Physicists in Japan have theoretically shown that an optical equivalent
of the Hall effect exists, and that this hypothesis could be borne out
with experiments with polarized light.
In the classic Hall effect, an electric current, pulled along a conductor
by an electric field, will be deflected sideways somewhat if in addition
a magnetic field (perpendicular to the electric field and to the plane
of the conductor) is applied. One can attribute to the sideways motion
a "Hall voltage" and a "Hall resistance."
If the experimental conditions are even more stringent---extremely
cold temperatures and high magnetic field---a quantum equivalent of
the Hall effect manifests itself. In this case the electrons execute
trajectories that are quantized; that is, the Hall resistance can take
only certain discrete values.
Something like this might be happening when a light ray moves from
one medium into another. The amount of the shift sideways at the deflection
will depend on the change in the index of refraction from the one medium
into the other.
Masaru Onoda (email@example.com, 81-29-861-2985) at the National Institute
of Advanced Industrial Science and Technology (Tsukuba, Japan) and his
colleagues at the University of Tokyo believe that the topological aspects
of light refraction in materials can be explored in upcoming experiments
using photonic crystals. In effect, they are predicting a correction
to Snell's law for spin-polarized light. (Onoda et al., Physical
Review Letters, upcoming article.)