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." 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", Journal of Modern Optics, 58, 339-364 (2011).
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", Journal of Modern Optics, 58, 339-364 (2011).