Angular momentum of the vortex ultrashort pulsed beam with a smaller beam waist

The angular momentum (AM) of light has important implications for many fields of optics research, such as optics communication, quantum information and laser-scan microscopy. Thus, in this paper, we intend to investigate the average AM of the vortex ultrashort pulsed beam (VUPB), which is generated and widely applied in the field of high-intensity and ultrafast regimes. According to the vector potential, we firstly derive the electromagnetic field of the VUPB, then analyze the spatial intensity, the phase profile and the polarization state of the beam. We explore that the total AM per photon of VUPB is not n ℏ value when the beam waist w₀ is of wavelength or sub-wavelength order, since the polarization of VUPB is changed from linear to circular polarization with the decrease of beam waist, which introduces the conversion of the orbital AM to the spin AM. Moreover, based on the conservation of the total AM, the minimum waist of VUPB can be obtained, which is dependent on the pulse duration time α and topological charge n. Finally, the average AM of the fractional VUPB expressed by the superposition of the integer VUPB with different weights, is analyzed, which is not equal to the AM of fractional CW beam μ - sin (2μπ)/2π (μ is the fractional topological charge), but is associated with the beam waist w₀ and α. Therefore, we think that the AM of VUPB can be controlled by adjusting the α and w₀.