Generalized vector diffraction model for tight focusing of light with arbitrary polarization state

Tight focusing of light with specific polarizations creates distinctive electromagnetic field distributions in the focal region, and plays an essential role in various applications such as scanning laser microscopy, light-matter interaction, and particle manipulation. Here, we investigate a generalized vector diffraction model for tight focusing of light with arbitrary initial polarization state. In such model, the focusing field of arbitrary incident electric vector could be calculated as coherent superposition of the focusing fields of two orthogonal polarization components with amplitude and phase differences. Based on the generalized vector diffraction model, we study the focusing distribution properties of both space-invariant and space-variant polarizations. Furthermore, the discrete form of the generalized vector diffraction integrals is also studied for the case of irregular incident polarizations. The proposed model could be applied to optical field modulation, polarizing element engineering, and others.