First-principle derivation of gain in high-index-contrast waveguides

From first principles we develop figures of merit to determine the gain experienced by the guided mode and the lasing threshold for devices based on high-index-contrast waveguides. We show that as opposed to low-index-contrast systems, this quantity is not equivalent to the power confinement since in high-index-contrast structures the electric and magnetic field distributions cannot be related by proportionality constant. We show that with a slot waveguide configuration it is possible to achieve more gain than one would expect based on the power confinement in the gain media. Using the figures of merit presented here we optimize a slot waveguide geometry to achieve low-threshold lasing and discuss the fabrication tolerances of such a design.