Focusing properties of Lorentz-Gaussian beam with azimuthally-variant phase filters

Optical vortex attracts many researchers for its interesting properties and promising applications. Focusing properties of the linearly polarized Lorentz-Gaussian beam with azimuthally-variant phase filters were investigated by vector diffraction theory. Results show that the focal intensity distributions can be altered considerably by phase variation parameter of phase filter and the beam parameters, changing phase variation parameter of the phase mask, focal shift, focal switch and focal split may occur, simultaneously, the focal shift direction may change. Moreover, altering phase variation parameter will change the energy distributions of maximum intensity peak and other small intensity peaks. And novel focal patterns also evolve considerably, such as from only one peak to multiple peaks. The focal pattern evolution principle is different with different beam parameter. The tunable focal shift can be used to construct controllable optical tweezers. In practice, azimuthally-variant phase filters can be implemented through phase-only spatial light modulator, which can conveniently alter the wavefront phase distribution of the incident laser beam in the control of computer.