Periodic, Diffraction Order, and Orthogonal Polarization Port features, all use plane-wave electric mode fields of the form

where Em, km, and r are the amplitude, the wave vector, and the position vector, respectively. Here, m is the mode index. Since, this field represents a plane wave, the amplitude must be orthogonal to the wave vector,

For the Periodic Port, the amplitude E0 is provided by the user (we set m = 0 here, as the Periodic Port represents the lowest diffraction order). The amplitude for the Orthogonal Polarization Port is orthogonal to the amplitude of the Periodic Port. That is,

For Diffraction Order ports, the amplitude for out-of-plane modes is calculated as

where n is the port normal.

For normal incidence, km is parallel to n. Then the amplitude is defined by a tangent vector to the port boundary.

From the amplitude definitions above, it is clear that in-plane modes are polarized in the plane spanned by the port normal n and the mode wave vector km, whereas out-of-plane modes have a polarization that is orthogonal to this plane.