  Light propagating in opposite directions around the same loop in general
shows a relative phase shift when recombined. This phenomenon is known as the
Sagnac effect after Georges Sagnac who, in 1913, demonstrated with an
interferometer on a rotating table that the phase shift depended on the angular
velocity of the table. In previous work we have given a very general formula
for the Sagnac effect, valid in full general relativity. The relativistic
effect not only contains the `classical' contribution from the rotation of the
laboratory but also contributions due its acceleration and due to incoming
gravitational waves. Here, we point out a major consequence of this
gravitational effect which may have implications for third generation
gravitational wave detectors. We describe an `antenna' design which picks out
specific components of the Weyl tensor describing the incident gravitational
waves.
