Phase singularities and energy fluxes of a noncanonical vortex dipole Airy beam in the far field

Based on the vector angular spectrum representation and stationary phase method, analytical far-field vectorial expressions of a noncanonical vortex dipole Airy beam, namely, a pair of noncanonical vortices with opposite charges embedded in an Airy beam are derived and used to investigate the phase singularities and energy flux distributions of the corresponding beam in the far-field regime, where the noncanonical characteristic of vortex is stressed. It is shown that the noncanonical strength, off-axis distance, and aperture coefficient affect the position and number of phase singularities, and the motion, creation, and annihilation of phase singularities are found by adjusting these parameters. For a low aperture coefficient, the energy flux distributions exhibit different numbers and orientations of lobes by varying the noncanonical strength. With increasing aperture coefficient, the symmetries of lobes are broken, and the energy flux distributions gradually become ellipses and the directions of their major axes vary with different noncanonical strengths. Finally, the energy flux distributions of an Airy beam carrying a single noncanonical vortex are discussed and compared.