  Recently, the possibility of the generation and interaction of unipolar
half-cycle electromagnetic pulses with quantum systems has been the subject of
active research. Such pulses can have many different and interesting
applications. They are able to excite quantum systems very fast. Based on the
numerical solution of Maxwell-Bloch equations, this paper theoretically studies
the possibility of guiding and ultrafast controlling population difference
gratings by a sequence of half-cycle attosecond pulses in a three-level
resonant medium. The parameters of the model medium (transition frequencies and
dipole moments of the transitions) are close to those found in the hydrogen
atom. We show the possibility of guiding periodic gratings and dynamic
microcavities on different resonance transitions of the medium. In this case,
the medium considered is an example of a spatiotemporal photonic crystal. The
refractive index varies rapidly in space and time. The possibility of the use
of such gratings as Bragg mirrors in ultrafast optics is discussed. The results
obtained are of interest in two actively developing areas of modern optics -
the physics of half-cycle pulses and space-time photonic crystals.
