Bias Field Gradient Effects of Large Superconducting Quantul Inteference Device (SQUID) Arrays (SQAs)

In this investigation we explore the effects of nonuniform magnetic bias fields on the voltage-flux curve of large two-dimensional arrays of superconducting quantum interference devices (SQUIDs). The SQUID arrays (SQAs) contain 1020 SQUIDs modeled with parallel coupling in the x-direction and series coupling in the y-direction. Each array is composed of individual SQUID elements having non-uniform size loop areas, resulting in a non-uniform inductance parameter $\beta_{L}$, and a single “anti-peak” feature at zero magnetic field in the voltage-flux transfer function. We examine the changed induced in the profile of the transfer function by gradients in the magnetic field in both the x- and y-directions. The height, slope, and symmetry of the anti-peak feature is compared with that from the same SQA exposed to a uniform field.