Floquet-Bloch theory of high-harmonic generation in periodic structures

Generation of high harmonics by the interaction of intense laser fields with periodic crystal structures is investigated theoretically. A nonperturbative Floquet-Bloch theory of the interacting system (crystal plus laser field) is developed and applied to obtain the field-modified band structure of the system. The mean energy spectrum, the dispersion and the fluctuation of the band energy in the photon space, and the associated standard deviation and spectral entropy are calculated. The harmonic generation spectra in a thin crystal, for the neodymium-doped yttrium aluminum garnet laser frequency $\ensuremath{\omega}=1.169$ eV, are obtained, both in the perturbative and nonperturbative intensity domains. The calculated emission spectra for an insulator, a semiconductor, and a metal film are compared. The semiconductor medium is found to be somewhat more efficient than the metal or the insulator. A ``transition intensity'' for strong harmonic generation in crystalline media occurs at about an intensity I=${10}^{\ensuremath{-}4}$ a.u., i.e., $3.51\ifmmode\times\else\texttimes\fi{}{10}^{12}$ W/cm${}^{2}$.