Analysis of effective coupling strength in high-frequency SQUIDs

Abstract

Understanding the coupling mechanism between SQUID (superconducting quantum interference device) loop and resonator in high-frequency SQUIDs is essential for the application of these devices in sensitive magnetometers or controllable microwave devices. We have investigated, therefore, two kinds of planar microstrip tank circuit resonators: (1) S-shaped λ/2-resonators with direct or indirect coupling to the SQUID loop with optional flux-focussing pads and (2) conventional rf-washer-SQUID structures for which we have found resonant modes of the washer providing a coupling to the SQUID loop. A lumped element representation of SQUID loop and resonator is presented in order to describe the effective SQUID-resonator coupling in case of direct or indirect coupling. According to this approach, the square of the effective coupling constant k in both cases is equal to the ratio of the magnetic energy stored in the SQUID loop to that stored in the resonator. For the indirect coupled S-shaped λ/2-resonators, k can be described in terms of a geometry-defined mutual inductance. The predictions of the lumped element description are compared with simulations using a standard full-wave analysis computer program in order to quantify the effect of the different layouts on microwave current distribution and on k. A method for the determination of k by simulation is described, leading to useful design rules for the optimization of high-frequency SQUIDs. The simulation results will also be compared with experimental data.