Understanding Optical Gain: Which Confinement Factor is Correct?

Photonic amplifiers and lasers require optical gain to be extracted from a medium. To optimize this process, the confinement factor (Gamma) connects the actual gain experienced by an electromagnetic mode in a device (modal gain) to the intrinsic gain available from the active medium (material gain). We might intuit that Gamma is simply the modal overlap with the gain region, either as a power or energy ratio. Indeed, such formulations are commonly used for Gamma. However, they fail to capture the physics, particularly when the amplified modes are confined in a waveguide. Here, we review a more general and accurate description of the confinement factor. Using numerical examples, we discuss the validity and limitations of different expressions. Only the general formula properly describes Gamma, especially for slow guided modes for which Gamma exceeds unity. This work aims to clarify the confinement factor for the design of nanophotonic and plasmonic devices.