FDE solves mode profiles of an infinite waveguide, which is on a cross section.
Yours is a cavity, as I pointed out previously it is similar to WGM. Thus you need to excite the cavity and pick up the correct modes. Maybe the 3rd party can solve cavity modes. But FDE is only from waveguide cross section, not for cavity. Only 3DFDTD can simulate 3D cavity. Please refer WGM examples online.
FDE calculates the modes at any cross section you specified. It assumes 3rd dimension is infinite.
I hope this clarifies.
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