Determining the Phase Gradient Parameter of Three-Dimensional Polymorphic Beams

Three-dimensional polymorphic beams (3D PBs) with arbitrary 3D curves have drawn increasing attention. In this paper, we introduce the concept of phase gradient parameter (PGP) to describe the accumulation of phase along the curvilinear trajectory of a PB. To determine the magnitude and sign of the integral and fractional PGP of 3D PBs, we present an effective method called slightly defocused interference (SDI). The idea is based on the coaxial interference of two polymorphic beams of the same shape but various PGP. One of the interfered beams is slightly defocused, enabling the identification of the sign of the PGP. The efficiency of the reported method has been demonstrated with numerical simulations and experimental measurements by applying it to determining the PGP of various types of polymorphic beams. The results show high quality, indicating great potential in the applications of beam shaping.