  Non-linear effects in photoemission are shown to open a new access to the
band structure of unoccupied states in solids, totally different from hitherto
used photoemission spectroscopy. Despite its second-order nature, strong
resonant transitions occur, obeying exact selection rules of energy, crystal
symmetry, and momentum. Ab-initio calculations are used to demonstrate that
such structures are present in low-energy laser spectroscopy experimental
measurements on Si previously published. Similar resonances are expected in
ultraviolet angle-resolved photoemission spectra, as shown in a model
calculation on Al.
