# Silicon Integrated Nanophotonic Devices for On-Chip Multi-Mode Interconnets
## 2 Silicon Multi-Dimensional (De)Multiplexers
### Silicon Hybrid (De)Multiplexers  
As discussed above, mode (de)multiplexing can efficiently enhance the link capacity, but it is still quite difficult to (de)multiplex very high-order modes in a multi-mode bus waveguide. Therefore, it is more cost effective to build multi-dimensional on-chip communication systems by combining MDM with WDM [86; 87; 88; 89; 90; 91; 92; 93; 94; 95] and PDM [96; 97; 98; 99; 100]. The wavelength/mode hybrid (de)multiplexers are able to simultaneously manipulate signals carried by wavelength and mode channels. WDM/MDM hybrid systems could be realized by using some special mode (de)multiplexers with strong wavelength-selectivity, e.g., asymmetric Y-junctions [86], grating-assisted ADCs [87], photonic crystals [88] and asymmetric micro-ring resonators [89; 90]. However, such wavelength-selective mode coupling is usually quite sensitive to parametric deviations, which make it difficult to align each wavelength/mode channel. A more general architecture is to cascade the broadband mode (de)multiplexers (e.g., cascaded ADCs) with the conventional wavelength (de)multiplexers, such as arrayed waveguide gratings (AWGs) [91; 92] and micro-ring resonators (MRRs) [94; 95], as summarized in Figure 6.  
Figure 6: The schematics for the silicon wavelength/mode hybrid (de)multiplexers with (**a**) bi-directional arrayed waveguide gratings (AWGs) [92] and (**b**) bi-directional micro-ring resonators (MRRs) [94]. The inset shows the wavelength and mode channel arrangement. Here, a \(4\times 4\) wavelength-division multiplexing (WDM)/MDM system is illustrated as an example. The silicon AWGs are most commonly used in the dense wavelength division-multiplexing (DWDM) systems because of the large free-spectral range (FSR) and small channel spacing [101; 102; 103; 104; 105; 106; 107], showing great potential for large-scale hybrid (de)multiplexing. In [91], a 64-channel WDM/MDM hybrid system was demonstrated on silicon by cascading four identical 16-channel AWGs with a four-channel mode (de)multiplexer. For each AWG, sixteen wavelength carriers are multiplexed into a single-mode waveguide with TM\({}_{0}\). These four waveguide channels are then converted to TM\({}_{0}\)-TM\({}_{3}\) and multiplexed into a multi-mode bus waveguide, which makes a total link capacity of 64 (\(16\times 4\)). For such a structure, the insertion losses and crosstalk were measured to be IL\(\approx\)7 dB and XT \(\approx-10\) dB, respectively. It should be noted that the AWGs can be bi-directional, which means that two 1 \(\times\) N AWGs can be replaced by one (N + 1) \(\times\) (N + 1) AWG with equivalent functionalities [101], as shown in Figure 6a. This idea was implemented to realize an improved wavelength/mode hybrid (de)multiplexer with an AWG number reduced to half [92]. The measurement results show insertion losses of IL \(\approx\) 5 dB and crosstalk of XT \(\approx-14\) dB for a 64-channel WDM/MDM hybrid system. Nevertheless, the device footprint is still quite large (a few millimeters) for AWG-based wavelength/mode hybrid (de)multiplexers even if bi-directional configurations are applied. As an alternative, the cascaded MRRs are also popular for WDMs because of the low insertion losses, high extinction ratios and, especially, the compact device sizes [108; 109; 110]. Moreover, according to the tight-binding model [111], the top-flattened transmission responses can be realized by simply cascading several side-coupled MRRs in a serial [112]. Additionally, both clockwise and counterclockwise propagations are allowed in MRRs, so the bi-directional configurations are also applicable, as illustrated in Figure 6b. In [94], a 32-channel WDM/MDM hybrid system was demonstrated on silicon by cascading two sets of bi-directional eight-channel MRR arrays with a four-channel mode (de)multiplexer. For the fabricated device, the insertion losses were measured to be IL \(<\) 4.5 dB while the crosstalk was measured to be XT \(<-18\)dB. The insertion losses and crosstalk can be further reduced by adopting flat-top MRR filters [95].