Tight focusing properties of phase modulated transversely polarized sinh Gaussian beam

We studied the tight focusing properties of an azimuthally polarized sinh-Gaussian beam phase modulated with multi belt vortex phase filter on the basis of the vector diffraction theory. The sinh-Gaussian beam can be considered as superposition of a series of eccentric Gaussian beams and it is observed that focusing such a beam with a properly designed dedicated vortex phase filter generates many novel focal patterns including transversely polarized optical needle of extended focal depth with sub wavelength scale lateral resolution and mutiple focal spots with different axial seperation distance. We expect that such a focal patterns are usefull in applications such as semiconductor inspection and multiple optical trapping.