## 2 Experimental Setup  
Figure 1 shows the experimental setup of frequency-tunable pulsed microwave waveform generation, which was achieved by using an unbalanced single-arm interferometer with frequency-to-time mapping. The optical source used in our experiments was a passive mode-locked fiber laser, of which the repetition frequency, pulse width, output power and center wavelength were 22 MHz, 500 fs, 5 mW and 1550 nm, respectively. In addition, the 3 dB spectral linewidth was about 20 nm to ensure that the spectral pattern is approximately flat-topped in the range from 1545 nm to 1555 nm. The optical spectrum of the mode-locked laser was first shaped into a rectangular profile through a bandpass optical filter (OF, 1550 nm \(\pm\) 5 nm). Then, an unbalanced single-arm interferometer with a frequency-to-time mapping was used and consisted in an optical circulator (OC), a group delay system (GDS), one section of dispersion compensation fiber (DCF, optical fiber type: BD NDCF-G652C), an erbium-doped fiber amplifier (EDFA) and a photodetector (PD). After port 2 of the OC, the pre-shaped femtosecond laser was divided into two parts by the GDS, which consisted of a physical contact ceramic insertion pin (PC pin) and a plane-parallel reflection mirror (M1) mounted on a motorized translation stage. The reflected laser beams, from the end of the PC pin and the M1, were named as \(A_{R}\) and \(A_{S}\), respectively. In addition, the group delay time, \(\Delta\tau\), between \(A_{R}\) and \(A_{S}\) could be adjusted by changing the optical path length difference, \(d\), in the GDS. After port 3 of the OC, the linear dispersion was introduced into the combined laser pulse using the DCF, which realized frequency-to-time mapping. Then, the linear chirped optical pulse train was amplified by the EDFA and then converted into a pulsed microwave waveform by the PD. Moreover, continuous microwave frequency tuning can be obtained by translating the stage to vary the value of \(d\). Finally, the waveform and frequency of the generated pulsed microwave were measured through a bandpass electrical filter (EF, 500 MHz to 40 GHz) by a digitizer and an electrical spectrum analyzer (ESA), respectively. In this scheme, the frequency-tunable pulsed microwave waveform generation originates from the temporal interferogram that was mapped from the spectral interference through the linear dispersion. The frequency of the temporal interferogram depends on the dispersion value and the group delay time between the two coherent beams in the unbalanced single-arm interferometer. The total dispersion value is usually a constant, while the optical fiber devices are fixed in the system. However, the group delay time can be simply varied without any polarization control. Therefore, the unbalanced single-arm interferometer with a frequency-to-time mapping configuration is considered a suitable frequency-tunable pulsed microwave waveform generator. Figure 2 shows the basic principle of the pulsed microwave frequency tuning. Figure 1: Experimental setup of frequency-tunable pulsed microwave waveform generation. OF, bandpass optical filter; OC, optical circulator; GDS, group delay system; PC pin, physical contact ceramic insertion pin; M1, plane-parallel reflection mirror; DCF, dispersion compensation fiber; EDFA, erbium-doped fiber amplifier; PD, photodetector; EF, bandpass electrical filter; ESA, electrical spectrum analyzer. Figure 2: The principle of pulsed microwave frequency tuning based on an unbalanced single-arm interferometer with frequency-to-time mapping. As shown in Figure 2, owing to the frequency-to-time mapping effect induced by the DCF, the pulses of \(A_{R}\) and \(A_{S}\) are broadened in the time domain and are described as follows:  
\[\left\{ \begin{array}{c}A_{i}(t)=a_{i}(t)cos\left[2\pi\int_{0}^{t}f_{i}(\tau)d \tau\right]\\ f_{i}(t)=t/\beta_{2}L\end{array} \right.