  We demonstrate full control of acoustic and thermal periodic deformations at
solid surfaces down to sub-nanosecond time scales and few-micrometer length
scales via independent variation of the temporal and spatial phase of two
optical transient grating (TG) excitations. For this purpose, we introduce an
experimental setup that exerts control of the spatial phase of subsequent
time-delayed TG excitations depending on their polarization state. Specific
exemplary coherent control cases are discussed theoretically and corresponding
experimental data are presented in which time-resolved x-ray reflectivity
measures the spatiotemporal surface distortion of nanolayered heterostructures.
Finally, we discuss examples where the application of our method may enable the
control of functional material properties via tailored spatiotemporal strain
fields.
