# Edge Couplers in Silicon Photonic Integrated Circuits: A Review
## 2 Operation Mechanism and Design Principles of Edge Couplers
### Performance Metric Parameters and Design Principles of Edge Couplers  
When evaluating the performance of an edge coupler, there are some general metric parameters including coupling efficiency (or coupling loss), device footprint, operating bandwidth, fabrication deviation tolerance, and misalignment tolerance [39]. Coupling efficiency is the most critical and fundamental parameter for an edge coupler, indicating the ratio of output power over the input power after light transmission and mode conversion inside the edge coupler. To achieve a high coupling efficiency is the main goal in designing optical couplers. The device footprint is another important parameter to define the advantage of an edge coupler considering the integration density, fabrication feasibility, and packing difficulty. Photonic devices with a compact size are desired for improving the integration density and reducing the cost. Since edge couplers generally consist of tapers that are longitudinal shaped, the main idea of achieving a compact edge coupler is to decrease the device length. When it comes to wavelength characteristics, an edge coupler has the inherent advantage of broad operating bandwidth, since it works based on the propagation property of light rather than the diffraction effect of light in grating couplers. The broad operating bandwidth implies that the edge coupler can work efficiently and stably in a wide wavelength range, insensitive to wavelength fluctuation. In addition, due to the structural symmetry and simplicity, edge couplers based on a single taper are easy and straightforward to fabricate and have good fabrication deviation tolerance and misalignment tolerance. Other figures of merits such as dependence on polarization status and adiabaticity are also taken into consideration for edge couplers in some application scenarios. As for polarization dependence, the very first step is to know about the idea of the transverse electric mode and transverse magnetic (TM) mode [40]. Light propagates in the waveguide along the X direction as illustrated in Figure 2a, while the polarization of the electric field (E) and magnetic field (M) is in the YZ plane perpendicular to the propagation X axis, since light is a transverse wave. If we define the waveguide width to be along the Y axis and its height along the Z axis, the TE mode means that the electric field oscillates along the Y axis,while the TM mode implies that the magnetic field oscillates along the Z axis. As mentioned previously, a Si photonic waveguide typically functions for TE mode applications and it has a larger width than its height to maintain consistency with E field distribution. However, such a flat strip structure does not match with the polarization status of the magnetic component well. Thus, the performance of typical edge couplers is slightly different for TE and TM modes. Edge couplers with low polarization dependence can work under a polarization-multiplexing regime, which helps increase the link capacity and data transmission rate. To improve the polarization independence of edge couplers, one possible solution may be to increase the Si waveguide height [41; 42; 43; 44; 45]. There are also other approaches to reduce the sensitivity to polarization status, including engineering an effective index for different modes with subwavelength gratings, which will be introduced later in Section 3.4. Moreover, adiabaticity usually implies no conversion or excitation to higher order modes during propagation [46; 47; 48; 49; 50]; thus, adiabaticity can prevent excess mode conversion loss and guarantee high coupling efficiency for a specific mode. It is feasible to obtain an adiabatic taper with gradual profile variation and on this basis, adiabatic tapers usually have higher fabrication tolerance. Nonetheless, a gradual variation in profile often means a large tapering length, which is not preferred for compact devices, so there is a trade-off between adiabaticity and device footprint when designing an adiabatic edge coupler.