## 3 Experiments
### Multi-Band Signal Generation and Phase Shifting for Multi-Band Phased Array Transmitter  
Two transmitting elements are selected to verify multi-band signal generation and phase shifting, as shown in Figure 3a. One of the transmitting elements is used as a reference to measure the phase difference between two transmitting elements. VODL3 and VODL4 are used to compensate for delay errors in differential signals. An AWG generates an LFM signal with the center frequency of 2.75 GHz and the bandwidth of 500 MHz. Four-band LFM signals with center frequencies of 2.75 GHz, 8.25 GHz, 13.75 GHz, and 19.25 GHz are generated. The single-end and differential output results are shown in Figure 3b, measured by the spectrum analyzer (R&FSFW43, Munich, Germany). Differential detection effectively suppresses the frequency components of the optical pulses, where the power reduction of 11 GHz is ~50.9 dB. The frequency components of the optical pulse are not completely suppressed mainly due to the inconsistent response of the BPD. The common-mode noise of the optical pulses is also effectively suppressed, reducing the noise floor of the generated multi-band signals by ~3.7 dB. The signal-to-noise ratio of the generated multi-band signal is 28.3 dB. The ratio of the signal to the frequency component of the optical pulse is about 13 dB. We observed the four-band signals via an oscilloscope (KEYSIGHT UXR0334B, Santa Rosa, CA, USA, bandwidth 33 GHz) and the time-frequency analysis result is shown in Figure 3c. Figure 3: (**a**) Schematic diagram of the experimental setup for multi-band signal generation and phase control. (**b**) Spectrum analysis for single-ended and differential output of BPD. (**c**) Time–frequency analysis of the multi-band signal. (**d**) Phase difference introduced by VODL. (**e**) Phase difference introduced by PS. (**f**) Phase difference introduced by VODL and PS. (**g**) Phase changes when the aperture fill time, \(t_{d1}\), exceeds 1/\(f_{s1}\). To validate the multi-band phase control capability, multi-tone signals at 2.45 GHz, 2.65 GHz, 2.85 GHz, 3.05 GHz, and 3.25 GHz are generated using an AWG and subsequently up-converted into four frequency bands via optical pulses. The multi-band phase control mechanism comprises two components: optical phase shifting and electrical phase shifting. First, the two phase-shifting methods are independently verified. Based on Equation (8), for the four generated multi-tone signal sets with center frequencies at 2.75 GHz, 8.25 GHz, 13.75 GHz, and 19.25 GHz, the phase shift introduced by the VODL is given by \(2\pi\)_nf\({}_{s1}\Delta t_{1}\)_, while the phase shift introduced by the PS is \(\pm\)_p\({}_{1}\)_. Here, \(n\) takes the values of 0, 1, 1, and 2, and the sign of \(\pm\)_p\({}_{1}\)_ alternates (+, -, +, -) for each corresponding band. To evaluate the VODL-based phase shifting, VODL2 is held constant while VODL1 is adjusted in increments of 4.55 ps, increasing \(\Delta t_{1}\) from 0 ps to 90.9 ps. The resulting phase differences across the four bands are illustrated in Figure 3d, with a four-band RMSE (root mean square error) of 2.87\({}^{\circ}\). For the PS-based phase shifting, PS2 is held constant, and PS1 is adjusted in 20\({}^{\circ}\) increments from 0\({}^{\circ}\) to 360\({}^{\circ}\). The corresponding phase changes in the four bands are shown in Figure 3e, with a four-band RMSE of 2.36\({}^{\circ}\). Subsequently, the two phase-shifting methods are combined to comprehensively verify multi-band phase control. Assuming the aperture fill time, \(t_{d1}\), varied from 0 to 1/_f\({}_{s1}\)_ in steps of 10 ps, VODL1 and PS1 are adjusted according to Equation (4). The phase changes in the multi-tone signals across the four bands, depicted in Figure 3f, exhibit a linear expansion along the frequency axis, consistent with the relationship 2\(\pi\)(\(n\pm 1\)/4)_f\({}_{s1}\)_t\({}_{d1}\)_. The RMSE is 3.91\({}^{\circ}\), which demonstrates a precise multi-band phase control capability.