Optical absorption spectra and dynamical fractional Stark ladders in semiconductor superlattices

The optical response of semiconductor heterostructure under a combined dc-ac fields, ${F}_{\mathrm{dc}}{+F}_{\mathrm{ac}}\mathrm{cos}{\ensuremath{\omega}}_{L}t,$ is studied by calculating absorption spectra based on semiconductor Bloch equations. First, we investigate the periodic motion of the carrier in a band under a ac field or dc field. Under the ac field with the frequency ${\ensuremath{\omega}}_{L},$ we find the periodic motion of ${\ensuremath{\omega}}_{L},$ which is very similar to the Bloch oscillation under the dc field. The ladder spacing of quasienergy states under the ac field is observed to be $\ensuremath{\Elzxh}{\ensuremath{\omega}}_{L}.$ Under combined ac-dc fields, we discover the absorption peaks corresponding to the so-called dynamical fractional Stark ladders with ladder spacing $m\ensuremath{\Elzxh}{\ensuremath{\omega}}_{B}{+m}^{\ensuremath{'}}\ensuremath{\Elzxh}{\ensuremath{\omega}}_{L}$ where m and ${m}^{\ensuremath{'}}$ are integers and ${\ensuremath{\omega}}_{B}$ is the Bloch oscillation frequency.