  Multiphoton excitation of a solid by a few-cycle, intense laser pulse forms a
very non-equilibrium distribution of charge carriers, where occupation
probabilities do not necessarily decrease with energy. We show that, under
certain conditions, significant population inversion can emerge between pairs
of valence- or conduction-band states, where transitions between the Bloch
states are dipole-allowed. This population inversion leads to stimulated
emission in a laser-excited solid at frequencies where the unperturbed solid is
transparent. We establish the optimal conditions for observing the
strong-field-induced optical gain.
