# Silicon Integrated Nanophotonic Devices for On-Chip Multi-Mode Interconnets
## 2 Silicon Multi-Dimensional (De)Multiplexers
### Silicon Mode (De)Multiplexers
However, the MMI/Y-junction structure still suffers from a relatively large footprint (\(\approx\)50 \(\upmu\)m). The device size can be effectively reduced to \(\approx\)36 \(\upmu\)m by using a subwavelength grating (SWG) metamaterial slab with engineered refractive index and mode dispersion [28]. Apart from the smaller footprint, this SWG-based structure also has a superior performance compared with the aforementioned MMI-based design. The working bandwidth can be as large as 300 nm, while low losses (IL \(<\) 0.84 dB) and low crosstalk (XT \(<\) -20 dB) can also be maintained. The second type of silicon mode (de)multiplexer is based on the asymmetric Y-junction. The mostly commonly used Y-junctions are symmetric [60; 61; 62; 63], which have been extensively applied for power splitting/combining and signal broadcasting. The asymmetric Y-junction is less common, which is usually characterized by the non-identical arms in term of the waveguide width. For the asymmetric Y-junction, the incident light from a single arm will be coupled into a higher-order mode with the closest effective index [64]. The mode conversion factor (MCF) can be used to determine the structural parameters of an asymmetric Y-junction [65]:  
\[\text{MCF}=|\beta_{\text{a}}-\beta_{\text{b}}|\text{\text{\text{\studied on low-contrast material platforms, e.g., silica waveguide or silica fiber [64; 66; 67]. In [29], a two-channel silicon mode (de)multiplexer was demonstrated based on asymmetric Y-junctions, as shown in Figure 3b. For such a design, the input TM\({}_{0}\) mode in the wider/narrower arm excites the first even/odd mode in the \"stem\", i.e., TM\({}_{0}\)/TM\({}_{1}\). The measurement results exhibit low losses (IL \(<\) 1.5 dB) and low crosstalk (XT \(<\) \(-\)30 dB) for the fabricated asymmetric Y-junction. However, this Y-junction-based design is quite sensitive to the structural parameters, especially to the divergence angle (\(\theta_{\text{d}}\)), since the mode-selective condition (MCF \(>\) 0.43) will no longer be satisfied when \(\theta_{\text{d}}\) is changed. Another drawback is the relatively narrow working bandwidth caused by the coupling-induced interference between two arms. These problems could be solved by introducing the novel shortcut-to-adiabaticity (STA) method [68]. The parametric sensitivity and interference effect can be dramatically inhibited for the asymmetric Y-junction by varying waveguide widths and waveguide separation along the arm section [69], leading to a robust and broadband mode (de)multiplexing. As an alternative, the two-channel mode multiplexer can also be realized by exploiting a \"two-step\" strategy [30]. The TE\({}_{0}\) mode in the wide/narrow arm is first converted to the symmetric/asymmetric super-mode (i.e., TE\({}_{\text{S}}\)/TE\({}_{\text{AS}}\)) by using an adiabatic coupler [70; 71]. Such TE\({}_{\text{S}}\)/TE\({}_{\text{AS}}\) super-modes are then injected into the \"stem\", which will directly excite TE\({}_{0}\)/TE\({}_{1}\) modes in the multi-mode bus waveguide. Here, the super-modes are used as a transition between the input fundamental modes and the output higher-order modes, which prevents the undesired crosstalk caused by direct mode conversion. The mode (de)multiplexer with low losses (IL \(<\) 1 dB) and low crosstalk (XT \(<\) \(-\)20 dB) was experimentally achieved over a broad wavelength span from 1.525 \(\upmu\)m to 1.60 \(\upmu\)m (BW \(\approx\) 75 nm). Moreover, for this design, the high-performance can be preserved even if the structural parameters are deviated over a \(>\)\(\pm\)30 nm range. There are also some other types of Y-junction-based MDMs, such as ones based on partially etched slab waveguides [31]. However, there are some clear disadvantages of the silicon mode (de)multiplexers based on MMIs or asymmetric Y-junctions.