# Silicon Integrated Nanophotonic Devices for On-Chip Multi-Mode Interconnets
## 2 Silicon Multi-Dimensional (De)Multiplexers
### Silicon Mode (De)Multiplexers  
The mode (de)multiplexer enables mode conversion and signal (de)multiplexing. Such functionalities can be achieved by various different structures, e.g., multimode interference couplers (MMIs) [23; 24; 25; 26; 27; 28], asymmetric Y-junctions [29; 30; 31] and asymmetric directional couplers (ADCs) [32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45], as summarized in Figure 3.  
The MMI is formed by an interference section and several input/output waveguides [46; 47; 48; 49; 50; 51; 52; 53; 54; 55]. The multi-mode interference can be excited by the incident light from the input port, leading to a series  
Figure 3: The schematics for the silicon few-mode (de)multiplexers based on (**a**) multimode interference couplers (MMI) [24], (**b**) asymmetric Y-junction [29] and (**c**) asymmetric directional coupler (ADC) [36]. Figure 2: A table of contents: the main topics that will be discussed in the following sections. of self-images in the interference section [46]. The phase and modal distributions of the output field can be tailored at each output port by appropriately choosing the MMI length/width [56; 57; 58; 59]. For example, the input even and odd modes can be separated into different output ports when the MMI length is set to L\({}_{\text{MMI}}\) = 3L\({}_{\pi}\)/4. In this way, the MMI can serve as a mode sorter [23]. Here, L\({}_{\pi}\) can be derived as [46]:  
\[\text{L}_{\pi}=\lambda/[2\cdot(\text{n}_{\text{eff},0}-\text{n}_{\text{eff},1} )]\approx 4\text{n}_{\text{s}}\text{W}^{2}_{\text{eff}}/3\lambda, \tag{1}\]  
where n\({}_{\text{eff},0}\) is the effective index for the fundamental mode, n\({}_{\text{eff},1}\) is the effective index for the first higher-order mode, n\({}_{\text{s}}\) is the slab effective index, w\({}_{\text{eff}}\) is the effective MMI width, \(\lambda\) is the working wavelength. This novel property enables a novel design of four-channel mode (de)multiplexer by cascading numerous MMI-based mode sorters and phase shifters [23]. However, for such a design, the output signal is not carried by the fundamental mode when the TE\({}_{2}\) mode is demultiplexed from the multi-mode bus waveguide, which hinders the further applications. In [24], a two-channel mode (de)multiplexer was proposed by combining a 3-dB MMI coupler (L\({}_{\text{MMI}}\) = 3L\({}_{\pi}\)/2) with a MMI-based mode sorter (L\({}_{\text{MMI}}\) = 3L\({}_{\pi}\)/4), as shown in Figure 3a. The input TM\({}_{0}\) mode from the edge port can be evenly split by a 3-dB coupler. The phase inversion is then introduced to the split beams by utilizing a \(\pi\) phase shifter. Finally, the two beams are combined by a cascaded mode sorter. The TM\({}_{0}\)-TM\({}_{1}\) conversion is also carried out in the meantime. On the other hand, the input TM\({}_{0}\) mode from the central port can directly propagate through the 3-dB coupler and mode sorter without mode conversion. This MMI-based structure can provide low insertion losses (IL \(<\) 1.8 dB), low crosstalk (XT \(<\) -20 dB) and a broad working bandwidth (BW \(>\) 60 nm) [25]. The major disadvantage is the relatively large device size (\(\approx\)80 \(\upmu\)m), which can be reduced by replacing the phase shifter with a tilted joint section [26]. The two-channel mode (de)multiplexer can also be realized by using a 2 \(\times\) 2 MMI coupler (L\({}_{\text{MMI}}\) = L\({}_{\pi}\)/2) assisted with a symmetric Y-junction [27]. The designed 2 \(\times\) 2 MMI coupler can evenly separate the input TE\({}_{0}\) mode with a phase difference of \(-\pi\)/2 or \(+\pi\)/2, which can be modified to 0 or \(\pi\) by inserting a \(\pi\)/2 phase shifter. The two beams with 0/\(\pi\) phase difference are then combined and converted to TE\({}_{0}\)/TE\({}_{1}\) modes by a symmetric Y-junction. The simulation results show low losses (IL \(<\) 0.1 dB), low crosstalk (XT \(<\) -17 dB) and a broad bandwidth (BW \(>\) 100 nm). Compared with the previous MMI-based structures, this improved design can provide a simplified configuration as well as a better performance.