# Effect of Process Parameters on Mode Conversion in Submicron Tapered Silicon Ridge Waveguides
## 2 Structure and Analysis
### Taper Design for Efficient Mode Conversion
#### 2.2.3 (0.4. H) Ridge Waveguide (Ridge Height < Slab Height)  
We finally consider a case of a low etched ridge waveguide in which ridge height is less than slab height. As seen from the 0.5 H waveguide analysis, the mode conversion efficiency increases as the etch-depth is reduced. For a low etched ridge waveguide, the mode conversion efficiency is maximum. It is not possible to further reduce the etch depth to enhance efficiency. Reducing the etch depth below certain limits causes TM fundamental mode to become leaky, and it is not well supported in the waveguide. However, it is still possible to increase the mode conversion efficiency and reduce the taper length requirement by accounting for enhanced mode hybridization due to angled sidewalls and asymmetric cladding. As depicted in Figure 8, a 100% conversion efficiency between TM\({}_{0}\) and TE\({}_{1}\) mode is obtained at a taper length of 440 \(\upmu\)m for an ideal case. The taper length is only 376 \(\upmu\)m when the waveguide is modeled with a sidewall angle of 8\({}^{0}\). When both angled sidewalls and upper air cladding are considered, the size reduces to 277 \(\upmu\)m. Additionally, low etch depth waveguides are reported to show lower propagation loss [37]. This is due to a reduction in the optical mode interaction with the ridge sidewall.  
Figure 8: (**a**) The mode conversion efficiency (\(\eta\)) as the function of taper length (L\({}_{\text{rp}}\)) when TM\({}_{0}\) mode is launched. (**b**) Light propagation with \(\theta\) = 0\({}^{0}\) and n\({}_{\text{cl}}\) = 1.445. (**c**) Light propagation with \(\theta\) = 8\({}^{0}\) and n\({}_{\text{cl}}\) = 1.445. The total height of silicon is H = 500 nm, ridge height (h) = 0.4 H and simulations are done at 1550 nm wavelength.  
Figure 7: The light propagation in the designed taper L\({}_{\text{rp}}\) = 200 \(\upmu\)m (**a**) \(\theta\) = 0\({}^{0}\) and n\({}_{\text{cl}}\) = 1.445 (**b**) \(\theta\) = 8\({}^{0}\) and n\({}_{\text{cl}}\) = 1.445 (**c**) \(\theta\) = 8\({}^{0}\) and n\({}_{\text{cl}}\) = 1. The total height of silicon is H = 500 nm, ridge height (h) = 0.5 H and simulations are done at 1550 nm wavelength.  
Since in a low etch-depth ridge waveguide, very strong mode conversion is observed, it is not recommended to design an ultra-short taper to preserve the TM mode. Figure 8 shows the light propagation in a taper with length Ltp = 10 \(\upmu\)m. Even for an ideal case without any sidewall angle, the TM mode is maintained with only 85% efficiency. This efficiency further reduces to 83% when modeled with sidewalls.  
Figure 9 shows FDTD beam propagation results along the designed taper with Ltp = 200 \(\upmu\)m. A considerable increase in mode conversion efficiency is observed as expected compared to the deeply etched ridge waveguide (see Figure 5).  
Table 1 summarizes the important results for all the cases. It is concluded that, for efficient mode conversion, taper length can be significantly reduced by choosing the optimum process parameters. For a 100% mode conversion, we showed that an 1820 \(\upmu\)m length taper could be reduced to a length of 277 \(\upmu\)m by using a small ridge height and by considering angled sidewalls in an air clad waveguide. This corresponds to a total of 1540 \(\upmu\)m (84.7%) decreases in the overall footprint. Even though an ultra-short taper successfully suppresses unwanted mode conversion, the TM\({}_{0}\) mode preserving efficiency is greatly improved if designed with a high etch-depth ridge waveguide.