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

## Transcript

The Finite Difference Eigenmode solver (or FDE solver) solves the full vectorial Maxwell’s

equations at a single frequency. The solver will use as inputs the material properties

through a cross section of the device and λ, the wavelength of interest. The outputs

will be the mode profiles E and H, and the propagation constant of the mode, β. If the

mode is lossy, the propagation constant will be complex.

The FDE solver uses a 2D rectangular mesh to discretize the cross section of the waveguide.

Maxwell's equations are then formulated into a matrix eigenvalue problem and solved using

sparse matrix techniques to obtain the effective index and mode profiles of the waveguide modes.

Note the mode loss can be calculated from the imaginary part of the effective index,

k. Furthermore, the fields are normalized such as the electric field intensity, |E|2

is 1. To increase the calculation accuracy and reduce

meshing errors, the conformal mesh technology is applied by default on all material interfaces.

In the next unit, we will discuss how the FDE solver deals with bent and helical waveguides.