ABSTRACT

In optics there are laser beams described by scalar complex amplitudes, which are exact solutions of the nonparaxial Helmholtz equation. These are well-known plane and spherical waves [59], as well as the recently obtained Bessel modes [1, 125], Mathieu beams [4, 116], parabolic laser beams [229], Hankel–Bessel beams [146], and asymmetric Bessel modes [88,124].