# Grating-Assisted Fiber to Chip Coupling for SOI Photonic Circuits
## 5 Lowering Footprint
### Linear Grating Based Compact Tapers  
Although focusing gratings are efficient, they require accurate alignment of the fiber tip and are fabrication intolerant. Linear Gratings along with adiabatic/non-adiabatic tapers are therefore preferable to couple light in photonic devices. When considering high-density circuit, it is indispensable to reduce the footprint of these tapers. Since the taper length depends predominantly on the starting and ending waveguide width and effective index, the transition between a grating coupler and a single-mode photonic waveguide in any material platform is one of the largest [33; 34; 35; 36; 37]. Thus, it is extremely advantageous to have non-adiabatic tapers along with linear GCs for a compact spot-size converter. Adiabatic tapers from waveguide to fiber dimensions have been proposed to enhance coupling efficiencies but are very long (mm) and usually suffer from strong back reflections. A taper 5.5 um long based on high refractive index materials has been shown but its fabrication is cumbersome and requires several steps [36]. Edge coupling based inverse tapers to enhance the mode size of the waveguide through evanescent field coupling have also been designed with low loss and broadband operation but they are disadvantaged by back reflections and long lengths [37]. [PERSON] et al. have proposed a short taper (40 um) for compact mode conversion with mode mismatch loss of -0.26 dB and back reflection less than -48 dB, which require a very high precision fabrication for realization of the nano-sized tip [6]. A robust fabrication based on \(SWG\) edge couplers have also been shown with coupling loss of -0.9 dB [38]. However, edge couplers, as mentioned before, can only be placed near the chip facets and hence requires precise chip arrangement and cannot be used to test individual devices on the wafer. Several designs of linear grating-based adiabatic tapers involving linear [39], exponential [40] and parabolic [41] profiles have shown. However, there is a tradeoff between the taper length and coupling efficiency due to the adiabatic transition [42]. A complex non-adiabatic taper 15.4 um long using multimode interference (efficiency 70%) [43] and lens-assisted focusing tapers with lengths varying from 10 to 20 um with a loss of about -1 dB for TE and -5 dB for TM mode [44] have been demonstrated. Discontinuous tapers with 90% efficiency for the fundamental quasi-TM mode [45] have been theoretically shown. However, the proposed structures are either difficult to fabricate, or suffer from low efficiencies and larger footprints. Recently, a novel design of large bandwidth, fabrication tolerant, CMOS-compatible and non-adiabatic compact tapers have been proposed and experimentally demonstrated in SOI (wire and ridge configuration) as well as Silicon Nitride platform [46; 47; 48]. These tapers along with linear gratings for spot-size conversion exhibits no degradation in the coupling efficiency compared to a standard focusing grating in 1.55 um band. Table 2 shows the comparison of various adiabatic and non-adiabatic tapers in SOI platform. The SEM image of the taper structure along with linear shallow-etched diffractive waveguide grating couplers is shown in Figure 11. Unlike an adiabatic taper, the compact taper works on multi-mode interference along the length of the taper. The length and width of the taper are optimized to obtain interference progressively between the resonance modes along the taper resulting in maximum coupling to the fundamental waveguide mode. The proposed taper structure to connect a broad waveguide section to a submicron waveguide section is defined using an interpolation formula,  
\[X=a(bz^{2}+(1-b)z)+(1-a)sin(c\frac{\pi}{2}z)^{2} \tag{17}\]  
here \(a\) lies between 0 to 1, \(b\) lies between \(-1\) to 1, \(c\) is any odd integer \(\geq\)3 (\(c=1\) creates the trivial case of half a sinusoidal oscillation). This formula meets the following boundary conditions: \(X(z=0)=0\) and \(X(z=1)=1\) where \(z\) is the relative length of the taper.