Fig. 2. Designed and measured optical spectra for
(a)~(e) Tunable bandpass Hilbert transformer with
90-degree phase shift. (f)~(j) Tunable lowpass Hilbert
transformer with 90-degree phase shift. (k)~(o) Tunable
bandpass fractional Hilbert transformer with 45-degree phase shift.
The soliton crystal is first flattened by a spectrum shaper (waveshaper
4000s), and then modulated with an RF input signal to broadcast the RF
waveform to all wavelength channels at the same time, generating 75
replicas, but we only use 38 or 39 of them as taps. The 98 GHz interval
(2*48.9 GHz), through 3.84 kilometers of standard single-film fiber
(SMF), provides a progressive time delay between wavelengths. The fibre
was approximately twice as long as that used in [58] in order to
yield comparable RF bandwidths. The dispersion of the SMF was
~17.4 ps/nm/km, corresponding to a time delay ∆t = 26.25
ps between adjacent wavelengths. Next, the second WaveShaper accurately
shaped the comb power according to the designed tap coefficients, with
the shaped comb spectrum shown in Fig. 2, for the integral order (90
degree phaseshift) tunable bandpass (a)~(e), integral
order (90 degree phaseshift) tunable lowpass (f)~(j),
and tunable fractional order (45 degree phaseshift) bandpass filter
(k)~(o). Note that all devices used a
~100GHz tap spacing (or more precisely 48.9 x 2 = 97.8
GHz), yielding 39 tap lines across the C-band. Note the fractional order
device used an extra single tap line at the centre wavelength, yielding
40 wavelengths overall, with the centre 3 wavelengths then being spaced
at 48.9 GHz. The result was that the Nyquist zone for the fractional
device was 24.5 GHz rather than 48.9 GHz for the integral order devices.
For standard Hilbert transformer, this extra specific tap coefficient is
not needed and so in principle the full 48.9 GHz comb (75 lines over the
C-band) could have been used although these results are not shown here.