# Edge Couplers in Silicon Photonic Integrated Circuits: A Review
## 4 Structural Transformations of Edge Couplers in Vertical Direction
### Edge Couplers Based on Three-Dimensional Taper  
Typical tapers only have tapering profiles in the longitudinal and lateral dimension, while the thickness of the taper stays constant. However, it is possible to transmit light from the fiber through a three-dimensional taper (3D taper) that can gradually converge. As shown in Figure 14a, a 3D taper is aligned to fiber with its wide end, which is comparable with the fiber core in the aspect of structure size. Then, it begins to taper in both the vertical and horizontal dimensions to connect with the silicon waveguide. Generally, three-dimensional tapers can be divided into two main types: one is purely silicon-based 3D tapers, and the other is 3D tapers assisted with other kinds of intermedium materials. As for the purely silicon-based 3D tapers [96; 97; 98; 99], there are also two different approaches to adjust the three-dimensional profile. In some previous works [96; 99], the wide end of the taper becomes narrower in both the vertical and lateral directions until it forms a narrow end with the same thickness and width as the silicon waveguide as presented in Figure 14b. In some other works [97; 98], the 3D taper firstly begins to reduce in thickness while the width remains unchanged. Then, the 3D taper transits into a thin silicon slab with the same thickness as the silicon waveguide, and then the lateral slab gradually tapers similar to a traditional two-dimensional taper, which connects with the silicon waveguide afterwards, as shown in Figure 14c. There are also some 3D tapers assisted with other materials to match with the fiber core considering both the size and the effective index as Figure 14d depicts. Amorphous silicon [100; 101], SU-8 [92; 102], SiON [92], and other kinds of index-matching materials are applied in such situations. These materials are compatible with silicon photonic platform and have a moderate refractive index between silicon  
Figure 14: (**a**) Diagram of a Si 3D taper (side view); (**b**) and (**c**) two types of 3D taper profile (top view); (**d**) a 3D taper assisted with other material. dioxide and silicon, which can help improve the modal match between the fiber and the waveguide. Figure 15a demonstrates a type of knife-edge 3D taper coupler following the regime depicted in Figure 14b. Compared with conventional inverse taper in Figure 15b, its taper tip is specially designed with a low aspect ratio. The i-line stepper is used for patterning and the silicon taper is prepared with inductive-coupler-plasma reactive ion etching (ICP-RIE) to form the slanted sidewall. Then, dry-etching is performed in CF4 atmosphere. A secondary core made of benzocyclobutene is introduced to engineer the refractive index as well as to protect the functional Si waveguide from the exposure of CF4 during etching. The narrow knife-edge shape tip is aligned with the fiber in practical measurement. As for the TE mode conversion presented in Figure 15c, it is clear that the confinement of mode is increasingly stronger when light propagates inside the taper. The TE mode conversion loss is 0.35 dB for this configuration, and the device size is 180 \(\upmu\)m. The bandwidth feature and fabrication tolerance are not given out in this research work. Although it is easy to think of connecting a large fiber core with a 3D taper, three-dimensional tapers are not easy, considering the fabrication process. Among the research works mentioned above, various fabrication techniques are utilized to make a 3D taper, including gray-tone optical lithography [96], KOH wet etching for slanted surfaces [97], shadow mask [100], annealing in hydrogen ambient [101], etc. These fabrication processes are difficult to operate and control to some extent, and thus, they limit the adaptability and practicality of the three-dimensional tapers. In other words, the design of ideal 3D tapers is indeed a matter of fabrication techniques.