Controllable dark-hollow beams and their propagation characteristics

A new mathematical model called "controllable dark-hollow beams" is introduced to describe hollow beams. The central dark size of this beam can be controlled easily by the beam order N and parameter epsilon. An analytical formula is derived for the propagation of a controllable dark-hollow beam through a paraxial optical system, and some numerical calculations are carried out. Some important propagation characteristics of this beam, such as the beam propagation factor and the kurtosis parameter, are studied in detail, and their variation rules versus the beam order N and parameter epsilon are presented and plotted.