  We report the results of Brillouin-Mandelstam spectroscopy and Mueller matrix
spectroscopic ellipsometry of the nanoscale "pillar with the hat" periodic
silicon structures, revealing intriguing phononic and photonic properties. It
has been theoretically shown that periodic structures with properly tuned
dimensions can act simultaneously as phononic and photonic - phoxonic -
crystals, strongly affecting the light-matter interactions. Acoustic phonon
states can be tuned by external boundaries, either as a result of phonon
confinement effects in individual nanostructures, or as a result of
artificially induced external periodicity, as in the phononic crystals. The
shape of the nanoscale pillar array was engineered to ensure the interplay of
both effects. The Brillouin-Mandelstam spectroscopy data indicated strong
flattening of the acoustic phonon dispersion in the frequency range from 2 GHz
to 20 GHz and the phonon wave vector extending to the higher-order Brillouin
zones. The specifics of the phonon dispersion dependence on the pillar arrays
orientation suggest the presence of both periodic modulation and spatial
localization effects for the acoustic phonons. The ellipsometry data reveal a
distinct scatter pattern of four-fold symmetry due to nanoscale periodicity of
the pillar arrays. Our results confirm the dual functionality of the
nanostructured shape-engineered structure and indicate a possible new direction
for fine-tuning the light-matter interaction in the next generation of
photonic, optoelectronic, and phononic devices.
