Optical characteristics of radially-polarised twisted light

Recent work has confirmed that radially-polarised optical modes, specifically those endowed with helical wave fronts can now be routinely generated in the laboratory. Here we show that such a paraxial mode carries only an axial total optical angular momentum (AM) where ℓ is the winding number and is a constant. This mode, however, is shown to have zero spin angular momentum (SAM), so it is endowed only with orbital angular momentum (OAM) and no SAM. The helicity is found to be proportional to ℓ , hence this kind of mode displays chirality. When applied to a Laguerre-Gaussian (LG) mode our treatment leads to a total helicity equal to , where is the action constant. The factor ( ℓ / | ℓ | ) = ± 1 , depends on the sign, not the magnitude of ℓ and so the result holds for any radially-polarised LG mode however large the magnitude of its winding number ℓ is. The magnitude of the action constant and hence the helicity are diminished for all such LG modes of large beam waist w 0.