During the Propagate step of the simulation, the S matrix for each cell interface, and
for the overall device are calculated, as well as the fields for profile monitors.
Once we have the S matrices for each cell interface, we can cascade the S matrices to
get a single S matrix for the full device which will give the transmission and reflection
coefficients between all the modes of the first and last cell.
This is returned as a result called the "internal s matrix".
Additionally, we can define ports on either end of the device at the first and last cell
interfaces where we can select port modes.
We calculate the S matrix of the device for only selected port modes, and this result
is called the "user s matrix".
Because we know the S matrices for each cell interface, we can get the coefficients of
forward and backward propagating modes in each cell, and this allows us to reconstruct
the field profile due to a specific source mode at any given position along the propagation
This field data is returned by profile monitors.
We will cover setting up ports and monitors, and how to view the simulation results in
later sections of this course.
The Propagate step is a relatively fast calculation compared to the Finding modes step, and it
can be performed again and again for different cell lengths without having to repeat the
Finding modes step.
This is one of the advantages of the EME method compared to the finite-difference time-domain,
or FDTD method where the full simulation needs to be repeated when any part of the structure
geometry is modified.
In addition to being more efficient for length scanning, we also get the full S matrix for
all port modes after running and propagating once, whereas with FDTD you need to run the
simulation once for each input source, and record the reflection and transmission through
the ports of the device each time in order to extract the full S matrix.