# Silicon Integrated Nanophotonic Devices for On-Chip Multi-Mode Interconnets
## 1 Introduction  
The modern micro-processors require an extremely large link capacity for data communications between multi-cores and local/distant caches [1]. However, it is becoming increasingly difficult to meet the ever-growing capacity requirement since the conventional electrical interconnects severely suffer from limited bandwidth and significant power consumption [2]. The on-chip optical-interconnect technology emerges as an attractive approach to break the bottleneck [2; 3; 4], taking advantage of its ultra-large bandwidth and ultra-low power consumption. Moreover, the link capacity can be further enhanced for the optical interconnects by utilizing novel multiplexing technologies, including wavelength-division multiplexing (WDM) [5; 6; 7; 8; 9], polarization-division multiplexing (PDM) [10] and mode-division multiplexing (MDM) [11; 12; 13]. WDM technology has been widely used in optical communication systems. For WDM, different signals are carried by different wavelengths, so WDMs always require a large number of laser diodes (LDs) each with an accurate temperature monitor, leading to complicated and expensive systems [11]. Therefore, it is necessary to expand the link capacity within a single-wavelength carrier by utilizing the cost-effective PDM and MDM technologies. Note that polarizations can only contribute two degrees of freedom, i.e., transverse electric (TE) and transverse magnetic (TM), so the PDM technology can only double the link capacity [10]. In contrast, the MDM system is much more scalable since the total mode capacity can be easily expanded by choosing a relatively wide multi-mode bus waveguide, showing enormous potential for achieving large-scale on-chip optical interconnects with great scalability. In recent years, silicon-on-insulator (SOI) has been regarded as a promising platform to develop multi-mode photonics for its ultra-high-index contrast (\(\mathrm{n_{Si}}\approx 3.46\), \(\mathrm{n_{SiO2}}\approx 1.45\)) and mature fabrication processes compatible with complementary metal oxide semiconductors (CMOS) [14; 15; 16; 17; 18; 19; 20; 21; 22]. Figure 1a shows the calculated effective indices for the higher-order modes in a SOI waveguide with varied core width (\(\mathrm{w_{wg}}\)). Here, the waveguide thickness is chosen to be \(\mathrm{h_{wg}}=220\) nm and the cladding material is chosen to be \(\mathrm{SiO_{2}}\). Figure 1b shows the calculated mode profiles for the first four TE/TM modes with \(\mathrm{w_{wg}}=2\)\(\mathrm{\SIUnitSymbolMicro m}\). From Figure 1a,b, one can observe the strong waveguide birefringence and mode dispersion, which makes it possible to realize selective mode handling without introducing much inter-modal crosstalk. Figure 1c shows the configuration for a typical MDM system (four channels with \(\mathrm{TE_{0-3}}\) modes are considered here as an example). The fundamental TE mode (i.e., \(\mathrm{TE_{0}}\)) from a single LD is firstly divided to four waveguide channels by power splitters. The waveguide channels are then independently modulated and converted/multiplexed to the higher-order modes (i.e., \(\mathrm{TE_{0-3}}\)) in the multi-mode bus waveguide by using the mode multiplexer. At the receiver terminal, \(\mathrm{TE_{0-3}}\) modes are reverted to \(\mathrm{TE_{0}}\) mode in different waveguide channels by the mode demultiplexer and received by the photodetectors (PDs). It can be seen from the configuration that the higher-order modes only exist in the multi-mode bus waveguide, while the other components (e.g., LDs, modulators and PDs) all work under the fundamental mode. Therefore, the basic MDM components could be classified into two categories:  
1. The mode (de)multiplexers for interfacing single-mode input/output waveguides and multi-mode bus waveguide. 2. The multi-mode routing devices (e.g., bend, crossing and splitter) for transferring higher-order modes in the multi-mode bus waveguide. Complex MDM systems can be built by simply combining these two kinds of basic MDM components with other conventional single-mode components.