Engineering axially polarized sub-wavelength scale focal structures using annular Walsh filter

Based on vector diffraction theory, the tight focusing properties of radially polarized Bessel Gaussian beam (BGB), phase modulated by annular Walsh function filters and focused by a high NA parabolic mirror system are studied numerically. The annular Walsh filter derived from the annular Walsh functions forms a complete set of orthogonal phase filters that takes values of either 0 or π phase corresponding to + 1 or −1 over the domain specified by the inner and outer radii of the annulus. Numerical results show that by properly modulating the annular obstruction of Walsh filter and pupil to beam ratio of the input BGB, one can generate many novel focal patterns such as three-dimensional multiple sub-wavelength scale focal spot segments, optical needle, axial flat top profile, etc. We expect that such three-dimensional chain of focal structures is useful for nano-lithography, particle trapping and transportation, as well as confocal and STED microscopy, microstructure fabrication and so on.