This demonstration will show how to set up a mode expansion monitor and interpret the
mode expansion results.
This is a structure with a wide ridge waveguide as the input waveguide followed by a taper
and a narrower output waveguide.
The device acts as a polarization converter, converting the mode from the first order TE
mode at the input waveguide to the fundamental TM mode at the output.
The efficiency of the conversion increases as the taper length is increased.
We will use the mode expansion monitor to determine how much of the power at the output
has been converted to the fundamental TM mode at the output and what fraction is still traveling
in the first order TE mode for this particular length of taper.
A frequency domain field and power monitor have already been set up at the output to
measure the fields to use for mode expansion.
Set up the mode expansion monitor.
Start by adding a mode expansion monitor from the Monitors drop down menu.
Edit the monitor and set the geometry to match the position of the frequency domain field
and power monitor.
Set the x position to 2.6 microns, the y position to 0 and y span to 4 microns, and the z position
to 0 and z span to 3 microns.
Next, in the Mode expansion tab, click the Add button to select the monitor to expand
the fields from.
Double click on "select monitor" and "select the power monitor".
You can also write a name to use for the expansion results to indicate the monitor that the results
I will use the name “output” since the monitor is located at the output waveguide.
Under mode selection on the left side of the window, choose “user select”.
This will allow me to calculate a list of modes and select multiple modes of interest.
Click the Select Mode(s) button and then in the window that pops up, click the Calculate
I want to know the fraction of power traveling in both the fundamental TM mode and first
order TE mode which are the second and third modes in the mode list.
With one mode selected, I can press the Ctrl key on my keyboard and select additional modes
using the mouse in order to multi-select modes.
Once the two modes in the mode list are selected, click the Select Mode(s) button to accept.
Click OK to accept the monitor settings.
Next, Click the run button to run the simulation.
After the simulation has completed, right-click on the mode expansion monitor and visualize
the expansion for output result.
This result contains multiple different sets of data, so I’ll simplify the plot by removing
all but one result so I can focus on one result at a time.
Across the x-axis of the plot, the value n is plotted, and n corresponds to the mode
number of the selected modes of interest of the mode expansion monitor, since I selected
the second and third mode which corresponds to the fundamental TM mode and first order
TE mode of the output waveguide there is data for n=2 and n=3.
For the T_total result which gives the net power transmitted through the field monitor
in all modes – this is a constant value over n since the result is for all modes and
is not specific to the mode you have chosen.
The result is close to 1 which means almost all power flowing through the monitor is travelling
in the positive x-direction.
Next, double-click on the Attribute and select T_forward.
This gives the power traveling in the positive x-direction in each of the selected modes,
so almost 80% of the power is still traveling in the first order TE mode and only less than
20% of the power has been converted to the fundamental TM mode.
T_backward gives the power traveling in the selected modes in the negative x-direction
which is very small.
T_net is T_forward minus T_backward.
Here are some tips for setting up mode expansion monitors.
For broadband simulations, you can set up the mode expansion monitor to calculate the
modes for expansion at multiple frequency points over the wavelength range.
Typically 3-5 frequency points is sufficient, and this does not have to match the number
of frequency points measured by the monitor for expansion since the mode profiles will
be interpolated onto the frequency points measured by the monitors.
The expansion calculation between the fields and selected modes is done relative to the
center position of the mode expansion monitor and frequency-domain field monitor, so it’s
important to make sure that both monitors are centered around the same relative position
in relation to the waveguide.
A single mode expansion monitor can be used to expand the fields from multiple frequency-domain
field monitors, as long as the cross section of the waveguide or fiber is constant.
For example here, the ring resonator has 4 ports and the expansion for all 4 ports can
be done by a mode expansion monitor since the waveguide cross section is the same at
The “align to frequency monitor center” option in the mode expansion tab needs to
be selected to in order to perform the overlap when the position of the waveguide at the
mode expansion monitor and field monitor for expansion are offset.
To get accurate mode expansion results, it’s important that the span of the monitor is
large enough to include the full profile of the supported modes of the waveguide or fiber,
otherwise the calculated modes that will be used for expansion won’t actually represent
the real supported modes of the structure.
You can check this by plotting the mode profiles and making sure that the fields decay to 0
by the edges.
If a fine simulation mesh is used, and many modes are selected for the mode expansion
calculation, the data of the calculated mode profiles may cause the simulation file size
to be large, even before running the simulation.
If you want to reduce the file size, you can clear the calculated mode data using the Clear
Mode Data button, and choose the “user select” mode selection option so the mode profiles
are not automatically calculated when you save the file.
Changes can be made to the mode expansion monitor settings while in analysis mode after
running the simulation to modify the mode expansion results to calculate.
For example, you can edit the mode expansion monitor and select additional modes of interest
to get the expansion results for more modes than were originally selected without having
to re-run the simulation.
Finally, for most applications where mode expansion types of results are required, the
Port objects are easier to use than Expansion monitors.
The Port objects will be covered in more detail in the following sub-section.
In contrast to Expansion monitors, which require the use of a separate source, frequency domain
monitor and expansion monitor, the Ports combine all three into a single object.