  We explore the nonlinear response of ultrafast strong-field driven excitons
in a one-dimensional solid with ab initio simulations. We demonstrate from our
simulations and analytical model that a finite population of excitons imprints
unique signatures to the high-harmonic spectra of materials. We show the
exciton population can be retrieved from the spectra. We further demonstrate
signatures of exciton recombination and that a shift of the exciton level is
imprinted into the harmonic signal. The results open the door to high-harmonic
spectroscopy of excitons in condensed-matter systems.
