# Demonstration of High-Speed Optical Transmission at 2 \(\upmu\)m in Titanium Dioxide Waveguides
## 2 Design and Fabrication of the Photonic Structure  
### Design and Fabrication of the Photonic Structure  
Whatever the platform involved for the design, a critical issue in integrated photonics is always how to efficiently couple the light into the device. In a dedicated article [25], we recently investigated and experimentally validated a new kind of metal grating that is embedded directly within the dielectric layer instead of being deposited on it [26]. Thus, we were able to efficiently couple a 1.55 \(\upmu\)m signal into a TiO\({}_{2}\) photonic waveguide. Here, a similar design is exploited, as depicted in Figure 1a. More precisely, the structure consists of a metal (Au) grating embedded between two TiO\({}_{2}\) layers on a glass substrate.  
Using a commercial finite element-based software (Comsol Multiphysics), we can optimize the parameters of the design to obtain the best coupling around the 2 \(\upmu\)m wavelength. We have taken into account the fabrication and experimental setup constraints, leading to fixed values for the bottom layer height \(h_{bottom}\) = 70 nm and of the incident angle \(\Theta\) = 30\({}^{\circ}\). Thus, using a Monte Carlo algorithm varying (\(h_{Au}\), \(h_{\text{top}}\), \(\Lambda\), \(w_{1}\)) in a 4D parameter space, the coupling efficiency could reach 52% for transverse magnetic (TM) mode when the gold height \(h_{Au}\) = 57 nm, the top layer height \(h_{\text{top}}\) = 234 nm, the period \(\Lambda\) = 1904 nm, and the width of grating lines \(w_{1}\) = 980 nm. However, with these parameters, the coupling efficiency for the transverse electric (TE) mode drops down to 10%. Similarly, the optimization of parameters for the TE mode gives an efficiency reaching up to 36% for \(h_{Au}\) = 45 nm, \(h_{\text{top}}\) = 234 nm, \(\Lambda\) = 1679 nm, and \(w_{1}\) = 356 nm, whereas those parameters give a poor efficiency of 1% for the TM mode.  
However, contrary to Reference [25], our aim is not to reach the best coupling efficiency. Here, we tried to find numerically the geometric parameters that allow a fair coupling efficiency in both the TE and TM modes for a slab. From the previous optimization, the top layer should be 234 nm and, given that \(h_{bottom}\) = 70 nm, the total TiO\({}_{2}\) thickness considered is 304 nm. The thickness of the gold lines \(h_{Au}\) is chosen to be 56 nm, while the period \(\Lambda\) = 1900 nm. To adjust the efficiency of the TM mode compared to the TE mode, we adjust the filling factor by sequentially varying the width \(w_{1}\), as shown  
Figure 1: (**a**) Embedded metal gratings in TiO\({}_{2}\) layout; (**b**) Numerical simulations of the coupling efficiency for one facet as a function of the width \(w_{1}\) of the grating lines for the following parameters: \(h_{\text{bottom}}\) = 70 nm, \(h_{Au}\) = 5 nm, \(h_{\text{top}}\) = 234 nm, \(\Lambda\) = 1900 nm at the central wavelength of our laser source (1.98 \(\upmu\)m). The results for the transverse electric (TE) mode are compared to those for the transverse magnetic (TM) mode. The circles highlight the values where the efficiencies of both modes are equal. The green circle corresponds to the best value; (**c**) Corresponding coupling efficiency per facet for the TE and TM modes as a function of the wavelength (for \(w_{1}\) = 700 nm—green circle on panel (b)).  
in Figure 1b. It appears that three values of \(w_{1}\) allow a similar coupling for the TE and TM modes, but the width of the grating lines that gives the best efficiency (\(-8.5\) dB) is around 700 nm.