Measurement of loss in superconducting microstrip at millimeter-wave frequencies

We have developed a new technique for accurate measurement of the loss of superconducting microstrips at mm-wave frequencies. In this technique, we optically couple power to slot antenna, which is connected to one port of a hybrid coupler. One of the output ports of the hybrid delivers power to a series of mm-wave microstrip resonators which are capacitively coupled to a feedline followed by an MKID (microwave kinetic inductance detector) that measures the transmitted power. Two other MKIDs are connected to the remaining ports of the hybrid to measure the total incident optical power and the power reflected from the mm-wave resonators, allowing \S2\\^ and \S\\\^ to be accurately determined and resonance frequency f and quality factor Q to be retrieved. We have fabricated such a Nb/Si02/Nb microstrip loss test device which contains several mmwave resonators with /^ -^100 GHz and measured it at 30 mK. All the resonators have shown internal quality factor Qi-^ 500 — 2000, suggesting a loss tangent of -̂ 5 x 10^ — 2 x 10^ for the Si02 in use. For comparison, we have also fabricated a 5 GHz microstrip resonator on the same chip and measured it with a network analyzer. The loss tangent at 5 GHz derived from fitting the fo and Q data to the two-level system (TLS) model is 6 x 10^ , about the same as from the mm-wave measurement. This suggests that the loss at both microwave and mm-wave frequencies is probably dominated by the TLS in Si02. Our results are of direct interest to mm/submm direct detection applications which use microstrip transmission lines (such as antenna-coupled MKIDs and transition-edge sensors), and other applications (such as on-chip filters). Our measurement technique is applicable up to approximately 1 THz and can be used to investigate a range of dielectrics.