We study the response of space-division multiplexed fiber links to an excitation by a short impulse of the optical intensity. We show that, in the presence of full mixing, the intensity impulse response is Gaussian, confirming recently reported experimental observations, and relate its variance to the mean square of the mode dispersion vector of the link τ(->). The good agreement between our theory and the previously published experiments provides solid foundations to the random coupling model of SDM fiber links, and provides a tool for efficient design of MIMO-DSP receivers.