Vortex laser beams with complex amplitude proportional to the product of two Bessel functions

The optical vortices with the complex amplitude which is presented by the product of the Gaussian function and two Bessel functions with a complex root dependence of the arguments on the cylindrical coordinates and a constant parameter that determines the type of intensity distribution. These beams can be named Bessel-Bessel-Gaussian beams (BBG beams). An explicit expression for the complex amplitude of such beams at any distance from the waist is presented. We have demonstrated that BBG beams have an anomalously high rotation speed: the intensity rotates by almost 45 degrees at a distance much smaller than the Rayleigh length. It is shown that the parameter allow to control the topological charge of the BBG beam. The topological charge increases in jumps by an even number with an increase in the positive value of the parameter.