  We present a theoretical study on the dynamical properties of
three-dimensional arrays of Josephson junctions. Our results indicate that such
superconducting networks represent highly sensitive 3D-SQUIDs having some major
advantages in comparison with conventional planar SQUIDs. The voltage response
function of 3D-SQUIDs is directly related to the vector-character of external
electromagnetic fields. The theory developed here allows the three-dimensional
reconstruction of a detected external field including phase information about
the field variables. Applications include the design of novel magnetometers,
gradiometers and particle detectors.
