# Silicon Integrated Nanophotonic Devices for On-Chip Multi-Mode Interconnets
## 2 Silicon Multi-Dimensional (De)Multiplexers
### Silicon Hybrid (De)Multiplexers
The idea is to optimally choose the core widths for each ADC, so that both TE and TM polarizations can be completely extracted from the multi-mode bus waveguide. The decoupled TE\({}_{0}\) and TM\({}_{0}\) modes are then separated by a PBS. To illustrate this idea, we show a design example of adiabatic ADC considering both TE\({}_{0}\)-TE\({}_{2}\) and TM\({}_{0}\)-TM\({}_{1}\) mode conversions. For waveguide #0, the core width is linearly varied from \(\rm{w_{wg,0}}\) = 270 nm to \(\rm{w_{wg,0}}\) = 470 nm, while for waveguide #1, the core width is linearly varied from \(\rm{w_{wg,1}}\) = 1.27 \(\rm{\upmu m}\) to \(\rm{w_{wg,1}}\) = 990 nm. Here, the gap width is set to be \(\rm{w_{gap}}\) = 150 nm. Figure 8b shows the calculated effective indices for TE\({}_{0}\)/TE\({}_{2}\)/TM\({}_{0}\)/TM\({}_{1}\) modes (see the solid lines) and TES\({}_{s}\)/TE\({}_{AS}\)/TM\({}_{S}\)/TM\({}_{AS}\) super-modes (see the dashed lines). Over this width variation range, the phase matching can be achieved for both TE\({}_{0}\)-TE\({}_{2}\) and TM\({}_{0}\)-TM\({}_{1}\) at different critical widths (see the curve intersections in Figure 8b). Thus, the input TE\({}_{2}\) and TM\({}_{1}\) modes can be simultaneously \"pushed\" into the single-mode waveguide (see the inset of Figure 8b). We then calculate the light propagation profiles for the optimized ADC when TE\({}_{2}\) and TM\({}_{1}\) modes are launched, as shown in the right panel of Figure 8c. Here, the coupling length is chosen to be 50 \(\rm{\upmu m}\) to satisfy the adiabatic condition. From the profiles, one can observe the efficient mode conversion and complete power transfer for both TE and TM polarizations. This idea was implemented to realize a 10-channel polarization/mode hybrid (de)multiplexer working with the first six TE and four TM modes (i.e., TE\({}_{0-5}\), TM\({}_{0-3}\)). The experimental results show low losses (IL \(<\) 1.8 dB) and low crosstalk (XT \(<\) \(-\)15 dB) over a 90-nm wavelength band. In Table 3, we summarize the reported silicon polarization/mode hybrid (de)multiplexers. One can see that the link capacity can be efficiently enhanced (up to 10 channels) by combining MDM and PDM technologies, while low losses (IL \(<\) 2 dB) and low crosstalk (XT \(\approx\) \(-\)20 dB) can still the preserved over quite a broad wavelength band (BW \(\approx\) 100 nm). Figure 8: **(a)** The calculated effective indices for TE\({}_{0}\)/TE\({}_{2}\)/TM\({}_{0}\)/TM\({}_{1}\) modes in the SOI waveguide with varied waveguide width (\(\rm{w_{wg}}\)). The inset shows the cross-section of an ADC with some key parameters labeled. **(b)** The calculated effective indices for TE\({}_{0}\)/TE\({}_{2}\)/TM\({}_{0}\)/TM\({}_{1}\) modes (solid lines) and TES\({}_{s}\)/TE\({}_{AS}\)/TM\({}_{S}\)/TM\({}_{AS}\) super-modes (dashed lines) in the ADC as the waveguide width (\(\rm{w_{wg,0}}\) and \(\rm{w_{wg,1}}\)) varying. The inset shows the mode profiles. **(c)** The calculated light propagation profiles for ADC (left panel) and adiabatic ADC (right panel) when TE\({}_{2}\) and TM\({}_{1}\) modes are launched. The link capacity can be dramatically scaled up by employing WDM/MDM or PDM/MDM hybrid systems. However, it is still challenging to realize WDM/PDM/MDM hybrid systems that involve all the three dimensions of light. So far, there have been only a few demonstrations on the wavelength/polarization/mode hybrid (de)multiplexing. Recently, [PERSON] et al. demonstrated an eight-channel hybrid (de)multiplexer with two wavelengths, two polarizations and two modes [129]. The device is based on the cascaded contra-directional couplers that assist with Bragg gratings. According to the Bragg condition, each coupling section can select a single carrier on a specific wavelength/polarization/mode channel. Nevertheless, the capacity is still restricted for this structure, and the insertion losses are also quite significant (IL \(\approx\) 6.6 dB).