ABSTRACT
Laser beams described by scalar complex amplitudes derived as exact solutions of a nonparaxial Helmholtz equation have been well studied in optics. These include well-known plane and spherical waves, as well as more recently proposed Bessel modes, Mathieu beams, parabolic laser beams, Hankel-Bessel beams, and asymmetric Bessel modes. This chapter proposes new vectorial nonparaxial vortex beams with their complex amplitude described by a Hankel function of semi-integer order, prompting us to call them vectorial Hankel beams. It calls these beams laser beams since their complex amplitude satisfies the Helmholtz equation for monochromatic field. The chapter derives explicit analytical expressions for amplitudes of all six components of the linearly polarized vectorial Hankel beam, which allow obtaining analytical expressions for the Poynting vector and the angular momentum (AM). It shows that for non-negative topological charges Hankel beams with clockwise and anticlockwise circular polarization propagate in free space differently.
