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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.


10 um taper (xz plot)

10 um taper (xz plot)

100 um taper (xz plot)

100 um taper (xz plot)


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.



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.



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