# Edge Couplers in Silicon Photonic Integrated Circuits: A Review
## 3 Structural Transformations of Edge Couplers in Horizontal Direction
### Edge Couplers Based on Subwavelength Gratings Structure  
The concept of a subwavelength gratings structure (SWG) was proposed as an innovative concept in silicon photonic waveguide design more than one decade ago by researchers at the National Research Council of Canada [66] and has been widely adopted [67; 68; 69; 70] due to its extraordinary characteristics in silicon photonic devices. The structure of a subwavelength grating is demonstrated in Figure 7a, where \(\Lambda\) stands for the grating pitch and B is the length of Si blocks. Subwavelength gratings refer to those gratings satisfying the relationship of pitch \(\Lambda\) and wavelength \(\lambda\) described as  
\[\Lambda<\frac{\lambda}{2*\text{N}_{\text{eff}}} \tag{2}\]  
where N\({}_{\text{eff}}\) is the effective refractive index of mode propagating inside the waveguide [71]. As shown in Figure 7b, when the grating pitch is much larger than the wavelength, light is blocked by the Si blocks, and radiation happens at the facet, which prevents further light propagation along the grating. Only a certain component of light that satisfies the Bragg condition can go through the grating structure, which acts as a conventional diffraction grating. In circumstances where the wavelength and grating pitch are comparable in length, reflection occurs. As for gratings with small pitches under the subwavelength regime, light can directly propagate through the grating, as it behaves in a general continuous Si waveguide. Figure 8a shows a taper based on a subwavelength gratings structure, and it can be divided into three parts as notated in the figure: namely, a tapered gratings region, buffer region, and solid waveguide. In the region of tapered gratings that is aligned with the fiber, there is a high degree of design freedom to optimize the taper performance. Referring back to Equation (1), modal overlap \(\eta_{1}\) is mainly dependent on the tip width and mode effective index at the front part of the tapered gratings, while the effective index is determined comprehensively by the tip width, pitch, and duty cycle of the grating. In other words, it is feasible to properly design geometry parameters in the tapered gratings region to engineer the effective index to match with the fiber mode maximally. Light can propagate through this pure subwavelength gratings region continuously, as depicted in the top subgraph of  
Figure 6: Modal distribution at the facet of (**a**) a single taper and (**b**) two bilateral tapers. Figure 8b. It is followed by the buffer region, where the structure is a hybrid with both subwavelength gratings and the solid taper. With the aid of the Si solid taper, an effective index in the buffer region can gradually increase along the propagation direction due to the increasing proportion of the solid taper, and the mode confinement in the Si taper becomes gradually stronger. This subtle transformation of the structure effective index enables the mode to propagate at an ultra-low conversion loss and prohibits modal transition to higher-order modes, which consequently contributes to the high mode conversion efficiency n\({}_{2}\) and good adiabaticity. In contrast, a sharp change in the effective index without the buffer region can lead to significant reflection and scattering loss at the interface of the tapered gratings and the solid waveguide. Finally, there is a solid straight waveguide for the SWG taper connecting with the following circuits. The above research works merely use one SWG-structured taper to function as an edge coupler [66; 67; 68; 69; 70]. However, it is intuitive to put forward a combination of subwavelength gratings structures with multi-tip tapers [72] and multiple tapers [73]. The structures of the multi-tip edge coupler and multi-taper coupler based on subwavelength gratings are shown in Figure 9a,b respectively. Introducing the subwavelength gratings structure can reach a lower effective modal refractive index than the Si waveguide at the coupler facet and achieve higher modal overlap with low-index fiber.