1 Polarization converter using a tapered silicon ridge waveguide
Tapered waveguides with an adiabatic change with respect to the propagation direction are very useful for enhancing of the coupling efficiency between two waveguides with different widths. Mode hybridization can occur in asymmetrical silicon on insulator (SOI) waveguides for certain waveguide widths, where the effective indices of two guided modes match [1-2]. Consequently, the field components of TE and TM modes are comparable and the polarization conversion becomes possible. The TE and TM modes refer to the modes with dominant \(E_{x}\) and \(E_{y}\) component, respectively.
In this article, OptiFDTD is used to model a polarization converter (TM0 to TE1) using an SOI taper waveguide connecting two SOI waveguides with different widths [1].
2 Design
The 3D design of the polarization converter is modelled by three sections i.e. the input waveguide (width \(w_{1}\)), the taper waveguide, and the output waveguide (width \(w_{2}\)). All three sections have an SOI ridge structure, see Fig. 1 and tables below for further details about the geometrical dimensions.
Input WG | Value (\(\mu\)m) |
---|---|
\(L_1\) | 1 (z = 0 to 1) |
H | 0.4 |
h | 0.2 |
\(w_1\) | 1.5 |
Tapered WG | Value (\(\mu\)m) |
---|---|
\(L_{tp}\) | 250 (z = 1 to 251) |
H | 0.4 |
h | 0.2 |
w | 1.5 to 0.8 |
Output WG | Value (\(\mu\)m) |
---|---|
\(L_2\) | 6 (z = 251 to 257) |
H | 0.4 |
h | 0.2 |
\(w_{2}\) | 0.8 |
simulation domain | Value |
---|---|
Length ( \(\mu\)m ) | 257 |
Width ( \(\mu\)m ) | 8 |
Substrate material | \(SiO_{2}\) (1.445) |
Substrate thickness ( \(\mu\)m ) | 1 |
Cladding material | Air |
Cladding thickness ( \(\mu\)m ) | 1 |
Ridge WG material | Si (3.455) |
All boundary conditions in x, y, and z directions are chosen as absorbing perfectly matched layer (PML).
To create the ridge waveguide, a channel waveguide profile with Si and thickness h is created and assigned to a linear waveguide with length and width matching that of the simulation domain.
The input and output waveguides are created on top of the Si slab using a linear waveguide set to the same channel waveguide profile as the slab. The taper section is created using an exponential taper waveguide with the alpha parameter is set to zero.
The optical source was configured using the input plane (positioned at z = 0.5 \(\mu\)m) set to Modal, see table 3 for further details.
Optical source features | Value |
---|---|
Wavelength ( \(\mu\)m ) | 1.5 |
Time domain shape | Sine-Modulated Gaussian Pulse |
Mode solver method | Finite-Difference |
Number of modes | 3 |
Observation areas (XY) are located at z = 0.7 \(\mu\)m and z = 254 \(\mu\)m for observing the mode profile inside the input and output waveguides, respectively.
A non-uniform mesh is used to reduce the simulation time. The minimum and maximum mesh size are chosen as 0.0434 \(\mu\)m and 0.1 \(\mu\)m, respectively, in the x and y direction. The predefined regions of the minimum mesh size for the x and y direction are defined from x = -0.75 \(\mu\)m to x = 0.75 \(\mu\)m and y = 0 \(\mu\)m to y = 0.4 \(\mu\)m, respectively. Testing also confirmed that 50e3 time-steps are required for accurate results.
3 Results
The mode solutions and corresponding refractive indices for the input and output waveguides using the OptiMode solver are shown in table 4. Note that the third mode of the input waveguide is TM0, which is the desired input mode. As OptiMode injects the last mode, the number of modes in table 3 is set to three.
The mode profiles for the first three modes of the input and output waveguides i.e. TE0, TE1 and TM0 can be seen in Fig. 2.
Input waveguide modes | Effective index | Output waveguide modes | Effective index |
---|---|---|---|
TE0 | 3.129 | TE0 | 3.058 |
TE1 | 3.026 | TM0 | 2.853 |
TM0 | 2.912 | TE1 | 2.761 |
TE2 | 2.859 | ||
TM1 | 2.807 | ||
TM2 | 2.668 |
Figure 3 shows the mode profiles obtained through the observation areas (XY) when the structure is injected with the TM0 mode. The mode profile observed at the output waveguide demonstrates the polarization conversion from TM0 to TE1.