Dual Frequency Mixing Products and Terahertz Hilbert-Transform Spectroscopy With Josephson Cantilevers in a THz Microscope

Josephson cantilevers, based on high-temperature superconducting yttrium barium copper oxide Josephson junctions, can be employed for the measurement of frequency and power of microwave and terahertz radiation. Each Josephson cantilever carries at least one Josephson junction with a dedicated antenna structure for better coupling. In the THz microscope, such cantilevers are employed for spatially resolved measurements of radiation distributions over either active emitting or passive samples that are irradiated by an external terahertz source. The power distribution can be reconstructed from Shapiro steps in the current-voltage characteristic of the cantilever's Josephson junction by methods including Hilbert spectroscopy. We show that simulations with simultaneous excitation with more than a single frequency result in the appearance of Shapiro steps at sum and difference frequencies. The amplitudes of these steps approximately follow Bessel functions, as with the Shapiro steps from single frequency excitation. This is confirmed by a setup in the THz microscope, where the Josephson cantilever is simultaneously subjected to 40 GHz radiation of variable power and 693 or 762 GHz radiation from a far-infrared laser system. Josephson mixing spectra show peaks at sum and difference frequencies following Bessel curves with increasing power, as it was predicted for the according Shapiro steps. These products should be avoided for a reconstruction of the original signals by Hilbert spectroscopy.