High harmonic generation of X-rays by carbon nanotubes

Abstract

We have shown that in order to achieve a selective generation of high harmonics, one has to devise a system possessing a very high order spatio-temporal symmetry. Using the dynamical symmetry approach to the formulation of the selection rules for the high harmonic generation spectra, we have derived that a planar molecular target, the N-th order symmetry axis of which is aligned with the wave vector of the circularly polarized laser beam, emits only kN/spl plusmn/1-th (k=1,2,...) harmonics of the incident laser frequency. We extend the method for the formulation of selection rules for high harmonic generation spectra beyond the dipole approximation and apply it to single wall carbon nanotubes interacting with a circularly polarized laser field. Our results show that the carbon nanotubes, especially the chiral ones, can be excellent systems for a selective generation of high harmonics, up to the X-ray regime. The exact symmetry analysis of carbon nanotubes has revealed that the interaction of chiral nanotubes and circularly polarized incident radiation is characterized by a very high order symmetry and can lead to the generation of harmonics of the order higher than 100 in a selective fashion. Thus, already the first high harmonic emitted by a nanotube can fall within the desired (soft X-ray or X-ray) range. For example, for the chiral (8,3) single wall carbon nanotube the first emitted harmonics are the 193-rd and 195-th. In such a case, the wavelength of the first harmonic, generated by a circularly polarized 200 nm incident radiation, is about 1 nm. The chiral nanotubes represent the first example of a realistic physical system giving rise to a high harmonic generation spectrum in which all harmonics but very high ones are forbidden by symmetry.