INTRODUCTION
The Hilbert transform is a fundamental signal processing function with
wide range of applications in radar systems, signal sideband modulators,
measurement systems, signal sampling, and many others [1-8].
Fractional Hilbert transforms provide an additional degree of freedom in
terms of a variable phase shift, which can meet the special requirements
of unilateral communication [2] and confidentiality of hardware keys
[3]. In practical applications such as multiplexing and
demultiplexing signals, analyzing individual sub-channel spectral
components, etc., Hilbert transformers are typically realized as a
truncated or windowed version of the ideal Hilbert transform impulse
response [5-7]. Therefore, Hilbert transformers covering a wide
range of different band pass regions are highly desirable.
Compared to electrical Hilbert transformers that suffer from intrinsic
bandwidth bottlenecks, photonic integrated devices have shown advantages
in high-speed signal processing. RF photonic Hilbert transformers have
been proposed based on fiber Bragg gratings [9-15], micro-ring /
micro-disk resonators [16, 17], and integrated reconfigurable
microwave processors [18]. However, most of these schemes focus on
generating the Hilbert transform of the complex optical fields rather
than the actual RF signal. In order to realize highly reconfigurable RF
photonic Hilbert transformers, transversal schemes with a high
reconfigurability have been investigated [19, 20]. However, the use
of multiple discrete laser sources presents limitations in the overall
system footprint, processing performance, and the potential for full
monolithic integration.
Recently, micro-combs that offer a large number of coherent wavelengths
from one compact device have attracted significant interest as a
fundamentally powerful tool for microwave processing [8, 21-40] .
They have been used for various advanced signal processing [8,
41-64] and neural networks [65-67]. In Ref. [1], we reported a
fractional Hilbert transformer with a RF bandwidth ranging from 5 to 9
octaves depending on the fractional order. It was based on a soliton
crystal micro-comb with FSR = 48.9 GHz, and 17 taps were selected from
the 75 wavelengths generated in the C band as discrete taps.
In this paper, we further demonstrate a photonic Hilbert transformer
with variable bandwidth and RF center frequency [1]. It is based on
a transversal filter system with a soliton crystal Kerr micro-comb
source. In the experimental demonstration, we used 40 comb lines in the
C-band [1]. By programming and shaping the comb lines according to
calculated tap weights, the center frequency of Hilbert transform was
tuned from baseband to 9.5 GHz, and the bandwidth of RF amplitude and
phase responses was tuned from 1.2 to 15.3 GHz, confirming the high
reconfigurability of our system. The experimental results show good
agreement with the theory, confirming the feasibility of our approach
towards the realization of high-speed reconfigurable Hilbert
transformers with reduced footprint, lower complexity, and potentially
reduced cost.