four-level lasers, relatively simple closed-form expressions for the pump absorption and the gain are derived. These expressions are also applicable to four-level laser fibers by a simple adjustment of some of the model parameters.