  Known methods for transverse confinement and guidance of light can be grouped
into a few basic mechanisms, the most common being metallic reflection, total
internal reflection and photonic-bandgap (or Bragg) reflection. All of them
essentially rely on changes of the refractive index, that is on scalar
properties of light. Recently, processes based on "geometric Berry phases",
such as manipulation of polarization states or deflection of spinning-light
rays, have attracted considerable interest in the contexts of singular optics
and structured light. Here, we disclose a new approach to light waveguiding,
using geometric Berry phases and exploiting polarization states and their
handling. This can be realized in structured three-dimensional anisotropic
media, in which the optic axis lies orthogonal to the propagation direction and
is modulated along it and across the transverse plane, so that the refractive
index remains constant but a phase distortion can be imposed on a beam. In
addition to a complete theoretical analysis with numerical simulations, we
present a proof-of-principle experimental demonstration of this effect in a
discrete element implementation of a geometric phase waveguide. The mechanism
we introduce shows that spin-orbit optical interactions can play an important
role in integrated optics and paves the way to an entire new class of photonic
systems that exploit the vectorial nature of light.
