Reverse canonical energy flow in the near field of a non-paraxial sinc beam without evanescent waves

Abstract In this paper it is shown that the reverse canonical energy flow (RF) in the near field for a non-paraxial two-dimensional sinc-beam with TE polarization occurs not only when evanescent waves exist in the initial field, but also when there are no evanescent waves. In this case, if the non-paraxiality of the beam decreases to a paraxial beam, then the magnitude of the RF will also decrease to zero. Also, RF decreases rapidly (tens of nanometers) during beam propagation. RF is formed near the intensity zeros in the initial field of the sinc-beam, since near the intensity zeros the phase of the field changes abruptly from zero to π . When propagating in space, a minimum intensity appears at the location of zero intensity, and the phase at this location must change smoothly, therefore, to eliminate the phase jump, part of the light field must propagate in the opposite direction. At the intensity zeros of a sinc beam, longitudinal optical vortices emerge, with the energy flow circulating around them. In certain sections of this circulation path, the flow reverses direction relative to the beam’s overall propagation.