Fano interference in microwave resonator measurements

Resonator measurements are a simple but powerful tool to characterize a material’s microwave response. The losses of a resonant mode are quantified by its internal quality factor Qi, which can be extracted from the scattering coefficient in a microwave reflection or transmission measurement. Here we show that a systematic error on Qi arises from Fano interference of the signal with a background path. Limited knowledge of the interfering paths and their relative amplitudes in a given setup translates into a range of uncertainty for Qi, which increases with the coupling coefficient. We experimentally illustrate the relevance of Fano interference in typical microwave resonator measurements and the associated pitfalls encountered in extracting Qi. On the other hand, we show how to characterize and utilize the Fano interference to eliminate the systematic error.