This video is taken from the EME 100 course on Lumerical University.

## Transcript

Scattering parameters relate the transmission and reflection coefficients for each port

and input or output modes of the device.

This is automatically calculated by the EME solver, and returned as the result of the EME

solver region.

Each of the port and mode combinations are labelled with a unique number, and the S-matrix

index mapping table reports this indexing for the selected modes of the ports.

In this S-matrix index mapping table, you can see that there are two ports: port 1 and

port 2, and each port has a single mode selected.

So, you have two S-matrix indices, 1 and 2.

The resulting user s matrix has the size of 2 by 2, with the first index of the subscript

corresponding to the output and the second to the input.

So, S11 is the complex reflection coefficient for output Port1, Mode1 from input Port1, Mode1

and S12 is the Transmission coefficient for output Port1, Mode1 from input Port2, Mode1.

When you have two modes selected at port 1 and a single mode for port 2, the you have

three unique S-matrix mapping indices.

The resulting user s matrix in this case will be 3x3 in size.

Generally speaking, if the S-matrix mapping table has N rows, the user s matrix

will be NxN in size.

The user s matrix is the main result of interest and in most cases will be enough to analyze

the response of the whole device in terms of the selected modes of the ports.

However, if you are interested in the information about the S-parameters

for all the modes of the first and last cell, you can use the internal s-matrix result.

The resulting size of the internal s matrix will be NxN, where N is the sum of all of the

modes in the first and last cell.