## 3 Experiment and Results  
The schematic setup based on Figure 1 was experimentally performed to verify the effectiveness of the proposed approach for the generation of square and triangular waveforms. The optical signal from the TLS (NKT, E15) with the wavelength of 1549.955 nm, and the power of 8 dBm was sent to the  
Figure 2: The calculated modulation index \(\beta\) versus the phase difference \(\theta\). DDMZM (EOSPACE, 40 GHz). The modulator had a half-wave voltage of 4.4 V. Furthermore, it was biased at the quadrature point. To simplify the experimental operation, a 180\({}^{\circ}\) hybrid coupler was used instead of a RF coupler and a phase shifter, on the condition that \(\theta=\pi\). A 5 GHz RF signal generated from the single frequency source (Agilent E4438C) was divided by the 180\({}^{\circ}\) hybrid coupler and then applied to the two arms of the modulator. Afterwards, the modulated optical signal was sent to the PD (Finisar, 50 GHz) for intensity detection. The responsivity of the PD was about 0.6 A/W. Additionally, the 3 dB bandwidth was 50 GHz. An electrical amplifier with a gain of 30 dB was employed after the PD to boost the generated pulse train signal. In order to fit the phase condition for the first and third order harmonics, a 90\({}^{\circ}\) hybrid coupler was applied afterward. In the end, the electric signal was divided by a power splitter. One part was sent to the electrical spectrum analyzer (ESA, Agilent, E4440A), and the other to the oscilloscope (OSC, Keysight, UXR0704 AP). For the generation of the square waveform, the DDMZM was first driven by a 5 GHz RF signal. Adjusting the input RF power to make sure that the modulation index \(\beta=1.15\), we got a square waveform from the 0\({}^{\circ}\) port of the hybrid coupler. The electric spectrum is shown in Figure 3a. The even-order harmonics were completely suppressed. The third-order harmonics at 15 GHz was 9.62 dB lower than the fundamental harmonic, which was very close to the theoretical calculation result. Figure 3b shows the generated square waveform compared with the theoretical waveform. The measured square waveform fit well with the theoretical waveform. The root-mean-square error (RMSE) between the measured and theoretical waveform was calculated as 0.053. By adjusting the input RF power, the triangular waveform could be obtained from the 90\({}^{\circ}\) port of the hybrid coupler. Figure 4 shows the electrical power spectrum and waveform of the generated triangular pulse train. As can be seen from Figure 4a, the even-order harmonics are completely suppressed and the power of the third-order harmonic is 18.8 dB lower than that of the fundamental frequency. This power is very close to the theoretical value (19.08 dB lower than the fundamental frequency). As given by Figure 4b, a full-duty-cycle triangular train with a time period of 0.2 ns is obtained. The RMSE is 0.042 for the triangular waveforms with a repetition rate of 5 GHz. In order to verify the tunability of the system, the frequency of the signal source was set to 8 GHz and 10 GHz, respectively. The corresponding electrical spectrum and time-domain triangular wave signal were also obtained, as shown in Figures 5 and 6. It can be seen from Figures 5a,c and 6a,c that the even-order harmonics are well suppressed. For both the 8 GHz and 10 GHz signals, the second harmonic is around 36 dB below the fundamental term. The corresponding square waveforms with the period of 0.125 ns and 0.1 ns are observed in Figure 5b,d. This is in good agreement with the theoretical waveform. It should also be pointed out that the frequency response of the DDMZM is not perfect and fluctuates within the operating bandwidth. Hence, the RF signal power should be adjusted accordingly as the frequency increases. Figure 3: Measured (**a**) electrical power spectrum and (**b**) waveforms of the generated square waveform with a repetition rate of 5 GHz.