# Silicon Integrated Nanophotonic Devices for On-Chip Multi-Mode Interconnets
## 3 Silicon Multi-Mode Routing Devices
### Silicon Multi-Mode Bends
Alternatively, a multi-mode bend can also be realized by adopting a pair of mode converters, as shown in Figure 13b. The incident SWMs are firstly converted to the corresponding BWMs by converter #1; thus, the light transport in the multi-mode bend will not introduce any inter-modal interference. At the output port, the SWMs are then restored from the BWMs by converter #2. Therefore, the key issue is to realize the mode converter enabling SWM-BWM conversion with a low IMC. In [169], the authors optimized a SWM-BWM converter working for TE\({}_{0}\) and TE\({}_{1}\) modes. The bending radius is as small as 5 \(\upmu\)m. The mode conversion efficiency could reach \(\approx\)100% by implementing a particle-swarm optimization (PSO) that defines the waveguide geometry. Low losses (IL \(<\) 0.2 dB), low crosstalk (IMC \(<\) -22 dB) and a broad bandwidth (BW \(>\) 100 nm) were experimentally demonstrated. However, this structure can only support two modes; meanwhile, the PSO process could be very time-consuming when a larger mode capacity is considered. Later, the SWG-based mode converter was proposed [170]. This converter consists of a multi-mode waveguide and a group of SWGs on the top-surface. The SWGs are non-uniform along both lateral and propagation directions, so the input SWMs can be gradually \"pushed\" to one sidewall, leading to the adiabatic conversion from SWMs to BWMs. Another identical mode converter is inserted at the output port to revert BWMs to SWMs. Such an SWG-based converter is able to support the first four TM modes (i.e., TM\({}_{0-3}\)) with a sharp bending radius of 30 \(\upmu\)m. The losses and crosstalk were measured to be IL \(<\) 1 dB and IMC \(<\) -20 dB over a broad wavelength band from 1.52 \(\upmu\)m to 1.60 \(\upmu\)m (BW \(>\) 80 nm). Multi-mode bends also need to be fabrication-friendly, given that the bending structures are recurring in the MDM system. However, the aforementioned designs usually require complex index mapping with subwavelength structures. A more convenient and robust scheme is based on the gradient curvature bend [171], as shown in Figure 13c. The idea is to engineer the bending trajectory by using some special curves with variant curvature, such as spline [162] or Euler curves [163; 164]. For a Euler bend, the curvature is minimal at the input/output port, and adiabatically reaches its maximum value at the middle point. Thus, the inter-modal coupling can be efficiently inhibited as long as the curvature gradient is small enough. By using this method, low losses (IL \(<\) 0.5 dB), low crosstalk (IMC \(<\) -20 dB) and a broad bandwidth (BW \(>\) 90 nm) can be achieved for the first four TM modes (i.e., TM\({}_{0-3}\)). The effective radius is also as small as 45 \(\upmu\)m. Actually, such gradient curvature bends can be regarded as special forms of mode converter-assisted bends, except that the \"mode converters\" are merged into the bending section, so that the footprint can be reduced. Another simple scheme is based on the corner bend [172], as illustrated in Figure 13d. The idea is to simultaneously change the propagation directions for all the supported modes at an inclined Si-SiO\({}_{2}\) interface, where total internal reflection (TIR) happens. The corner bend is intrinsically lossless and crosstalk free (IL \(<\) 0.5 dB, IMC \(<\) -20 dB) since there is no SWM-BWM conversion. In theory, the working bandwidth can be as large as \(>\)420 nm and the capacity can be scaled up to ten modes. However, it should be noted that the core width has to be wide enough (typically \(>\)10 \(\upmu\)m) to lower the diffraction losses at the corner junction; thus, one has to use two additional mode size converters (e.g., adiabatic tapers) as connectors between the bus waveguide and corner bend [173; 174]. We give a summary of the reported silicon multi-mode bend in Table 5. One can find that MDM-compatible bending structures can be realized with a small radius (\(<\)20 \(\upmu\)m) and a high performance (IL \(<\) 1 dB, IMC \(<\) -20 dB).