# FEM port Boundary definition for electromagnetics and wave guides

We are currently in the process of implementing ports in our EM FEM simulation SW. We have come across the definition of boundary conditions for the ports, and we do not understand the equation for the boundary. In the book “The Finite Element Method in Electromagnetics” they start from the understandable idea of it being a super position of the incoming and reflected wave. And because it is a Homogeneous waveguide the field follows the analytical TE10 mode.

To find the equation for the field they take the curl of both sides. We do not understand how this makes sense in a physical way. The $$\hat{n}$$ vector is the normal to the waveguide port. We assume that this is used to isolate the field along the port surface. Do you have any suggestions on how and why this is done?

• Can you type the relevant equations using MathJax? That way is easier to follow what you mean. Apr 13, 2021 at 15:56
• After you perform integration by parts on the vector wave equation (to move one of the curls into the testing side), the remaining surface integral requires boundary data for $\hat n \times \nabla \times E$. That's what motivates this "curl both sides, cross both sides" step, they are seeking to impose "outgoing TE10 mode" as a 2D boundary condition on the original 3D problem. Apr 14, 2021 at 16:10