Singularity Points in the Phase Distribution near the Focus of a 2D Non-Paraxial Light Field

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This paper provides a detailed analysis of the instantaneous phase distribution near the autofocus of a 2D nonparaxial sinc-beam with TE-polarization, obtained using a finite-difference solution of the Maxwell’s equations. Singular phase points are identified: phase screw dislocation points and nearby phase saddle points. Around the phase screw dislocation points (optical longitudinal vortex), the phase increases (or decreases) linearly from zero to 2π as the azimuthal angle increases. Therefore, the energy flow, which is proportional to the phase gradient, rotates around the phase singularity points. Between a phase screw dislocation point and its nearest neighboring phase saddle point, the energy flow is backward. That is, the saddle points limit the width of the energy backflow. Paraxial 2D beams do not have saddle points and there is no energy backflow.