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 Q_i, which can be extracted from the scattering coefficient in a microwave reflection or transmission measurement. Here we show that a systematic error on Q_i arises from Fano interference of the signal with a background path. Limited knowledge of the interfering paths in a given setup translates into a range of uncertainty for Q_i, 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 Q_i. On the other hand, we also show how to characterize and utilize the Fano interference to eliminate the systematic error.