Optical absorption spectra and dynamical fractional Stark ladders in semiconductor superlattices

The optical response of semiconductor heterostructure under a combined dc-ac fields, (formula presented) 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 (formula presented) we find the periodic motion of (formula presented) 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 (formula presented) Under combined ac-dc fields, we discover the absorption peaks corresponding to the so-called dynamical fractional Stark ladders with ladder spacing (formula presented) where m and (formula presented) are integers and (formula presented) is the Bloch oscillation frequency.