Achieving optical gain in waveguide-confined nanocluster-sensitized erbium by pulsed excitation

We use a rate equation approach to model the conditions for optical gain in nanocluster sensitized erbium in a slot waveguide geometry. We determine the viability of achieving net gain for the range of reported values of the carrier absorption cross section for silicon nanoclusters. After accounting for the local density of optical states modification of the emission rates, we find that gain is impossible in continuous wave pumping due to carrier absorption, regardless of the carrier absorption cross section. We, therefore, propose a pulsed electrical operation scheme which mitigates carrier absorption by taking advantage of the short lifetime of silicon nanoclusters compared to erbium. We show that pulsed excitation of a 10 nm layer achieves a modal gain of 0.9 dB/cm during each pulse. Furthermore this gain can be increased to 2 dB/cm by pumping a 50 nm layer.