# Grating-Assisted Fiber to Chip Coupling for SOI Photonic Circuits
## 7 Dual Band Grating Couplers  
Due to their diffractive nature, surface gratings are inherently bandwidth limited. Typically, a generic grating coupler exhibits 3 dB optical bandwidth of more or less 60 nm. This would be insufficient for applications requiring a wide band operation. One such application envisaged is fiber to the home networks (FTTH), where upstream signals are channelled through O-band and downstream signals through C-band. A single on-chip grating that simultaneously couples and splits both of these bands would significantly reduce both cost and footprint of an optical transceiver. As observed in the case of polarization splitting couplers, the Bragg condition for gratings can be tailored to couple two distinct bands. The analogy used here is similar to the 1-D and 2-D PSGCs described above except that instead of polarization, it is the corresponding wavelength determining the phase matching criteria. A 1-D dual band single polarization duplexer was proposed in [57] with polysilicon overlays (see Figure 16). In this case, a 1-D grating with 520 nm period at an identical inclination angle of 14.3\({}^{\circ}\) diffracts 1.31 \(\upmu\)m to \(m=1\) order and 1.49 \(\upmu\)m to \(m=-1\) order. The calculated theoretical coupling efficiency was estimated to be -2.5 dB for both 1.31 and 1.49 \(\upmu\)m wavelengths  
Figure 15: **(a)** Complex scatterers for better polarization tolerance. (**b**) Experimental results for coupling fundamental TE mode in either waveguide for the two polarization states (Images reprinted with permission from [54]). \begin{table}
\begin{tabular}{c c c c c c} \hline
**SOI** & **Max** & **Polarization 1** & **Polarization 2** & **Type (1D,2D)** & **PDL** \\
**Couplex** & **CE (-dB)** & **(\(\lambda_{1}\)) (\(\upmu\)m)** & **(\(\lambda_{2}\)) (\(\upmu\)m)** & **Focusing/Non-Focusing** & **(-dB)** \\ \hline Ref [50] & 2 & \(TE_{0}\) (1.559) & \(TM_{0}\) (1.551) & 1D Non-focusing & High \\ Ref [51] & 5.8 & \(TE_{0}\) (1.54) & \(TE_{0}\) (1.535) & 2D Non-focusing & 0.2 \\ Ref [53] & 5.6 & \(TE_{0}\) (1.54) & \(TE_{0}\) (1.53) & 2D Focusing & 0.4 \\ Ref [54] & 3.2 & \(TE_{0}\) (1.492) & \(TE_{0}\) (1.492) & 2D Focusing & 0 \\ \hline \end{tabular}
\end{table} 
Table 3: Performance comparison of various SOI based polarization splitting grating couplers (PSGCs). Columns 3 and 4 pertain to the polarization state of the coupled waveguide modes. PDL denotes the minimum polarization dependent loss. with a 3 dB bandwidth of 55 nm in each band. A 2-D variant of polarization splitting focusing dual band grating coupler was demonstrated in [58]. Here two focusing gratings are overlapped to produce scatters that couple into orthogonally placed waveguides similar to the polarization splitting configuration described above. Except in this case, cross mode phase matching using Equation (18) ensures that the device co-directionally couples fundamental TE mode of C-band and the corresponding TM mode of O-band into either waveguides. This would imply that, the sum of power coupled to corresponding fundamental mode in both arms of the orthogonally placed waveguides is invariant of the incoming polarizations of either band. The experimental results of this 2-D design are plotted in Figure 17b. Table 4 summarizes the few experimentally demonstrated dual band couplers on SOI. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**SOI** & **Max CE** & **Max CE** & **Polarization** & **Polarization** & **Bandwidth** & **Bandwidth** \\
**Coupler** & **(-dB) (\(\lambda_{1}\))** & **(-dB) (\(\lambda_{2}\))** & **(\(\lambda_{1}\)) (\(\mu\)m)** & **(\(\lambda_{2}\)) (\(\mu\)m)** & **3 dB (nm) (\(\lambda_{1}\))** & **3 dB (nm) (\(\lambda_{2}\))** \\ \hline Ref [59] & 8 & 7 & \(TE_{0}\) (1.3) & \(TE_{0}\) (1.55) & - & - \\ Ref [60] & 6.5 & 6 & \(TE_{0}\) (1.485) & \(TE_{0}\) (1.53) & 30 & 30 \\ Ref [58] & 8.2 & 7.1 & \(TM_{0}\) (1.31) & \(TE_{0}\) (1.55) & 18 (1.5 dB) & 35 (1.5 dB) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance comparison of various SOI based Dual band grating couplers.