The two-slit interference of vector optical fields with radially-variant polarization

Recently, the studies about the vector optical field have attracted a lot of interest due to its novel properties and potential applications. Compared to a scalar optical field with the uniform distribution of states of polarization (SoP), the vector optical field with nonuniform SoP in the field cross-section has many unique properties. Here we explore theoretically a vector optical field with hybrid states of polarization through the Young's two-slit. The analytical expression for far-field distribution of the vector optical field is obtained. The optical field distribution with periodic stripes in the far-field which are resulted from the interference of the vector optical field with different phases and hybrid SoP through the Young's two-slit is analyzed in detail. It is found that the far-field distribution through the Young's two slits can be manipulated by the initial phase and SoP distributions of the incident vector optical field. In particular, the radially-variant polarization distribution plays an important role on the interference pattern. With different radially-variant cycles, the interference patterns including intensity, phase and polarization are different. Therefore, the distribution of SoP in the initial optical field as an additional freedom can be used to control the interference pattern distribution including intensity, phase and polarization. These results provide a more comprehensive understanding for the transmission characteristics of a vector optical field with a hybrid SoP through the young's two-slit, especially the impact of the distribution of SoP. Thus this approach provides a new method which may further expands the functionality of an optical system by considering the distribution of SoP in field cross-section.