Tight focusing of azimuthally polarized Laguerre-Gaussian vortex beams by diffractive axicons

This study presents a comprehensive theoretical investigation into the focusing properties of azimuthally polarized Laguerre-Gaussian vortex (APLGV) beams when interacting with different optical elements, including a linear axicon, binary axicon, and lens based on the Debye approximation. The research findings highlight the intriguing combination of polarization and vortex singularities within the APLGV beam, which result in distinctive focal shapes when interacting with these optical elements. The focal shapes achieved include multiple tightly focused spots and optical needles, which can be controlled by adjusting optical system parameters and beam characteristics such as the numerical aperture (NA), truncation parameter, beam order, and annular obstruction. These parameters can be carefully selected to achieve specific focal shapes with applications in multi-optical manipulation, particle acceleration, and trapping. By harnessing the unique properties of APLGV beams and optimizing the optical setup, researchers can explore new possibilities for advanced optical manipulation and control.