Pump absorption, laser amplification, and effective length in double-clad ytterbium-doped fibers with small area ratio

We use numerical simulations with the beam propagation method (BPM) and rate equations to investigate the pump absorption and amplification characteristics in double-clad ytterbium-doped fibers with small cladding-to-core area ratios, in the range 1-3. The presence of modes with low overlap with the doped region (or alternatively, skew rays) hampers the pump absorption in a circular geometry, but we find that the effect is small for area ratios of ∼2.5 or less. We derive ray-based expressions for the small-signal absorption which show similar results. However, even when the small-signal absorption scales nearly ideally with the inverse of the area ratio, the absorption in an operating amplifier is much lower, and the dependence on the area ratio much weaker, when a large fraction of the Yb-ions is excited in a small-area-ratio fiber. We derive equations which show this, and that in contrast to conventional area ratios of, e.g., 100, the fiber length depends more strongly on the required gain than on the required pump absorption. However, fibers substantially shorter than 1 m still allow for adequate pump absorption and gain. The effective length for nonlinear interactions is less affected by this, since the Yb-excitation is low where the signal power is high. Although we treat single-mode cores, the BPM amplifier simulations show there are a few percent of the signal power in cladding-guided modes with high overlap with the Yb-doped core. Nevertheless, according to our simulations, it is possible to achieve high efficiency and mode purity with a small-area-ratio circularly symmetric double-clad fiber.