  We theoretically demonstrate the possibility to tune the temporal waveform of
optical unipolar pulses upon their coherent interaction with a multi-level
resonant medium. This is achieved through the coherent control of the response
of a multi-level resonant medium by means of half-cycle unipolar pulses. We
show that despite the ultrabroad spectrum of half-cycle pulses one can
efficiently steer the induced medium polarization through the proper choice of
the parameters of the excitation pulses. As the result, producing of unipolar
optical pulses of varying profile, like rectangular or triangular ones, from an
extended layer of a multi-layer medium was obtained when excited by a pair of
half-cycle pulses. Besides, we find out that the response of a multi-level
medium for the amplitude of the driving pulses below a certain threshold can be
quantitatively well approximated by the two-level model.
