Optical intensity distributions in the focal region play an important role in many optical systems. In this paper, the tunable focusing properties of azimuthally polarized sinh Gaussian beams induced by cosine phase masks are investigated theoretically by vector diffraction theory. Results show that when the azimuthally polarized sinh Gaussian beam with cosine phase plate is focused, the focal pattern differs considerably with frequency parameter (C) in the cosine function term. Increasing the value of frequency parameter in the cosine part of the phase mask, focal shift may occur, including multiple-peak focal pattern were also given to show that the focusing properties of this kind of sinh beams may be used to construct tunable optical traps.
