2D optical vortices and a reverse energy flow occuring near the intensity zeros

This Letter demonstrates that non-paraxial 2D TE-polarized light fields form 2D optical vortices near intensity zeros, with the amplitude having the form x+iz, where x and z are the transverse and longitudinal Cartesian coordinates. Near the intensity zeros, the longitudinal projections of the wave vector have gigantic values of both signs. Negative values of the longitudinal projections of the wave vectors indicate that a reverse energy flow occurs near the intensity zeros. Around the intensity zeros, the energy flow circulates both clockwise (if the topological charge of the optical vortex is -1) and counterclockwise (if the topological charge of the optical vortex is +1). The gigantic values of the wave vectors near the intensity zeros indicate that the wavelength of the light is small, and therefore the phase velocity of rotation of light around the intensity zero is small, compared to the speed of light in a vacuum. A giant wave vector, energy flow circulation, and energy return flow are formed in a substantial subwavelength region around intensity zeros of fractions of a wavelength in size, demonstrating the presence of superoscillations.