Transverse mode dynamics in VCSELs: Spatiotemporal versus modal expansion descriptions

We discuss the range of validity of a modal description for the
spatiotemporal dynamics of the optical field in vertical-cavity
surface-emitting lasers (VCSELs). We focus on the secondary
pulsations that appear during the turn-off transients when the
injection current is modulated by a square-wave signal. We compare
the results obtained with both a full spatiotemporal model
and a modal expansion derived from
this model. We find that the results obtained from the
two descriptions agree for strong lateral guiding.
However, for weak lateral guiding we find differences because the
optical field profile changes significantly due to
spatial changes in refractive index induced by the
carrier density. The reason is that in the full spatiotemporal
model a shrinkage of the mode profile occurs which leads to an
enhancement of the secondary pulsations. This effect is not
included in the modal expansion, and it determines the limits of
validity of such an approach for gain-guided devices.