Periodic Port Mode Fields
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,
.
As plane-wave mode fields are assumed, the material properties in the domain adjacent to the port boundary must be homogeneous and isotropic.
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,
,
where HT,0 is the tangential magnetic mode field amplitude for the periodic port and n is the port normal. Since ET,orth is tangential to the port boundary and thereby orthogonal to the port normal, it can be written
.
So, the tangential electric mode field amplitude for the Orthogonal Polarization Port is polarized in the direction of the conjugate of the tangential magnetic mode field amplitude for the Periodic Port.
For Diffraction Order ports, the amplitude for out-of-plane modes is calculated as
.
For normal incidence, km is parallel to n. Then the amplitude is defined by a tangent vector to the port boundary.
For in-plane modes, the amplitude is defined by
.
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.
The mode fields described above are the unnormalized mode fields. The normalized mode fields are scaled to produce a mode power that equals the specified port input power (for excited ports) or 1 W for listener ports.