  Laguerre-Gaussian (LG) beams reflected from a multi-layered dielectric
experience a shift in their centroid that is different than that from a single
interface. This has been previously investigated for linearly polarized beams
and, to a much lesser extent, beams with spin angular momentum. Here a
combination of perturbation and computational analyses is used to provide a
unified quantification of these shifts in layered dielectrics with two parallel
interfaces. The approach is then extended to consider the qualitatively new
behavior that results when the light is endowed with an intrinsic orbital
angular momentum--i.e. vortex beams. Destructive interference causes singular
lateral shifts in the centroid of the reflected vortex beam for which spin
alone produces only a mild modulation. In the case of total internal
reflection, both spin and intrinsic orbital angular momentum contribute to an
enhancement of these lateral shifts as the interlayer thickness is decreased.
This is just the opposite of the trend associated with longitudinal shifts. Two
geometries are considered: air/glass/air and glass/air/glass multi-layers. A
commonly available glass is used to show that vortex beams can result in
centroid shifts on the order of microns for beams with a significant reflection
coefficient.
