SELECTION-RULES FOR THE HIGH HARMONIC-GENERATION SPECTRA

For three-dimensional many-electron time periodic Hamiltonians which a re invariant under dynamical symmetry of order N we prove that only th e (nN +/- 1)th, n = 1,2,..., harmonics are generated. We discuss the a pplication of the dynamical symmetry based selection rules to the gene ration of high harmonics by thin crystals. The derived selection rules are demonstrated numerically for a one-dimensional model, showing tha t the dynamically symmetric systems can be used not only as ''filters' ' of the very high harmonics but also as their ''amplifiers.''