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.