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Output Port Boundary Condition

The output port boundary condition is used to model the electromagnetic field exiting the computational domain through an attached waveguide. Similarly to the input port boundary condition, the output boundary condition assumes that the radiation leaving the computational domain corresponds to a well-established waveguide mode with the propagation constant \(\beta\). The corresponding equation for the complex amplitude \(\tilde{\mathbf{E}}\) of the electric field at the boundary of the output port can be written as

\[\hat{\mathbf{n}} \times \left(\frac{1}{\mu} \nabla \times \tilde{\mathbf{E}}\right) = -\frac{i\beta}{\mu} \hat{\mathbf{n}} \times \left(\tilde{\mathbf{E}} \times \hat{\mathbf{n}}\right),\]

where \(\hat{\mathbf{n}}\) is the unit vector normal to the boundary.