Wavelength dependence of high-order harmonic yields in solids

We theoretically investigate the wavelength dependence of high-order harmonic yields in solids driven by a mid-infrared laser field. By solving the three-dimensional two-band density matrix equations in the wavelength range of 2.0-7.5 mu m, it is shown that, in the limit of slow dephasing (dephasing time T-2 -> infinity), the high-order harmonic yield from a crystal follows a scaling of lambda(-4) for a fixed energy interval. The lambda(-4) scaling is attributed to the wave-packet spreading (lambda(-3) ) for the overall yield and the energy distribution effect (lambda(-1)) due to the increase of the cutoff. For the crystal with a finite dephasing time T-2 , we find that the exponential factor x of lambda(-x) increases with a decay of T-2. An apparent and rapid fluctuation on a fine wavelength mesh is also observed in the harmonic yields. The fine-scale oscillation originates from the quantum interference effect, and the corresponding modulation period delta lambda scales as lambda(-1).