Mode expansion monitors allow you to analyze the fraction of power transmitted into any
modes of interest travelling in a waveguide or fiber.
It works by expanding the field profile measured across the cross section of a waveguide or
fiber onto the supported modes of the waveguide or fiber.
In this example, the fundamental mode is injected into the narrow waveguide.
An expansion monitor is used to determine how much power couples into the fundamental
mode of the wider waveguide.
In this case, the coupling efficiency is about 75%.
The mode expansion monitor includes an integrated mode solver to find the supported modes of
a waveguide of fiber given the cross section of the device by using the finite-difference
eigenmode solving algorithm.
This is the same mode solver as used for mode sources that we saw in the Sources section
of the course.
You can edit the monitor and select the modes of interest.
The mode expansion monitor itself does not measure any simulation data, but instead it
takes field data measured by the specified frequency-domain field monitors and expands
the monitor data onto the selected modes of interest.
Frequency-domain field and power monitors are recommended for this since there is less
interpolation error compared to frequency-domain field profile monitors.
Recall that the frequency-domain field profile monitors use the specified position interpolation
method discussed in the common features unit of this section.
For broadband simulations, it is recommended to increase the number of frequency points
over the wavelength range to calculate the supported mode profiles of the waveguide or
fiber since the supported mode profile can change as a function of wavelength.
This can be set under the Mode expansion tab of the mode expansion monitor edit window
and since the modal fields usually change slowly over wavelength using a small number
of frequency points such as 3 or 5 points is usually sufficient in order to get accurate
Overlap calculations are performed between each selected mode and the fields measured
by the frequency domain monitor in order to determine the coefficient giving the fraction
of power which is travelling in that mode.
For broadband simulations, it’s fine if the number of frequency points over which
the modes are calculated doesn’t match the number of frequency points measured by the
frequency-domain field monitor since the mode profiles will be interpolated to the frequency
points measured by the frequency domain field monitor.
After selecting the modes to expand, the effective indices of the modes and mode profiles can
be viewed as results from the mode expansion monitor.
After running the simulation, the mode expansion monitor returns expansion results listed here.
The transmission results T_total, T_net, T_forward, and T_backward give the total transmission
through the monitor, the net transmission into the selected modes, the forward propagating
transmission in the selected modes and the backward transmission in the selected modes
Forward and backward here refer to the positive and negative axis directions.
The a and b results are the complex transmission coefficients of the forward and backward propagating
waves of the selected modes, and these can be used to calculate S-parameters.
More details about the results can be found on the Using Mode Expansion Monitors page
Mode expansion monitors can be useful for simulating devices like polarization converters
where you want to extract the conversion efficiency from input mode to output mode, or extract
s-parameters of a device.
However, if extracting s-parameters, the port object can also be used, and we’ll go over
ports in more detail after we first demonstrate the setup and use of a mode expansion monitor
in the next unit.