# Silicon Integrated Nanophotonic Devices for On-Chip Multi-Mode Interconnets
## 3 Silicon Multi-Mode Routing Devices
### Silicon Multi-Mode Bends  
The waveguide bend is a basic component that constitutes the cornerstone of a photonic integrated circuit. The SOI waveguide can support an extremely small bending radius [162; 163; 164; 165], taking advantage of its ultra-high-index contrast. However, most of the reported silicon waveguide bends only work for the fundamental modes (i.e., TE\({}_{0}\), TM\({}_{0}\)) since the higher-order modes are vulnerable in the bending section. The underlying reason is the significant inter-modal crosstalk (IMC) induced by the distinct modal profiles between straight/bent waveguides. Here, we give a calculation example to explain this phenomenon. Figure 12a shows the calculated field profiles for the first four TE and TM modes (i.e., TE\({}_{0-3}\), TM\({}_{0-3}\)) in a straight multi-mode waveguide with a 220-nm thickness and 2-\(\upmu\)m width. From the profiles, each straight-waveguide mode (SWM) has a symmetric power distribution over the core region. In contrast, the power distribution is asymmetric for each bent-waveguide mode (BWM), as shown in Figure 12b. Here, the bending radius is chosen to be 15 \(\upmu\)m as an example. Thus, when the incident light meets the straight-bent junction, a single SWM will be decomposed into multiple BWMs, which will interfere with each other along the waveguide bend, leading to the significant IMC. The light propagation profiles are calculated for the multi-mode bend when TE\({}_{0-3}\) and TM\({}_{0-3}\)  
Figure 11: The configuration for MDM-enabled interconnects with multi-mode routing devices. modes are launched, as shown in Figures 11d and 12c, where a strong inter-modal interference can be observed. Thus, one has to adopt an extremely large bending radius (typically \(>200\)\(\upmu\)m) to relax the perturbation at the straight-bent junction and depress the undesired IMC [11; 166]. Over the past few years, great attention has been paid to developing multi-mode bending structures, including gradient index bends [167; 168], mode converter-assisted bends [169; 170], gradient curvature bends [171] and corner bends [172], as summarized in Figure 13.  
To eliminate the bending-induced IMC, the modal mismatch between SWMs and BWMs should be depressed. In 2012, [PERSON] et al. reported the first sharp multi-mode bend on silicon [167], as illustrated in Figure 13a. Transformation optics (TO) is utilized to map the lateral index profile. The transformed BWMs and SWMs have identical power distributions; thus, the incident higher-order modes will directly propagate through the multi-mode bend without any disturbance since the modal mismatch is eliminated. However, complicated grayscale lithography is needed to attain a non-uniform index distribution by pattering the thickness profile, leading to a CMOS-incompatible fabrication. Additionally, the bending radius is still quite large (\(\approx\)78.8 \(\upmu\)m). In [168], an improved design was proposed to overcome these obstacles. For this design, the gradient index profile is generated by patterning a series of SWGs on the waveguide's top surface. The effective medium index can be precisely mapped by tailoring the SWG duty cycle. Furthermore, this novel structure can be easily fabricated by performing a simple shallow etching, which is a standard fabrication process in silicon  
Figure 12: The calculated field profiles for (**a**) straight-waveguide mode (SWM) and (**b**) bent-waveguide mode (BWM). The calculated light propagation profiles for a 15-\(\upmu\)m multi-mode bend when (**c**) TE\({}_{0-3}\) and (**d**) TM\({}_{0-3}\) modes are launched. Figure 13: The schematics for different silicon multi-mode bends: (**a**) gradient index bend [167; 168], (**b**) mode converter-assisted bend [170], (**c**) gradient curvature bend [171], (**d**) corner bend [172]. photonics foundries. Such SWG-based multi-mode bends can provide low losses (IL \(<\) 0.7 dB), low crosstalk (IMC \(<\) -22 dB) and a broad bandwidth (BW \(>\) 80 nm) for the first three TE modes (i.e., TE\({}_{0-2}\)).