Fig. 4. Simulated (dashed curves) and experimental (solid curves) results of tunable bandpass Hilbert transformer with 90-degree phase shift. ( a: purple, 5.6 GHz. b: green, 7.1 GHz. c: blue, 1.2 GHz. d: yellow, 4.1 GHz. e: red, 2.6 GHz.)
Figure.4 shows the measured results for the RF amplitude and phase response of the lowpass Hilbert transformer, showing tunable bandwidths ranging from 1.2 to 7.1 GHz that match closely with the simulated results. We also performed a demonstration of a fractional Hilbert transformer with switchable RF bandwidths ranging from 3.5 to 15.2 GHz. The simulated and measured RF amplitude and phase responses are shown in Fig. 6. We achieved a fractional order of 0.5, which corresponds to a 45-degree phase shift, using up to 39 wavelengths or taps. The increased number of taps used here compared with our previous work (39 here versus 17 taps in [58]) only resulted in an increase in overall bandwidth of about 0.6 GHz, although the performance in octaves was improved a bit more than this (5 octaves for 17 taps versus 6.3 octaves achieved here, as shown in Table I). These results have significant implications for the broader field of microwave photonics [81-127] including the wider use of micro-comb sources, [128-241] even potentially for applications in the mid-IR [242-248] since this approach has a wide range of microwave and RF applications and functions.