# Improved SPGD Algorithm for Optical Phased Array Phase Calibration
## 4 Experimental Results and Analysis  
To test the performance of the improved SPGD mentioned in Section 3, NSPGD, SPGD, and HC algorithms are used to verify their performance. The performance is shown in Figure 4.  
As the convergence trend is shown in Figure 4, the NSPGD convergence rate is faster than that of SPGD and HC, and NSPGD takes about 10 min to over 10 dB while SPGD takes about 20 min. Furthermore, NSPGD converges to a better level (larger than 10 dB) than SPGD because it avoids the local maxima. It can be found that the convergence curve of NSPGD is more stable than SPGD, which can attribute to the momentum added to the NSPGD. It has been proven that the momentum term can improve the performance of SPGD. After running for 30 min, only SMSR of 6.3 dB is obtained with HC method. This proves that NSPGD has good convergence performance. Both thermo-optic (TO) and electro-optic (EO) phase shifters are applied in OPA widely [22; 23; 24; 25; 26; 27; 28; 29; 30]. Low loss can be obtained in TO shifters, while high power consumption and poor bandwidth follow. EO shifters hold high modulation up to GHz and low power consumption but induce extra loss because of the free carrier absorption effect. In order to ensure low loss, we use TO shifters in our OPA, which means watt level power concentrated in one mm\({}^{2}\) scale chip. Heat accumulation severely affects the chip's performance because Si is sensitive to temperature [31; 32]. Many researchers tend to find ways to reduce the power consumption and thermal crosstalk to alleviate the adverse effect of heat brought by TO shifters [22; 24; 28]. One of the reasons for the performance degradation of OPA caused by TO shifters is that heat accumulation breaks the thermal equilibrium and makes the temperature around the waveguide unstable. So, some work attempts to conduct the heat to Si substrate [31; 32; 33], but they need an unconventional silicon process to grow material with high thermal conductivity. Therefore, we designed a temperature-controlled packaging module shown in Figure 5. The OPA chip is bonded to the printed circuit board (PCB), and we cut a slot in the PCB to ensure good thermal contact. A thermistor is set between the thermoelectric cooler (TEC) to get the average temperature of the chip and TEC. The TEC is controlled by a proportional integral differential (PID) algorithm. Figure 4: Convergence time of NSPGD, SPGD, and HC on 512-channel OPA. In order to test a 512-OPA with temperature-controlled packaging, 25 \({}^{\circ}\)C is set as the target temperature of the thermistor. The PID algorithm controls TEC to maintain a stable thermal environment. The influence of temperature control packaging on the convergence of the algorithm is verified by experiments. We applied NSPGD to the test. The convergence curve with temperature-controlled packaging meant that the target temperature of thermistor was set at 25 \({}^{\circ}\)C and the TEC worked to reach this goal. No temperature control means that the TEC is disabled and the heat accumulation is hard to dissipate. The results are shown in Figure 6, and was found that temperature control helps the algorithm converge better because it maintains a relatively stable environment for silicon waveguides and ensures it can only be impacted by TO shifters as much as possible. However, if temperature control is absent, there is a dynamic heat offset between the heat from TO shifters and heat accumulation, which may mess the algorithm up and hinder the convergence. Figure 5: Schematic of 512-channel OPA with temperature-controlled packaging. Figure 6: Convergence curve of under and without temperature control by NSPGD. Temperature control helps obtain better calibration and saves calibration time. Repeated calibration will be implemented if the temperature control is absent because the room temperature and heat accumulation will change with time. Without temperature control and repeated calibration, up to 20% more (depending on room temperature variation) gray value degradation will be observed.