High harmonic generation of X-rays by carbon nanotubes

The dynamical symmetry method is applied to the formulation of the selection rules for the high harmonic generation spectra. Results show that a planar molecular target of the N-th order symmetry axis emits only kN±1-th (k = 1, 2, ..) harmonics of the incidence laser frequency. The method is extended beyond the dipole approximation and is applied to single wall carbon nanotubes interacting with a circularly polarized laser field. Results show that the carbon nanotubes can be excellent systems for the selective generation of high harmonics, up to the X-ray regime.