  Several recent contributions have envisioned the possibility of increasing
currently exploitable maximum channel capacity of a free space link, both at
optical and radio frequencies, by using vortex waves, i.e. carrying Orbital
Angular Momentum (OAM). Our objective is to disprove these claims by showing
that they are in contradiction with very fundamental properties of Maxwellian
fields. We demonstrate that the Degrees of Freedom (DoF) of the field cannot be
increased by the helical phase structure of electromagnetic vortex waves beyond
what can be done without invoking this property. We also show that the
often-advocated over-quadratic power decay of OAM beams with distance does not
play any fundamental role in the determination of the channel DoF.
