# Grating-Assisted Fiber to Chip Coupling for SOI Photonic Circuits
## 6 Polarization Splitting Grating Couplers (PSGC)  
SOI based gratings couplers are strongly polarization selective. The Si wire waveguide due to its high index contrast renders a considerable difference between effective indices of orthogonal TE and TM modes. This implies that amount of light coupled to waveguide depends on the input fiber polarization which constantly changes due to polarization mode dispersion (PMD). One way to reduce this dependence is by designing a polarization splitting grating coupler (PSGC). Such a grating can be designed with both 1-D and 2-D orientations. In case of the former, the phase matching condition of Equation (2) is applied in a way so as to couple TE modes to \(m=1\) order diffraction and TM modes to \(m=-1\) order diffraction [49]. The matching leads to a common fiber tilt angle at which a single grating coupler can contra-directionally couple the two orthogonally polarized modes as depicted in Figure 14a,b. In [50], [PERSON] et al. have demonstrated such a grating coupler on SOI with a  
Figure 12: Optical intensity profiles of the compact taper at length = 14.5 \(\upmu\)m for (**a**) various \(a\), \(b\), \(c\) values and (**b**) Optimized Value (95% efficiency) and 3-D Mode Profile along the length (L) of a Compact Taper on SOI Platform. Figure 13: Variation in Transmission Efficiency of Compact Taper with the Width of the Waveguide for the (**a**) C + L (1.53–1.63 \(\upmu\)m) band and (**b**) O-band (1.26–1.36 \(\upmu\)m), (**c**) Variation in transmission efficiency for different \(b\) values. Experimental coupling efficiency of the adiabatic (long), focusing grating and compact taper configurations of GC on SOI Platform for (**d**) C + L and (**e**) O band, (**f**) Alignment tolerance of the focusing and linear grating coupler. bottom reflector where TE and TM polarizations exhibited an efficiency of -2 and -2.3 dB respectively with the polarization extinction ratio better than -25 dB (see Figure 14c). Even though splitting is achieved, the 1-D PSGC is highly polarization dependent and would also occupy enormous chip-estate due to the need for adiabatic tapering. Another alternative approach for achieving polarization splitting is by implementing a 2-D surface grating. Such a grating is formed by superposing two 1-D surface gratings orthogonally. The superposition creates an array of scattering elements formed by the intersection of the two gratings. The grating would decouple the incoming elliptically polarized light into its constituent linear components along orthogonally placed waveguides. Depending on whether the electric field orientation is perpendicular or parallel to the propagation axis, power is coupled into the fundamental TE or TM mode in either or both of the orthogonal waveguides, however the sum of total power coupled from fiber to the two waveguides remains almost constant in each case, making the 2D grating polarization invariant. Unlike the case of 1-D gratings, the fiber is tilted at 45\({}^{\circ}\) along the bisector axis of the superposed gratings in order to break symmetry. In this kind of splitting, both adiabatic tapering [51; 52] as well as focusing grating schemes [53; 54] were demonstrated. In the case of the latter, the scatterers lie along the intersection points of two families of orthogonally oriented confocal ellipses (see Figure 15). The fiber projection along bisector axis would then be an additional factor to be incorporated in the eccentricity of ellipses defined by the phase matching condition of Equation (16) as:  
\[p\lambda=n_{g}\sqrt{x^{2}+y^{2}}-(x+y)n_{c}sin\theta cos(\frac{\pi}{4}) \tag{18}\]  
Figure 14: (**a**) Phase matching in _k-space_ for 1D polarization splitting grating coupler. (**b**) Design schematic of mode of operation. Polarization splitting results in contra-directional coupling of the fundamental modes. (**c**) Measured coupling efficiency for the two polarization states (reprinted with permission from [50]).