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.