Basically, The field of a

*x*polarized light focused by a high numerical aperture (NA) objective will not only have a*x*polarized component, but also have*y*and*z*component. The figures below in the first row is the simulated field (Ex, Ey, Ez) at the focal plane. The*y*and*z*component is clearly seen. The total field intensity is elongated along the*x*direction as shown in the figure in the second row.An exact solution for this problems is solved in 1959 by Richards & Wolf:Richards, B. & Wolf, E. "Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system."

In the following years, there are several approximations for this solution are developed to quickly calculate the field with a computer. A good review article about this is shown below:

Foreman, Matthew R. & Török, Peter, "Computational methods in vectorial imaging",

*Proc. R. Soc. London A*, 253, 358-379 (1959).In the following years, there are several approximations for this solution are developed to quickly calculate the field with a computer. A good review article about this is shown below:

Foreman, Matthew R. & Török, Peter, "Computational methods in vectorial imaging",

*J**ournal of Modern Optics*, 58, 339-364 (2011).