# Edge Couplers in Silicon Photonic Integrated Circuits: A Review
## 4 Structural Transformations of Edge Couplers in Vertical Direction
### Edge Couplers Based on Cascaded Multi-Stage Tapers  
The last section shows the structural transformation of edge couplers in the vertical direction via assisting waveguides grown above the silicon inverse taper with an isolation layer of SiO\({}_{2}\). Accordingly, it is also feasible to achieve a vertical transition of the propagating mode via cascaded tapers, as presented in Figure 11. An edge coupler based on multi-stage tapers consists of multiple unidirectional tapers in different layers with their wide end near the fiber and narrow end close to successive photonic waveguides. At the wide end where tapers in different layers merge, the edge coupler has a large cross-section area which is comparable with the fiber core, and light can couple into the coupler facet at a relatively low discrepancy. In the region of multi-stage tapers, the taper at the top layer has the shortest length, while the one at the bottom layer has the longest length. When light propagates in the cascaded multi-stage tapers and arrives at the first taper tip where the top-layer taper ends, light cannot be confined well in the top layer due to a too small cross-section area, and it inclines to transmit into the successive layer below, which has a higher refractive index than the surrounding SiO\({}_{2}\) cladding. Likewise, light propagates in the second layer taper for a certain distance and then continues to transmit downwards when it propagates to the second taper tip until it reaches the bottom layer. Considering the material of each layer, it can be silicon, silicon oxide, silicon nitride, or other kinds of polymers that have proper refractive index and compatibility. Edge couplers based on cascaded multi-stage tapers can be divided into two main types according to the mechanism following, in which the bottom layer connects with the silicon waveguides. Under the first type illustrated in Figure 11a, the silicon taper acts as the bottom layer, and it is cascaded with upper layers in the same direction with the wide end near the fiber and narrow end connected with photonic circuits [77; 78; 79]. In each layer, light firstly exists as a fully supporting mode, and as it propagates to the narrow taper end, the mode is transited into the lower layer, which is longer in size. After all, the mode can be transmitted into the bottom Si device layer; then, it propagates within the following photonic circuits. As for the  
Figure 10: Silicon inverse taper assisted with multiple waveguides (cross-section view). second type shown in Figure 11b, an inverse silicon taper is buried in the bottom stage to enable mode conversion [80; 81; 82]. The structure and mechanism of the upper stages are the same in both regimes; however, in the type of cascaded multi-stage tapers above an inverse taper, the bottom stage is different regarding its cuboid shape, which acts as an equivalent cladding in fact. One key design principle is that the bottom stage should have a lower refractive index than silicon, so that the mode can convert into the buried silicon inverse taper and then the silicon photonic waveguides. Figure 12 presents the modal distribution in a cascaded multi-stage mode converter under the regime where an inverse silicon taper is buried in the bottom stage [82]. There are three SiO\({}_{2}\) stages in this configuration, and the yellow taper-shape envelope stands for the first stage, while the blue taper-shape envelope stands for the last stage. In the right part of Figure 12, it shows that the optical field is transmitted downwards between each layer. This fiber-to-waveguide mode converter exhibits a low loss of 1.5 dB and a broad 1-dB bandwidth that is more than 100 nm within a total length of about 200 \(\upmu\)m. Assisted with the multi-stage upper waveguides, this coupler can couple directly with the SMF near the 1550 nm operation wavelength. Multiple (more than five) lithography and etch processes are adopted to form the Si and SiO\({}_{2}\) tapers, and chemical mechanical polishing (CMP) is applied before the deposition of each stage.