Fig. 1. Group delay and intensity split of one-dimensional Swallowtail-Gaussian beam without potentials for different Lévy indexes of α=1, 1.4, 1.8, and 2. White dotted lines: the evolutions of the main lobe

Fig. 2. (Color online) Intensity and spectral distributions of SG beams with a linear potential for different Lévy indexes α and linear potential coefficients a.

Fig. 3. Peak intensities and their positions of SG beams with a linear potential for different Lévy indexes α and linear potential coefficients a during propagation. (a) a = 8, (b) a = 4, (c) the peak intensity (Max) of the longitudinal coordinate in transmission varies with the change of the Lévy indexes α(a = −4, +4, −8, +8)

Fig. 4. Intensity evolution of the SG beams with parabolic potential for different Lévy indexes and parabolic potential coefficients. White solid lines in (j)−(l): evolution trajectories of main lobes; Red and white dotted circles: inversion and focus positions of main lobes

Fig. 5. (a) Peak intensities of SG beams for different parabolic potential coefficients during propagation; (b) peak intensity in reversal positions versus parabolic potentials

Fig. 6. The evolution dynamics of SG beams for different Gaussian potentials and Lévy indexes. (a)−(c): α=1, w₀=1; (d)−(f): α=1, x₀=20; (g)−(i): x₀=20, w₀=1

Fig. 7. The evolution dynamics of SG beams in a larger Gaussian potential width of w₀=10 for different Lévy indexes (x₀=20)