## 5 Experimentally Measuring the PSL of LFM Pulse
### The Process of Measuring the PSL  
To measure the PSL, we follow the steps in Figure 7a. The process involves [3]: (i) Fourier transformation of the received pulse, (ii) removal of the quadratic phase by multiplying the pulse Fourier transform by \(\exp[+jT(f-f_{0})/2B]\), (iii) multiplication by a Hamming window to achieve a peak having a 3 dB width of \(1.3/B\) and a PSL of 42.68 dB, and finally, (iv) inverse Fourier transformation of the result.  
Figure 5: Experimental results for measuring the RF magnitude response of the optical buffer using the VNA when the delay system is made of (**a**) only the LC-FBG, (**b**) only the CS-FBG, and (**c**) the combination of LC-FBG and CS-FBG.  
When we perform the PSL measurement process on our LFM pulse of \(B=1\) GHz at \(f_{0}=10\) GHz that is recorded in the electronic back-to-back configuration, we obtain a PSL of 42.68 dB as shown in Figure 7b.  
Experimentally Measuring the PSL Performance of the LFM Pulse after Delaying It Using the Optical Memory Buffer  
We experimentally measure the PSL performance of the LFM pulse after delaying it using the optical memory buffer. We feed the optical memory buffer with the LFM signal at the RF input port and capture the delayed signal at the buffer output using the optical spectrum analyzer as shown in Figure 8a. Given that our comb FSR is approximately 192 GHz and not fully aligned with the 50 GHz ITU grid, we concentrate on three comb line carriers in the vicinity of the CS-FBG center frequencies at 1535.43 nm, 1545.72 nm, and 1556.55 nm as illustrated in Figure 8b, to ensure that the LFM pulse is fully contained in the flat magnitude response region of the channel. We select these channels because we assume the microresonator can be fabricated in any desired dimensions and FSR to exactly match the CS-FBGs, while the currently available devices may be sufficient for proof of concept. We individually select each channel using the tunable filter and detect the channel using the photodiode of the optical memory buffer.  
Figure 6: (**a**) Experimental configuration for back-to-back generation and detection of an LFM pulse at 10 GHz center frequency and with 1 GHz bandwidth. (**b**) The captured LFM pulse in the time domain. (**c**) The captured LFM pulse in the frequency domain.  
Figure 7: (**a**) The process of measuring the PSL of a compressed pulse. (**b**) The ideal LFM pulse of \(B=1\) GHz at \(f_{0}=10\) GHz after compression shows the maximum PSL to be 42.68 dB in the back-to-back configuration.  
In our assessment, we start by measuring the PSL for the LFM pulse at the output of the optical buffer when we bypass the FBGs. The compressed pulses' results are shown in Figure 9a, with PSL values of \(\sim\)35 dB (lower than the RF back-to-back 42.67 dB baseline), indicating the non-flatness of the modulator and detector frequency response when bypassing the delaying FBGs. Next, we design an offline digital filter \(H(f)\) to compensate for this non-flatness of the system response for every optical delay channel. We apply this filter to the detected signal, and the result of the compressed pulse shows obtaining an ideal PSL of 42.68 dB, as in Figure 9b, representing an improvement of 6.45-8.76 dB. Afterward, we insert the FBGs into our optical memory buffer system and measure the PSL. Our results in Figure 9c show PSL values of 34.43-35.45 dB for the compressed LFM pulse after delay, indicating an overall penalty in the PSL of 7.23-8.25 dB.  
Figure 8: (**a**) Setup for measuring the PSL of an LFM pulse that is delayed using the optical memory buffer. (**b**) The selected wavelengths from the Kerr comb source, where each wavelength carrier represents a different delay value.