Spot size converter

The design of the spot-size converter is based on reference [1]. The goal of this design is to efficiently couple light from a strongly confined high index contrast silicon waveguide into an optical fiber, which has a much larger mode field size. In this design, the spot-size conversion is achieved by using an Si adiabatic taper covered by a low-index waveguide. Once the mode is converted from the silicon waveguide to that of the larger low-index waveguide, it can be coupled much more efficiently into the optical fiber.

The EME method is ideal for taper designs because one can sweep the taper lengths quickly without having to calculate any additional modes. In this case, FDTD-based methods are not as efficient because not only does the simulation time increase with taper length exponentially but also separate simulations are required for each taper length.

Learning objectives

In this example, we show how MODE'  eigenmode expansion (EME) solver can be used to design a spot size converter. The user will learn to:

• Set up an EME simulation
• Quickly scan the length of the spot size converter to find the optimal design
• Compare results with 3D FDTD results

Modeling instructions

The first two sections (Create the structure, and Add EME Solver and monitors) describe how to setup the simulation from a blank simulation file. If you prefer to skip this section, a copy of the completed simulation file is provided with this tutorial.

Create the structure

The structure will consist of a substrate, the input high index waveguide with uniform y span, the tapered portion of the high index waveguide with varying y span, and the low index polymer waveguide.

• Begin by starting MODE. You can save the MODE Simulation Project file (.lms) at any point in this process. To do so, choose SAVE in the FILE menu.

Add the substrate

• Press on arrow on the STRUCTURES button

  

  and select a RECTANGLE from the drop-down menu. Set the properties of the substrate rectangle according to the following table. To open the edit properties window for an object, click on the edit tool button

  

  on the side toolbar, or right click on the object in the Objects Tree and select EDIT OBJECT from the right-click menu.

Add the input high index waveguide

• Press on arrow on the STRUCTURES button

  

  and select a RECTANGLE from the drop-down menu. Set the properties of the rectangle according to the following table.

Add the tapered section of the high index waveguide

• Press on arrow on the COMPONENTS button

  

  and select EXTRUDED POLYGONS from the pull-down menu. This will open the object library window.
• Select ISOSCELES TRAPEZOID from the list and press the INSERT button.
• Set the properties of the isosceles trapezoid according to the following table.

Add the low index polymer waveguide

• Press on arrow on the STRUCTURES button

  

  and select a RECTANGLE from the drop-down menu. Set the properties of the rectangle according to the following table.

By setting the mesh order of one material to be larger than that of another material, the material will have lower mesh priority in the regions where objects overlap.

• Select the model analysis group in the Objects Tree. Click on the zoom extent button

  

  on the side view toolbar to zoom the view ports around the completed structure.

Add EME Solver and monitors

• Press on the arrow on the on the SIMULATION button

  

  and select the EME SOLVER from the drop-down menu. Set the properties according to the following table.

• Set the properties of the table in the CELL GROUP DEFINITION section of the EME setup tab of the simulation region object according to the following table.

The number of cell groups is set to 3 for the three distinct regions of the structure, the input waveguide, the tapered region, and the output waveguide. In each cell group we can specify the span of the region the cell group will cover, and the number of cells to use in the cell group. The number of cells corresponds to the number of locations where the modes of the device will be solved.

In the cell group regions where the cross section of the device does not change (ex. the input/output waveguide regions), it is not necessary to use more than 1 cell, and the subcell method should be set to "none". In regions where the cross section of the structure changes, more cells are required to resolve the change in the geometry. In cases where the cross section is changing continuously over the region, the CVCS subcell method is recommended since it will give better results by reducing the staircasing effect from using a finite number of cells.

The DISPLAY CELLS option in the EME setup tab shows the cell boundaries in the CAD view. We can ignore the section in the EME setup tab for periodicity since this structure does not include any periodic regions.

Set up Ports

• Expand the EME object in the Objects Tree by clicking on the triangle symbol next to the object name. Then expand the Ports group under the EME object. Edit the properties of both port_1 and port_2 according to the following table.

The selected modes will be the ones the user S-matrix will return results for.

Add Mesh Override

The mesh override region is used to set a finer transverse mesh over the tapered section of the high index waveguide

• Select the model analysis group at the top of the Objects Tree. Press on the arrow on the on the SIMULATION button

  

  and select MESH

  

  from the drop-down menu to add a mesh override region. Set the properties of the mesh override region according to the following table.

• Press the VIEW MESH button

  

  in the side toolbar to display the transverse mesh in the CAD.

Add Monitors

• Press on the arrow on Monitors button

  

  and select EME INDEX from the drop-down menu. Set the properties according to the following table.

• Press on the arrow on Monitors button

  

  and select EME PROFILE from the drop-down menu. Set the properties according to the following table.

Calculate and extract results

Run

• Press on the RUN button

  

  . This will calculate the supported modes in each cell and switch the simulation from the layout to analysis mode. When the simulation finishes running, the EME Analysis window will be opened.

Propagate fields

• In the EME Analysis window, set the SOURCE PORT setting to PORT 1. This will use the fundamental mode from PORT 1 as the source when generating profile monitor results.
• Note that since we are not using periodicity we can ignore the warning in the CELL GROUP SEQUENCE section of the EME Analysis window.
• Press the EME PROPAGATE button.

Plot refractive index and field profile

• Once the propagation is complete, the EME object and the monitors in the Objects Tree will be populated with data. The Results View window (which can be opened by enabling " Result View - EME" in the top menu View Windows) will display all the results and their corresponding dimensions/values for the selected object. Plot the refractive index by right-clicking on the "index" monitor and selecting Visualize - index profile. The field profiles can also be visualized in the same way.
• To see the values of the user S-matrix, right click on the EME object, select Visualize - user s-matrix. Then in the visualizer under the Attributes section, double click on the "VIEW DATA" cell for the EME:user s-matrix dataset. The values of the rows and columns correspond to the S-matrix. For example, the value in row 1, column 1 corresponds to S11, and the value in row1, column 2 corresponds to S12. And abs(S(21))^2 is the transmission. Since the device behaves symmetrically, S12=S21.

Change taper length

• To recalculate results for a longer taper, go to the CELL GROUP DEFINITION section of the EME Analysis window and change the GROUP SPAN of the second cell group region. Change this from 10um to 100um, which will correspond to the same device geometry but now with a 100um long taper region.
• Press the EME PROPAGATE button to re-calculate the results, then visualize the new results for the longer taper. Note that this calculation is almost instant since it does not require any additional mode calculations.

Scan taper length

To scan the taper length over a range of values, the propagation sweep widget in the EME analysis window can be used.

• In the EME Analysis window, select the PROPAGATION SWEEP checkbox, and set the settings of the propagation sweep according to the following table.

• Press the EME SWEEP button to run the sweep over taper lengths.

Plot sweep results

• After the sweep is complete, press the VISUALIZE EME SWEEP button. The S-parameters will be plotted in a new visualizer.
• The transmission corresponds to |S12|^2. To plot this, remove the other results from the list of attributes in the Visualizer, and set the SCALAR OPERATION of the result to Abs^2.

Discussion and results

The EME solver in MODE is a fully vectorial bi-directional Maxwell's equations solver. The solver relies on modal decomposition of electromagnetic fields into a basis set of eigenmodes, which are computed by dividing the geometry into multiple cells and solving for the modes at the interface between adjacent cells. This method accounts for multiple-reflection events, and only one simulation is needed for all input/output modes and polarization so it is ideal for simulating tapers and performing length scanning.

In the EME solver setup, we define the cross sections where the modes are solved by defining cell groups. For uniform regions where the cross section of the structure does not change in the propagation direction (ex. cell group 1 and 3, or the input/output waveguide regions), only one cell is necessary in the cell group since using additional cells will not affect the results.

For regions such as a taper where the cross section of the device varies, you can specify a number of cells within the cell group where the modes of the structure will be calculated, and in these regions we want to set the subcell method to CVCS which reduce the staircasing effect due to the discrete changes in cross section of the structure between each adjacent cell. The number of basis modes to use for the calculation can also be set in the EME solver object. It is recommended to start with a small number of modes for the initial calculation. Once everything is working as expected, one can increase the number of modes until the result converges.

The cell boundaries of the structure can be seen in the CAD view below.

The modes at the center each cell are calculated on a finite mesh transverse mesh. Mesh override regions can be added to force a finer mesh where necessary. For this spot size converter, we add a mesh override region over the tapered silicon waveguide to better resolve the geometry. The view mesh button displays the transverse mesh in the CAD view as shown below.

We can select the mode (or a set of modes by multi-selecting) of interest by editing the ports and choosing the desired modes. The user s-matrix result that is calculated by the EME solver will return the results for the selected mode(s) only. For this device we are interested in the fraction of power transmitted from the fundamental mode of the silicon waveguide at port 1 to the fundamental polymer mode at port 2 which is given by |S21|^2 with port 1 at the input side, and port 2 at the output. However, since the device behaves symmetrically, we can get the same result by looking at |S12|^2. For more information about the S-matrix index mapping see EME solver analysis.

Analysis and Results

Pressing the run button will calculate the modes at each cell. You can visualize the calculated modes by expanding the EME solver and cell group in the Objects Tree, then right-clicking the individual cell and selecting the result to visualize.

To see the final field profile of the device as well as the S-matrix results, press the EME PROPAGATE button in the EME analysis window. Once the propagation is complete, profile monitor results and S-matrix results will be available, and can be visualized by right-clicking on the objects in the Objects Tree. The results for different propagation lengths can also be changed without having to re-calculate any modes. The field profile for a tapered region of length 10 um and 100 um are shown below.

Scattering parameters relate the transmission and reflection coefficients for each port and input/output modes of the device. This is automatically calculated by the EME solver, and returned as the result of an EME solver region. The internal s-matrix includes all of the s-parameters for all the modes of all the ports, whereas the user s-matrix will contain only the s-parameters for the modes selected in the ports. Since we have 2 ports, and we are only interested in the fundamental mode at each port, the user s-matrix will be a 2 by 2 matrix, with elements S11, S12, S21 and S22.

Length scanning

The propagation sweep widget allows you to scan the length of any cell group and calculate s-matrix results automatically. The S-matrix index mapping table allows you to quickly identify which s-matrix components correspond to which port and mode.

Below, the transmission through the taper is plotted over taper lengths from 10 um to 200 um.

The length scanning can also be done by running the script spot_size_converter.lsf.

EME vs 3D FDTD

We also compare the EME results with 3D FDTD. The results between two solvers agree reasonably well, however they are done with completely different time scale. The EME simulation takes 3 minutes to simulate 101 different taper lengths (blue squares), whereas 3D FDTD takes 6 hours to simulate 11 different taper lengths (green squares).

None vs CVCS subcell method

To see the effect of staircasing, change the subcell method for group span 2 from "CVCS" to "none" and re-run the eme sweep.

One can see that when the CVCS subcell method is not used for the tapered portion of the structure in cell group 2, the staircasing effect will result in a transmission curve that is much rougher than before.

References

[1] T. Tsuchizawa et al, “Microphotonics devices based on silicon microfabrication technology”, IEEE J. Select. Topics Quantum Electron., 11, 2005, 232-240

See also

EME Solver Analysis