Sine hollow beam and its propagation property

The normal sine hollow beam (NSHB) and anomalous sine hollow beam (ASHB) are proposed to describe the dark hollow beam (DHB). Based on the Collins formula, an analytical formula for NSHB (ASHB) through the ABCD optical system is derived. The intensity distributions of NSHB (ASHB) are characterized by the beam parameters and the propagation size. As the numerical example, the propagation properties of NSHB (ASHB) through the ABCD optical system have been demonstrated graphically. It is shown that NSHB (ASHB) will be evolved to the solid beam having the maximum light intensity in the beam center in free space. However, it will make the laser energy concentrate in the small area for NSHB (ASHB) through the convergent optical system.