Analysis of the periodicity of voltage versus applied flux curves of planar and three-dimensional SQUIDs in the presence of coupling inhomogeneity

Coupling inhomogeneities in the Josephson junctions of planar 0-SQUIDs and π-SQUIDs and of three-dimensional SQUIDs are considered. Starting from the properties of planar SQUIDs, it is shown that slight non-homogeneous couplings of the twelve junctions in three-dimensional superconducting interferometers do not affect the periodicity properties of voltage versus applied flux curves. The results are obtained by applying a rigorous and general analytic approach to planar and three-dimensional superconducting devices.