In antenna technology we distinguish between nearfield and widefield. In the nearfield the electric and the magnetic fields are shifted by 90°. If you look closer you can see that there are two possibilities of this shift, 90° and -90°.
To explain it you have to remember what this 90° means. Let (in vacuum) the coordinate systems X axis be parallel to the E field, let the Y axis be parallel to the B field and the Z axis is parallel to c * t . In Z equal zero let the E field be maximum and directed in the X direction. The B field is zero.
90° later (in terms of E = E(max) * cos α and B = B(max) * sin α) and this is a quarter of the wavelength the B field can be directed to the left or to the right. And this is natural because B = B(max) * - cos α is the second possible state of the nearfield radio waves.
Regardless of the approach to see radio waves as one electromagnetic wave (statistical method) it is obvious that all radio waves are made from photons which are emitted during the electrons acceleration in the antenna rod.
My question is, do these photons all have the same sequence of the E and B fields? The same question appears for quantum dots which produce single photons.
Edit: There has to be a right or left hand rule because if half the photons have B-field with 90° to E and half have -90° then there wouldn't be magnetic field at all.
Update: I get it. It's the right hand grip rule (conventional direction of current) because there is no principal difference to a straight wire.