  Typically, strong gain saturation and gain dynamics play a crucial role in
semiconductor laser mode-locking. While there have been several investigations
of the ultrafast gain dynamics in vertical-external-cavity surface-emitting
lasers (VECSELs), little is known about the associated refractive index
changes. Yet, such refractive index changes do not only have a profound impact
on the pulse formation process leading to self-phase modulation, which needs to
be compensated by dispersion, but they are also of particular relevance for
assessing the feasibility of Kerr-lens mode-locking of VECSELs. Here, we
measure both refractive index as well as gain dynamics of a VECSEL chip using
the ultrafast beam deflection method. We find that, in contrast to the gain
dynamics, the refractive index dynamics is dominated by an instantaneous
($\sim$100~fs) and a very slow component ($\sim$100~ps). The time-resolved
measurement of nonlinear refraction allows us to predict a pulse-length
dependent, effective nonlinear refractive index $n_{2,eff}$, which is shown to
be negative and in the order of $10^{-16}$ $m^2/W$ for short pulse lengths
($\sim$100~fs) . It becomes positive for large excitation fluences and large
pulse lengths (few ps). These results agree with some previous reports of
self-mode-locked VECSELs for which the cavity design and pulse properties
determine sign and strength of the nonlinear refractive index when assuming
Kerr-lens mode-locking.
