Hyperbolic-cosine-Gaussian beam with sine-azimuthal variation wavefront

Intensity distribution in focal plane plays an important role in many optical systems and has attracted much attention. In this paper, focusing properties of hyperbolic-cosine-Gaussian (cosh-Gaussian) beam with sine-azimuthal variation wavefront is investigated. Wavefront distribution is the sine function of the azimuthal angle. Results show that the sine parameter in the sine part of the cosh-Gaussian and decentered parameter associated with the cosh parts affect focal pattern considerably. Many novel focal patterns may occur, including cross-shape focal pattern with four intensity peak, intensity peak array, intensity peak wheel, and swallowtail multiple-peak focal pattern. The focal pattern evolution principle on increasing decentered parameter differs remarkably for different sine parameter. In addition, some focal spots are smaller than focal spot with incident Gaussian beam, which means super resolution effect appears under condition of certain sine parameter and decentered parameter.