# Automatic Initialization Methods for Photonic Components on a Silicon-Based Optical Switch
## 4 Algorithm Training and Benchmark
With \(N_{r}\) = 10, the points near a local maximum had almost no chance to be selected as the new starting points. This made the GBNM method really efficient when the target function had multiple local optima. Indeed, it pushed the restarts far from the already known attraction basins. We obtained a similar scenario also for the interleaver, if we considered the one channel width (200 GHz) integrated optical signal at one output as the target function to optimize. Indeed, the interleaver transfer function demonstrated a local maximum when a flat top channel shape was recovered (see Figure 2, bottom panels). In this particular condition, the photo-diode had its  
Figure 5: Starting points and local optima found by the Globalized Bounded Nelder-Mead (GBNM) method for different parameter configurations of \(N_{r}\) (number of random points sampled at each restart) and \(N_{max}\) (maximum number of iterations) when launched to optimize the spectral response of a switching node. The upper left panel shows the (re)starting points and local maxima when \(N_{r}\) is set to 1 and the \(N_{max}\) is set to 200. The upper middle panel is the outcome with \(N_{r}\) = 2, \(N_{max}\) = 1000. The upper right panel shows the optimization history obtained when \(N_{r}\) = 1 and \(N_{max}\) = 10000. The lower left panel is obtained with \(N_{r}\) = 500 and \(N_{max}\) = 200. The lower middle panel is the output of the optimization when \(N_{r}\) is 100 and \(N_{max}\) is 1000. The lower right panel is with the optimization parameters set to \(N_{r}\) = 10 and \(N_{max}\) = 10000. In the rightmost plots, the GBNM converges to a different global optimum with respect to the other four plots, because a different switching node has been involved in these tests. maximum read-out because all the optical signal injected at the interleaver input was tied to one of the interleaver output channels. For the purpose of automatically aligning the whole IRIS chip, we implemented the GBNM optimization in a NI LabView routine, which drove a tunable diode laser Tunics BT as the source and exploited the on-chip integrated Ge photo-diodes as the feedback monitors. At each step, the routine set a different couple of bias values to the heaters of one photonic component, and followed the instruction of the optimization algorithm. Once the global optimum was determined, the routine moved to the next photonic components to align, and so on. Of course, the duration of a single GBNM search depended on both \(N_{r}\) and \(N_{max}\). The higher these values were, the higher was the reliability of the global optimum and, consequentially, the higher the time taken by the optimization search. With \(N_{r}\) = 2 and \(N_{max}\) = 150, the optimization search recovered the wanted passband of an MRR-based switching node (repeatedly) in less than 5 s. For an interleaver, the same process took almost 10 times more. This was because, at each evaluation of the target function, the routine had to sweep the tunable laser on one channel width (200 GHz) and to integrate the photo-diode read-out signal over the channel bandwidth. To align the whole IRIS switching matrix and accomplish the LUT (for 12 interleavers and 384 switching nodes), the routine took about 12 h. This process could be significantly shortened by increasing the communication speed between the chip and the microcontroller ATxmega128A1U (currently @ 9600 bps). However, once the LUT was completed, it could be accessed at any time, allowing the complete reconfiguration/restoration of the IRIS chip in the microsecond regime. Figure 6 demonstrates the effect of the optimization algorithm on one interleaver. Specifically, Figure 6a shows the transmission spectrum on the two arms of the interleaver in the as-received chip (before alignment). The colored slots in the picture represent the 12 ITU channels to which the IRIS device had to be aligned (between 193.6 THz and 195.8 THz with 200 GHz channel spacing).