  We develop a semiclassical theory of the nondegenerate parametric
amplification in a single miniband of superlattice. We present the formulas
describing absorption and gain of signal and idler fields in superlattice and
analyze the limiting cases of strong and weak dissipation. We show how the
well-known Manley-Rowe relations arise in the tight-binding lattice in the weak
dissipation limit. Our results can be applied to an amplification of THz
signals in semiconductor superlattices and a control of nonlinear transport of
cold atoms in optical lattices.
