## 3 Results and Discussion  
Figure 3 shows the frequency-tuning characteristics of the generated microwave signals that were detected by the ESA with a resolution bandwidth of 10 Hz. When optical path length difference, \(d\), was varied from 10 mm to 90 mm, the microwave frequency was continuously tuned from 2.0 GHz to 19.7 GHz. As shown by the red line in Figure 3, linear fitting is performed for the experimental data. The measured conversion constant  
between \(f_{\rm{i}}\) and \(d\) equals the slope of the fitting curve, which is 0.22209 GHz/mm. It is clear that the calculated and measured values of the conversion constant are very close. In addition, the goodness of fit (R-square) is 0.99999 in this system. Such a high linearity is attributed to the same optical fiber path for the \(A_{R}\) and \(A_{\rm{S}}\) in the interferometer, which could eliminate the nonlinear effects caused by optical devices. Additionally, rapid frequency tuning was achieved by a fast-moving scan of the motorized translation stage in the GDS. The scan speed was 3000 mm/s with repeatability of less than 1 \(\upmu\)m, corresponding to a frequency-tuning response time of 0.66627 MHz/us in our experiment. Moreover, it is deduced that a higher microwave frequency could be obtained by increasing the optical path length difference. However, limited by the frequency response bandwidth of the PD, a higher frequency was not attempted in our experiment. The inset in Figure 3 shows the train of generated microwave pulses, which indicates that the time interval between two contiguous pulses is about 45.5 ns. Figure 4a shows the measured electrical spectrum of the pulsed microwave signals at 10.6 GHz. It is obvious that the generated microwave signal has a relatively narrow center frequency with broadband noise, of which the signal-to-noise ratio was higher than 15.4 dB. The details of the generated microwave frequency lines, marked with a red box in Figure 4a, are enlarged and shown in Figure 4b. Owing to the high phase stability of the mode-locked laser and the high dispersion linearity of the DCF, these frequency lines have a steady frequency interval of 22 MHz, which could be extracted to generate spectrally pure microwaves via electrical filtering processing [28]. In addition, the maximum power peak of \(-\)3.6 dBm was located at 10.592 GHz. Except for the frequency lines at 10.570 GHz and 10.614 GHz, the power difference between 10.592 GHz and the other frequencies was higher than 8.7 dB. Moreover, the linewidth of frequency line at 10.592 GHz was measured by the ESA with a resolution bandwidth of 1 Hz and is shown in Figure 4c. The 3 dB bandwidth of each frequency line was estimated to be less than 2 Hz through Gaussian fitting. Furthermore, based on Equation (2) in [29], the single-sideband phase noise of the  
Figure 3: The frequency-tuning characteristics of the generated microwave signals. Inset: the train of generated microwave pulses. 10.592 GHz carrier was calculated. As shown in Figure 4d, the single-sideband phase noise was about \(-28\) dBc/Hz, \(-69\) dBc/Hz and \(-94\) dBc/Hz at the offset frequencies of 10 Hz, 100 Hz and 1000 Hz, respectively. Using our method, since the microwave pulse signal was generated by the beat frequency of two coherent laser signals that were split by the same laser pulse, the noise caused by the initial phase jitter was avoided. Therefore, a slight time jitter of the mode-locked laser will not affect the performance of the proposed experimental setup. The noise of the microwave pulse mainly came from the photodetector noise. To better characterize the generated microwave waveform, temporal interferograms were detected using a digitizer with an impedance of 50 \(\Omega\). Figure 5a,b show the measured microwave pulse waveforms at different frequencies and the details of the red-dotted box, respectively. The peak-peak values of the voltage amplitudes for the microwave waveforms were measured to be about 2.7 V at 5.4 GHz, 2.2 V at 10.9 GHz and 1.8 V at 15.3 GHz, respectively.