A pseudo non-diffracting microwave vortex

Computations, performed with the well-known Mathematica program, have produced rigorous, closed-form, symbolic expressions of the cylindrical E-field, and H-field components of a planar, circular-aperture field-distribution that appears to generate a radiation-pattern exhibiting the propagation-invariance of the so-called "pseudo non-diffracting" optical Bessel-beams. The new planar, circular-aperture field-distribution obtained includes radial-, azimuth-, and axial-components of both the E-field, and H-field with different linearly-dependent azimuth phases. Further, only the axial-(S_z*), and azimuth-(S_phi*) components of the complex poynting vector are non-zero, while the radial component S_r* is identically-zero, everywhere on and above the aperture-plane, at all radial distances from the broadside-axis, and at all axial-distances from the aperture-plane. The generated wave-front has the shape of a 3D helicoid-surface, with a pitch being a function of the k_z/k_r ratio. The diffraction-properties of the generated radiation- pattern are being computed by using the "direct electromagnetic field integration " method, reported by Walter Franz in 1948, and reviewed by Chen-To Tai in 2000.