Focus shaping of the radially polarized Bessel–Gauss beam with a sine-azimuthal variation wavefront

Focusing properties of the radially polarized Bessel–Gauss beam with a sine-azimuthal variation wavefront was investigated by the vector diffraction theory. The wavefront distribution is the sine function of the azimuthal angle with one phase parameter that indicates the phase change frequency. Results show that the focal pattern can be altered by the phase parameter, and many novel focal patterns may occur, such as multiple dark-foci focal pattern, crescent shape, and wheel shape. For case of a higher phase beam, the whole focal pattern turns on a symmetric wheel shape with multiple reduplicate intensity elements. When the phase parameter is an odd number, the number of reduplicate elements equals the phase parameter, while when the phase parameter is an even number, the number of reduplicate elements is two times the phase parameter. In addition, the effect of the phase parameter on the focal pattern is more considerable than that of the beam parameter under low numerical aperture. Under higher numerical aperture, the effect of the beam parameter on the focal pattern gets stronger.