Polarization of almost-plane waves

The general polarization behavior of almost-plane waves, in which the electric field varies slowly over a circular pupil, is considered, on the basis of an axial Hertz potential treatment and expansion in Zernike polynomials. The resultant modes of a circular aperture are compared with the well-known waveguide (or optical fiber) modes and Gaussian beam modes. The wave can be decomposed into partial waves of electric and magnetic types. The modes for a square pupil are also considered. The particular application of the effect on polarization of focusing the waves is discussed. Another application discussed is the Fresnel reflection from a dielectric interface, it being shown that the Fresnel reflection alters the relative strength of the electric and magnetic components.