This video is taken from the FEEM Learning Track on Ansys Innovation Courses.

## Transcript

In this video we will learn about the solver physics behind the Finite Element Eigenmode

solver (or FEEM solver) in DEVICE.

This solver calculates the solutions to the full vectorial Maxwell’s equations at a

single frequency on a cross section of the device.

The inputs to the solver are the material properties on that cross section and the frequency

or wavelength of interest.

The outputs will be the mode profiles for the electric and magnetic fields, E and H,

and the propagation constant of the mode, beta.

If the mode is lossy, the propagation constant will be complex.

Like all other solvers in DEVICE, this eigenmode solver uses a finite element 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 propagation loss of the waveguide

modes.

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

k.

The electric and magnetic field profiles of the waveguide modes are also calculated.

The fields are normalized so that the optical power calculated from the Poynting vector

is 1 Watt.

The finite element mesh can be automatically refined depending on the material index allowing

the user to find an optimum balance between accuracy and simulation time or memory.

This type of mesh also makes it possible to resolve complex geometries with curved surfaces

very accurately, as can be seen in this figure.

The finite element method allows the use of higher order basis functions to represent

the electric field.

The user can choose the polynomial order of this basis functions.

A higher polynomial order offers higher accuracy while using a relatively coarse mesh.

However, the simulation time will increase as the polynomial order is set to a larger

value.