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Broadband microwave spectroscopy can probe material properties in widespectral and temperature ranges, including superconductors at cryogenictemperatures. The quality of such measurements crucially depends on thecalibration, which also removes from the obtained spectra signatures ofstanding waves. Here we consider low-temperature reflection measurements inCorbino geometry, and we show that the non-linear response of superconductingsamples close to the critical temperature can lead to strong signatures ofstanding waves even in a well-calibrated Corbino spectrometer. We demonstrateour findings with microwave measurements as a function of frequency andtemperature for a variety of superconducting samples and for different lengthof the microwave transmission line. Finally we show that such non-lineareffects extend beyond the case of superconductors by probing a VO$_2$ thin filmat the insulator-metal transition.

Role of non-linear effects and standing waves in microwave spectroscopy: Corbino measurements on superconductors and VO$_2$