Generation of multiple focal pattern via phase modulated radial and azimuthal variant vector beam

The multiple focal patterns such as longitudinally/transversely polarized multiple focal spots/holes, longitudinally/transversely polarized annular dark multiple spots with petal shapes are in high demand for applications such as multiple optical trapping and manipulating, light-sheet fluorescence microscopy and optical lithography. This article numerically demonstrated the possibility of achieving the above task by subjecting phase modulation of radial and azimuthal variant vector beam through suitable annular Walsh function filter. Here it is demonstrated that the inherited self similarity properties of annular Walsh function and the flexibility of tuning the radial and azimuthal index of input beam is a state of art in landscaping multiple focal segment of desirable spatial and polarization distribution.