Periodic ports and Diffraction order ports launch and absorb plane waves propagating in homogeneous domains (adjacent the port boundary). For a plane wave propagating with the wave vector k, the polarization must be orthogonal to the wave vector. For each wave vector, there are two possible orthogonal polarizations. We can select one such set of orthogonal polarizations by first defining the out-of-plane polarization as the field in the direction e1 = k×n, where n is the normal direction to the port. Then the in-plane polarization direction is defined as e2 = e1×k.

Assuming now that e1 and e2 are normalized base vectors, the electric field can be expanded as

where E1 and E2 are the elements of the Jones vector

If the Jones vector elements have the same phase or a π phase difference, the Jones vector represents a linear polarization state. A phase difference of ±π/2 between the two Jones vector elements defines a circular polarization state. For other phase differences, the Jones vector represents elliptic polarization states.