Understanding the Confinement Factor—Shaping Light to Optimize Optical Gain

Photonic integrated circuits utilize waveguides to route electromagnetic signals. To amplify these signals, a gain material must be included. In this case, design optimization requires the relationship between amplification and waveguide geometry to be understood. The confinement factor links the gain experienced by the guided mode to the geometry-independent amplification strength of the gain material. Several expressions for the confinement factor have appeared in the literature. Unfortunately, not all of these expressions apply to strongly confined waveguide modes, which are desired in miniaturized optical components. Here, we elucidate the most general description of the confinement factor. Further, we clarify which simplifications have led to other formulations. While related to confinement, these are not generally applicable to the determination of the amplification of a guided mode. Using two numerical examples, we demonstrate the validity and limitation of various expressions of the confinement factor. In high-index-contrast or metallic waveguides, it is typically found that the confinement factor exceeds unity. This counter-intuitive result can be explained by a slowdown of the guided light. Only the general expression of the confinement factor can capture this behavior. Our discussion here provides the necessary understanding to correctly employ the confinement factor for optimization of designs in nanophotonics and plasmonics.