As mentioned in the previous unit, one of the main sources of error in EME is the finite
number of modes used for the mode expansion.
If too few modes are used in a cell, the fields in that cell cannot be represented accurately
by a linear combination of the modes.
Increasing the number of modes will typically help reduce this error.
We can perform convergence testing by increasing the number of modes used in each cell, and
monitoring the S parameters result.
In general, as the number of modes used increases, the S parameters should converge towards the
correct answer, like shown in this plot.
The mode convergence sweep tool which is in the EME analysis window can be used to automate
the convergence test.
The tool works by performing the Propagate step of the simulation starting with using
the number of modes specified in the start mode setting, and increasing the number of
modes used in each in subsequent iteration by the specified interval up to the maximum
number of modes in each port and cell.
Visualizing the mode convergence sweep result will show a plot of the S parameters from
the user s matrix over the range mode modes that was swept.
One thing to be careful of when setting up the sweep is that the start mode should be
set to be at least equal to maximum number of modes selected in each individual port,
otherwise the mode convergence sweep results won't include all of the S parameters of the
For example, if you have a 2 port device, with 2 modes selected in each port, the user
s matrix of the device should be a 4 by 4 matrix with 16 S parameter elements.
However, if you set up the start mode to 1, then for the first point in the mode convergence
sweep, only 1 mode will be used in each port, and the user s-matrix will be a 2 by 2 matrix
with 4 elements, so the mode convergence sweep plot will only show 4 S parameters instead
Instead, the start mode should be set to 2 in this case.
From the mode convergence sweep plot, you can see if the maximum number of modes was
sufficient for the results to converge, and if so, what number of modes was required before
the results converged to an acceptable level of accuracy.
If the results are still changing by the maximum number of modes, then you can switch back
to layout mode, increase the number of modes, and repeat the mode convergence sweep.
Now I'll show a demonstration using the mode convergence sweep.
Here is a simulation file with a polarization converter device.
The polarization converter is essentially a taper which can convert input TE light from
the wide waveguide at port 1 into TM light which gets output at port 2 into the narrower
I can plot the "mode profiles" result from each port to check the number of modes selected.
Three modes have been selected in each port.
I'll edit the EME solver region and set the number of modes for all cell groups to 25,
and click "OK".
Next, I'll click run to perform the Finding modes step of the simulation.
The maximum number of modes found during this step will determine the range of modes that
can be swept using the mode convergence sweep.
Here we are using the same number of modes in each cell group region, but for example
if we had 25 modes in one of the cell group regions and 20 modes in the rest, then the
mode convergence sweep can sweep up to 25 modes, but in the range above 20 modes, it
will use 20 modes for the cells where only 20 modes were found.
Once this is complete, in the EME Analysis Window, click on the "mode convergence sweep"
checkbox, and set the start mode and mode interval.
Since there are 3 modes selected in each port, set the "start mode" to 3.
Now click the "mode sweep" button to start the sweep which will perform the Propagate
step 23 times using 3 modes up to 25 modes.
If you have a large number of modes, then you could increase the mode interval to reduce
the number times the Propagate step is performed.
After the sweep is complete, click the "visualize mode sweep" button.
To simplify the plot, I will remove all results other than S52 which is the S parameter for
light transmitted in the fundamental TM mode from port 2 due to first order TE light at
By default, the real part of the S parameters is plotted, so to get the power, you need
to apply the Abs^2 scalar operation.
You can see that the result converges to about 0.1289 when using 15 modes or more.
In the next unit we will cover potential problems that can arise when using too many modes.