Tight focusing of linearly and circularly polarized vortex beams; effect of third-order spherical aberration

A simple analytical model of the angular momentum transformation in strongly focused light beams

“…The fact that, in a beam with radially symmetric profile, the transverse energy flow possesses no radial component means that the beam transverse intensity profile does not change in the first order upon small longitudinal displacement of the observation plane (e.g., from z = 0 to z = dz). Therefore, z-derivatives of the xand y-components of ( ) (19), which are proportional to |E| 2 , really vanish, and this is an additional confirmation of possibility to omit the zderivatives in the spin flow calculation, which was substantiated in the last paragraphs of Sec. 3.…”

“…In the terms of Eqs. (11) or (19) these factors compensate each other, so in the first order in dz these terms do not change, and the longitudinal derivatives of quantities (11) and (19) vanish. Additional arguments to support this reasoning will be given below by direct calculation of the transverse energy flows in the field described by Eqs.…”

“…For the incident beam with circular polarization (13) the SAM is calculated directly by substituting expression (19) into first Eq. ( 2).…”

“…That is why the study of special features and interrelations between the two forms of the optical AM is an insistent problem of the contemporary optics. An important aspect of this problem, intensively addressed in the last few years, is the spin-to-orbital AM conversion induced by the beam transformations destroying its paraxial character, for example, sharp focusing [14][15][16][17][18][19]. Putting aside the theoretical subtleties concerning the unambiguous division of the beam angular momentum into the spin and orbital parts in the non-paraxial conditions, one can formally separate the contribution owing to the beam non-planar polarization and that originating from the beam spatial inhomogeneity, operating as follows [11,14,20].…”

Phase Singularities to Polarization Singularities

“…e focal plane intensity distribution under the influence of spherical aberration [419][420][421][422], astigmatism [329,330,423,424] and coma [425][426][427][428] are also studied. Astigmatism was used to invert the sign of the topological charge of a vortex [429].…”