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 three-dimensional superconducting quantum interference devices (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 magnetometers, gradiometers, and particle detectors.
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