  This thesis studies the interaction between near-infrared light and gigahertz
sound in nanoscale silicon waveguides. Chapter 2 introduces photon-phonon
coupling and its theoretical description, describing basic mechanisms and
developing a quantum field theory of the process. Chapter 3 explores the
dynamical effects in both waveguides and cavities. It also proves a connection
between the Brillouin gain coefficient and the vacuum coupling rate. Chapter 4
deals with the observation of Brillouin scattering in nanoscale silicon
waveguides. The waveguides tightly confine $193 \, \text{THz}$ light and $10 \,
\text{GHz}$ acoustic vibrations. The acoustic quality factor remains limited to
about $300$ because of leakage into silica substrate. These waveguides are
optically transparent in a narrow band of frequencies at a pump power of $25 \,
\text{mW}$. Besides this amplification, we translate a $10 \, \text{GHz}$
microwave signal across $1 \, \text{THz}$. Chapter 5 extends the experimental
work of chapter 4 by fabricating a cascade of fully suspended nanowires held by
silica anchors. This enhances the mechanical quality factor from $300$ to
$1000$, enabling the observation of Brillouin amplification exceeding the
propagation losses in silicon. The amount of amplification is mostly limited by
a rapid drop in acoustic quality as the number of suspensions increases. We
propose a mechanism to cancel this inhomogeneous broadening. Chapter 6 looks at
the potential of narrow silicon slot waveguides to enhance the optomechanical
coupling. For certain dimensions, these waveguides support opto-acoustic modes
with an interaction efficiency simulated an order of magnitude above those of
single-nanobeam systems.
