The Eigenmode Expansion, or EME, method solves Maxwell's equations in the frequency domain to calculate the supported modes at the cross-section of the waveguide along the propagation direction. In this video, we will show the key working principles of the EME: slicing the waveguide into cells, expressing an arbitrary field as a superposition of the eigenmodes of individual cells, and reconstructing the propagating field using the boundary conditions at the cell interfaces.
Once the eigenmodes for each cell are found, the solver determines how the modes in the neighboring cells are coupled. In this video, you will learn about the S-matrices which store the information about the coupling between cells.
Once the S-matrices are calculated, it is possible to propagate the input field to obtain the transmission/reflection of the whole device as well as the profile of the propagating field.