Fig. 1. (a) The dispersion relationship of light in the FWE (for α=1). (b) The plane wave spectrum of the ideal BSTVP (for l=3).

Fig. 2. The propagation of narrowband BSTVP in the FWE with different l. (a1)–(a4) l=1; (b1)–(b4) l=3; (c1)–(c4) l=50; (d1)–(d4) l=80. For (a1)–(a4) and (b1)–(b4): −250≤xc≤250, −250≤zc≤250; and for (c1)–(c4) and (d1)–(d4): −300≤xc≤300, −300≤zc≤300. Here Δk=k0/400.

Fig. 3. (a) The phase-intensity distributions of the BSTVP (for l=3). (b) The phase-intensity distributions of linear chirp modulated BSTVP (for l=3, v=2Δk). The brightness is proportional to the intensity while the color indicates the phase. (c) The plane wave spectrum of the linear chirp modulated ideal BSTVP (for l=3).

Fig. 4. The propagation of the narrowband linear chirp modulated BSTVP in the FWE with different l. (a1)–(a4) l=1; (b1)–(b4) l=3; (c1)–(c4) l=50; (d1)–(d4) l=80. For (a1)–(a4) and (b1)–(b4): −250≤xc≤250, −250≤zc≤250; and for (c1)–(c4) and (d1)–(d4): −300≤xc≤300, −300≤zc≤300. Here Δk=k0/400.

Fig. 5. The propagation of the broadband BSTVP in the FWE with different l. (a1)–(a4) l=1; (b1)–(b4) l=3; (c1)–(c4) l=50; (d1)–(d4) l=80. For (a1)–(a4) and (b1)–(b4): −250≤xc≤250, −250≤zc≤250; and for (c1)–(c4) and (d1)–(d4): −300≤xc≤300, −300≤zc≤300. Here Δk=k0/4.

Fig. 6. The propagation of the linear chirp modulated broadband BSTVP in the FWE with different l. (a1)–(a4) l=1; (b1)–(b4) l=3; (c1)–(c4) l=50; (d1)–(d4) l=80. For (a1)–(a4) and (b1)–(b4): −250≤xc≤250, −250≤zc≤250; and for (c1)–(c4) and (d1)–(d4): −300≤xc≤300, −300≤zc≤300. Here Δk=k0/4.

Fig. 7. The plane wave spectrum and phase-intensity distributions of the half Bessel spatiotemporal vortex pulse with l=20. (a1) and (a2) E+; (b1) and (b2) E−; (c1) and (c2) E++E−. Note that to clearly display the vortex phase information of the beam, the linear phase [exp(ik0z)] of the beam has not been added.

Fig. 8. The amplitude |E+|, phase arg[E+ exp(ik0z)], and NLy of half-BSTVP with different topological charge l. (a1)–(a3) l=1. (b1)–(b3) l=3. (c1)–(c3) l=50. (d1)–(d3) l=80. The center of the amplitude and phase plots is x=ctDα2k0, z=ct. The r1, r2, and r3 in the diagram of NLy correspond to the three circles from the inside to the out in the intensity and phase diagrams.