In this article, MODE will be used to study the modes of a SOI waveguide and analyze its dispersion properties.

## Simulation setup

The SOI waveguide in the previous example can be further analyzed using MODE eigensolver. Under the modal analysis tab, there is the option to analyze the modes of a bent waveguide for user defined radius of curvature and bend orientation. The results are those of a doughnut shaped waveguide and can be incorporated in the analysis of a bent waveguide. In this example, losses in a waveguide with one 90 degree bend are analyzed and the bend position is optimized for minimal losses.

## Loss Analysis

Since the propagation loss in the straight SOI waveguide is negligible, there are two major sources that contribute to the losses of a waveguide depicted in Fig.1 above:

-Propagation losses of the mode in the bent region

-Mode overlap losses between the bent and the straight sections of the waveguide

By checking the "Bent waveguide" option in the modal analysis tab, we can locate the same TE mode we found for a straight waveguide previously. The propagation losses of this mode in the bent waveguide are much greater and about dB/um.

In order to calculate the overlap mismatch losses between the two modes in the straight and bent sections of the waveguide, we need to first calculate the modes for the straight waveguide by unchecking the bent waveguide option, locating the desired mode, right clicking on the mode and selecting " Add selected mode to global D-card". Doing so will add the selected mode to the table on the right where the mode can be used later on for overlap analysis with another mode.

Next, we can check the "bent waveguide" option, and calculate the mode in the bent section of the waveguide. For this example, the bent radius is chosen to be 1.5 um and since the bend is in the same plane as the straight section, the orientation angle is zero. The propagation loss of this mode in this case is about 0.0009 dB/um.

Once this mode is located, we can switch to the overlap analysis tab. In order to compare the profile of this mode to that of the straight waveguide, we can click on the Deck window and to pick the d-card we had previously added to the deck. Finally we can calculate the overlap between the two modes to be about 98.8%.

Therefore the total loss of the structure is obtained by adding the contributions of the overlap mismatch at the two interfaces between the quarter ring and the two straight waveguides with the propagation loss of the mode in the curved section:

$$\text {Loss }=-2_{\text {interfaces }} \times 10 \log 10(0.988)[d B]+\left(1.5[u m] \times \frac{\pi}{2}\right)(0.0009[d B / u m])=0.107 d B$$

Since the mode mismatch loss is the more prominent cause of the total loss, optimizing the structure to lead to higher overlap between the two modes can drastically improve the losses. By checking the shift d-card center, one can new position values for the straight waveguide. Alternatively, we can check the optimize position option to let MODE calculate and optimize the position that leads to maximum overlap.

In doing so, we find that if we shift the straight waveguide section by 0.02 um in the x-direction, power overlap increases to 99.7%. The leads to a total loss of :

$$Loss=-2_{\text {interfaces }} \times 10 \log 10(0.998)[d B]+\left(1.5[u m] \times \frac{\pi}{2}\right)(0.0009[d B / u m])=0.019 d B$$

Hence, optimizing the positions of the end waveguides can give about an order of magnitude improvement in the overall loss.

### Related publications

1). A. Sakai, G. Hara, and Toshihiko Baba, "Sharply bent optical waveguide on silicon-on-insulator substrate", Proc. SPIE physics simulation of optoelectronic devices, OE09-562 (2001)