Nonparaxial Hankel vortex beams of the first and second types

We consider new solutions of the nonparaxial Helmholtz equation in the cylindrical coordinates, which are treated as nonparaxial scalar vortex Hankel beams of the 1st, 2nd and 3rd types. The beams can be obtained from each other by differentiation. Higher-order types of Hankel beams show lower divergence than the lower-order types. The lowest- (zero-) order Hankel beam of the first type represents a spherical wave.