# Silicon Integrated Nanophotonic Devices for On-Chip Multi-Mode Interconnets
## 2 Silicon Multi-Dimensional (De)Multiplexers
### Densely Packed Waveguide Array  
For the MDM system, the signals are usually carried by multiple higher-order modes in a wide multi-mode bus waveguide. However, from the above discussions, one might find that the high-performance mode (de)multiplexers are not easily realized. Instead of using the higher-order modes, the MDM can also be obtained by using the super-modes supported by several closely placed single-mode waveguides, leading to the novel concept of a densely packed waveguide array (DPWA) [154; 155; 156; 157; 158; 159; 160], as shown in Figure 10.  
In [154], the DPWA-based MDM was proposed for the first time. The structure consists of three single-mode SOI waveguides each with different core widths and narrow gap widths in between, as shown in Figure 10a. Three super-modes can be supported by the DPWA. Unlike the conventional guided modes that are supported by a single isolated waveguide, the super-modes are supported by an array of waveguides, so the field contribution can be engineered by modifying parameters for each waveguide. If the core widths are uniform (\(\mathrm{w_{wg0}}=\mathrm{w_{wg1}}=\mathrm{w_{wg,2}}\)), each super-mode will have power distributions in more than one waveguide. In contrast, if the core widths are non-uniform (\(\mathrm{w_{wg0}}\
eq\mathrm{w_{wg1}}\
eq\mathrm{w_{wg,2}}\)), each super-mode will be well confined in a single core region due to phase mismatching (see the inset of Figure 10a). Moreover, such distinguishable distribution can be kept for all the three super-modes even if the gap widths are deep-subwavelength (\(\mathrm{w_{gap}}=100\) nm), so the waveguide array can be regarded as a multi-mode bus waveguide with a small lateral-dimension. For DPWA, mode (de)multiplexing can be achieved by using a simple fan-in/out structure since the mode profiles are perfectly matched between super-modes and individual TE\({}_{0}\) mode, leading to a simple device layout. Such DWPA-based MDM can provide low losses (IL \(<0.1\) dB), low crosstalk  
Figure 10: The schematics for the silicon (**a**) densely packed waveguide array (DPWA) [154; 157], (**b**) densely packed multi-mode waveguide array (DPMWA) [158] and (**c**) densely packed bent-waveguide array (DPBWA) [159; 160]. (XT \(<-20\)dB) and a broad bandwidth (BW \(>\)100 nm). Furthermore, the DPWA can also be used as a sub-cell in an even larger waveguide super-lattice structure [155; 156]. For DPWA-based MDM, the total capacity can be expanded further by introducing dual polarizations or higher-order modes [157; 158]. In [157], a five-channel polarization/mode hybrid multiplexing was demonstrated with a DPWA supporting three TE super-modes and two TM super-modes. The fabricated device exhibits low losses (IL \(<0.6\) dB) and low crosstalk (XT \(<-15\) dB) over an 80-nm wavelength span. However, the scalability is limited for this design since there are only two orthogonal polarizations. The densely packed multi-mode waveguide array (DPMWA) was proposed to break the limit [158]. The DPMWA structure is comprised of three parallel multi-mode waveguides each supporting three TE modes (i.e., TE\({}_{0-2}\)), leading to a transmission capacity of nine super-modes, as shown in Figure 10b. Each super-mode can be effectively restricted within a single core region (see the inset of Figure 10b) because of the core width differences. To realize the mode multiplexing, the higher-order modes are firstly excited in each waveguide by using the cascaded ADCs; the excited higher-order modes can directly convert to the corresponding super-modes through a simple butt-coupling process. From the experimental results, one can find low losses (IL \(<1\) dB) and low crosstalk (XT \(<-15\) dB). For DPWA, large effective-index difference is always desired between the adjacent cores in order to reduce the crosstalk in the MDM system. Phase mismatching can be achieved by changing the core widths, as discussed above. However, the width variation design requires a high-resolution fabrication process. An alternative is to engineer the waveguide curvature.