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In this paper, we obtain an accurate description of single-cycle vortex pulse beams (SCVPBs) beyond the slowly varying envelope approximation. The SCVPBs are produced by an annular loop composed of oscillating electric dipole arrays. Based on the theoretical model of SCVPBs, simulation results show that the original donut-shaped distribution will evolve into a multi-ring pattern because of the interference effects during transmission. Unlike the π -phase jump effects in different rings in Laguerre–Gauss beams, the spiral isophasal lines of the SCVPBs show continuous change and spatially curved configurations in various donuts which are closely related to the energy distribution of the propagating pulses. In addition, we find the counter-rotating effects of the longitudinal Poynting vector of SCVPBs and calculate the rotation angle. Finally, we discuss the spatiotemporal coupling phenomenon of SCVPBs.

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.