We theoretically and numerically study the propagation dynamics of a Gaussian beam modeled by the fractional Schrodinger equation with different dynamic linear potentials. For the limited case α = 1(α is the Lé...We theoretically and numerically study the propagation dynamics of a Gaussian beam modeled by the fractional Schrodinger equation with different dynamic linear potentials. For the limited case α = 1(α is the Lévy index) in the momentum space, the beam suffers a frequency shift which depends on the applied longitudinal modulation and the involved chirp. While in the real space, by precisely controlling the linear chirp, the beam will exhibit two different evolution characteristics: one is the zigzag trajectory propagation induced by multi-reflection occurring at the zeros of spatial spectrum,the other is diffraction-free propagation. Numerical simulations are in full accordance with the theoretical results. Increase of the Lévy index not only results in the drift of those turning points along the transverse direction, but also leads to the delocalization of the Gaussian beam.展开更多
基金Project supported by the Natural Science Research Project of Anhui Provincal Education Department of China(Grant Nos.KJHS2018B01 and KJ2018A0407)the National Natural Science Foundation of China(Grant No.11804112)+1 种基金the Natural Science Foundation of Anhui Province of China(Grant No.1808085QA22)Start-up Fund of Huangshan University,China(Grant No.2015xkjq001).
文摘We theoretically and numerically study the propagation dynamics of a Gaussian beam modeled by the fractional Schrodinger equation with different dynamic linear potentials. For the limited case α = 1(α is the Lévy index) in the momentum space, the beam suffers a frequency shift which depends on the applied longitudinal modulation and the involved chirp. While in the real space, by precisely controlling the linear chirp, the beam will exhibit two different evolution characteristics: one is the zigzag trajectory propagation induced by multi-reflection occurring at the zeros of spatial spectrum,the other is diffraction-free propagation. Numerical simulations are in full accordance with the theoretical results. Increase of the Lévy index not only results in the drift of those turning points along the transverse direction, but also leads to the delocalization of the Gaussian beam.
