## 4 Characterization of the Optical Memory Buffer
### Characterizing the Latency of the Delay System  
We characterize the induced latency (i.e., non-functional added delay) by each of the components in the system: (i) FBG1, (ii) FBG2, (iii) optical amplifier (EDFA), and (iv) tunable LCoS optical filter. The measurement is performed by connecting only one optical component between the optical modulator and photodiode in the optical memory buffer and characterizing the vector network analyzer waveform after transmitting the signal through the component. The results are presented in Table 1. The first column in the table represents the optical component under test. The second column describes the internal element causing the latency. We observe that most of the measured latency is due to the wiring fibers connecting the different components inside the off-the-shelf item, which could be minimized if the components are carefully packaged. The third column presents the measured values of the latency at \(\lambda=1527.27\) nm (zero-delay \(\lambda\)). The fourth column shows the minimum possible latency for the element if the internal fiber jumpers are eliminated or shortened.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Component**} & \multirow{2}{*}{**Internal Element Responsible for the Latency**} & **Measured Latency** & **Minimum Viable** \\  & & **(ns)** & **Latency (ns)** \\ \hline FBG1 & Fiber jumpers at the circulator ports and the FBG terminal. & 144.3 & \textless{}1 \\ \hline FBG2 & Fiber jumpers at the circulator ports and the FBG terminal. & 11.6 & \textless{}0.5 (at zero-delay \(\lambda\)) \\ \hline EDFA & Fiber jumpers at the terminals of isolators and the 1.2 m & 10.1 & \textless{}2.5 \\  & erbium-doped fiber segment. & 35 & \textless{}1 \\ \hline Optical LCoS filter & Fiber jumpers connecting input/output ports to the lenses. & 201 & \textless{}5 \\ \hline TOTAL & & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Latency for the components in the optical delay system.  
Figure 3: (**a**) The configuration for measuring the wavelength-dependent delay in the optical memory buffer induced by the concatenation of off-the-shelf LC-FBG and CS-FBG. A waveform from an electrical vector network analyzer (VNA) is sent from the RF input port of the optical memory buffer. The output is retrieved in the VNA, and the delay is measured by analyzing the phase waveform. (**b**) The delay curve of the optical memory buffer. We observe a delay tuning range of 76 ns over the wavelength range of 1527.7 nm to 1567.9 nm.  
The effective length of FBG1, contributing to the tuning of the delay range, is 7 m, while the effective length of FBG2 is 10 cm. The measured latency induced by the combination of FBG1 and FBG2 at the zero-delay \(\lambda\) is in the order of \(\sim\)155 ns, which we believe is due to the internal circulator connectors and fiber jumpers linking between the device port and FBG; through proper packaging, this latency can be eliminated to below 1.5 ns. The optical amplifier (EDFA) used has a functional length of 1.2 m, and the functional length of the LCoS filter is determined by the distance between the collimators and the internal spatial light modulator, which is in the order of centimeters. Therefore, we estimate that the optical buffer latency can potentially be reduced to less than 5 ns by eliminating the sources of latency. This assumption entails that the wiring fibers for each component are no longer than 20 cm.