# Silicon Integrated Nanophotonic Devices for On-Chip Multi-Mode Interconnets
## 4 Inverse Design in Multi-Mode Photonics  
A variety of building blocks need to be assembled to construct a practical MDM system with full functionalities, as discussed in Section 1. However, the design methodologies and working principles are various for different types of mode-handling devices (see Sections 2 and 3), which hinder the standardization of MDM modules. Furthermore, most of the reported MDM components are optimized by hand-tuning a small collection of parameters, so designers are not aware of how close a particular device comes to the performance limits, especially when a great number of modes are involved. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Ref. **} & \multirow{2}{*}{**Year**} & \multirow{2}{*}{**Size (\(\upmu\)m)**} & \multirow{2}{*}{**Capacity**} & \multirow{2}{*}{**SR**} & \multicolumn{2}{c}{**IL (dB)**} & \multicolumn{2}{c}{**XT (dB)**} & \multicolumn{2}{c}{**BW (nm)**} \\ \cline{6-10}  & & & & & **Sim. ** & **Exp. ** & **Sim. ** & **Exp. ** & **Sim. ** & **Exp. ** \\ \hline
[211] & 2016 & 15.2 & 2 & 0.5 & \(<\)0.1 & \(<\)0.7 & \(<\)\(-\)17 & \(<\)\(-\)14.3 & 60 & 30 \\
[213] & 2016 & 120 & 2 & 0.5 & 0.47 & 0.86 & \(<\)\(-\)19 & \(-\)15.7 & 100 & 80 \\
[212] & 2018 & 800 & 3 & 0.5 & \(<\)0.12 & / & \(<\)\(-\)18.5 & / & 165 & / \\
[219] & 2018 & 2.88 & 2 & 0.5 & \(<\)0.9 & \(<\)1.5 & \(<\)\(-Photonic inverse design uses computational algorithms to discover an optimal set of parameters \(\varepsilon\)(x,y) as incident/scattering responses are given [221; 222], as shown in the upper panel of Figure 18. Based on this method, different types of MDM components can be designed under the same framework, because such target-first optimization requires no prior knowledge or user intervention. A major obstacle is the tremendous computational cost caused by the full-space parameter searching. In recent years, various algorithms have been developed to solve this problem, e.g., genetic evolution [223], the level-set method [224], topological optimization [225], the adjoint method [226] and direct-binary search (DBS) [227; 228]. For example, in 2016, [PERSON] et al. reported the first experimental demonstration of an inverse-designed three-channel mode (de)multiplexer [84]. Low losses and low crosstalk were measured (IL \(<\) 1.7 dB, XT \(<\) -14 dB). Remarkably, this inverse-designed structure has an ultra-compact footprint (\(\approx\)5 \(\times\) 6 \(\upmu\)m\({}^{2}\)) much smaller than any previously reported ones. Generally, inverse-designed nanophotonics can be \"analog\" or \"digital\". The analog nanophotonic devices have free-form geometries with continuous boundaries. However, the analog structures usually have an irregular feature size over the pattern region, so one has to redefine the pattern parameters to compensate for random errors induced by line-width broadening [229] and lag effect [130; 230]. On the other hand, the digital nanophotonic devices are formed by a series of identical pixels, each with a regular shape (e.g., circle or square), so the fabrication errors can be easily predicted according to pre-treatment results. Therefore, by adopting a digitized configuration, the inverse design could be more reliable and fabrication-friendly. In the lower panel of Figure 18, we have summarized the reported \"digital\" MDM components, including mode (de)multiplexers [85], multi-mode bends [175; 177], multi-mode crossings [204] and multi-mode splitters [219; 220]. The working performances are summarized in Table 1, Table 5, Table 6, Table 7. These reported devices all exhibit ultra-small footprints (\(<\)10 \(\upmu\)m), which is helpful for dense integration. Moreover, it can be seen that all these mode-handling devices share a similar template, leading to feasible MDM systems based on a standardized component library. For example, in [176], an arbitrarily routed multi-mode circuit with a bit rate of 112 Gbit/s was demonstrated where several different kinds of inverse-designed MDM components were integrated on a single chip.