# An Integrated Photorefractive Analog Matrix-Vector Multiplier for Machine Learning +
## 4 Discussion  
The results presented here constitute important milestones in the development of the integrated photorefractive crossbar array.  
The photorefractive effect is well studied in bulk crystals [10,12]. Here, we report that semi-insulating GaAs can be thinned down to 1 \(\upmu\)m thick films and that photonic circuits can be fabricated therein, while preserving photorefractive behavior (Figure 11a).  
The two-wave mixing signal observed in the free-space measurement (Figure 11a) implies that the photorefractive coupling strength in the circuit is adequate for a similar demonstration in the integrated processor (Figure 8a). Both experiments are configured to resolve the intensity cross term between the transmitted and diffracted field components (Section 2.1.3). Then, the relative modification of both fields may be estimated to assess the impact of switching to the integrated experiment. The transmitted beam amplitude is estimated to increase by 15 dB, since it is not blocked by an output polarizer. The diffracted  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Trace \#1** & **Trace \#2** & **Trace \#3** & **Average** \\ \hline
**Heating** & 4.3 & 4.3 & - & 4.3 \(\pm\) 0.1 \\
**Cooling** & 6.0 & 6.1 & 5.9 & 6.0 \(\pm\) 0.1 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Fitted response times (\(\tau\)) for the electric tungsten-heater-based thermo-optic amplitude modulator in \(\upmu\)s (Figure 10c).  
Figure 11: Photorefractive two-wave mixing in thin-film GaAs structures (Section 2.1.3). Graph (**a**) shows data from the photonic chip and was measured by focusing the laser beams on the interaction area of the photorefractive photonic processor (Figure 8). Graph (**b**) was measured on a 3 \(\upmu\)m thin-film sample.  
beam amplitude is expected to increase by 23 dB. Namely, the beam interaction length will increase from 1 \(\upmu\)m to 200 \(\upmu\)m (Equation (1)). Moreover, the photorefractive coupling constant \(\gamma\) is equal or larger for the integrated circuit configuration [12]. Then, at the same laser power, the two-wave mixing modulation signal (Figure 6) should be around 10 dB larger for the integrated experiment, after 26 dB of coupling and propagation losses (Figure 10d).  
It is implied that response times constitute the main experimental challenge in demonstrating two-wave mixing in the prototype processor (Figure 8a). Compared to the free-space experiment (Figure 7), at the same laser power, the grating is expected to form two orders of magnitude faster. Namely, the optical intensity is increased by the confinement of the field in integrated photonics. Then, the photorefractive response time would be similar to the response time of the thermo-optic phase modulator (Table 1). If the grating responds sufficiently fast to track the phase modulation, the optical intensity will not be modified. The photorefractive response time can be increased by lowering the laser power. However, longer integration times will be required to compensate for the loss in signal. For future chip designs, faster phase modulators should be implemented to avoid this limitation.  
Lastly, this work demonstrates that a thin-film of photonic quality can be realized by a top-down fabrication approach and using CMP (Figure 10). Still, bottom-up fabrication approaches should yield an enhanced film thickness homogeneity and offer an opportunity for performance enhancement.