摘要
基于分数阶薛定谔方程研究在由周期势和线性势组合而成的位势中艾里光束的布洛赫振荡和齐纳隧穿。结果发现,在弱横向力的情况下,艾里光束呈现出光学布洛赫振荡的演化行为,并且与系统的能带结构有关联,即随着Lévy指数的减小,能带宽度减小,同时其振荡振幅也随之减小。增加线性势横向力将导致光学齐纳隧穿的出现,但是Lévy指数可以有效地抑制这种现象。
In the last few years,the fractional Schrodinger equation(FSE)received a lot of attention in various areas of physics.In particular,since Longhi suggested a scheme to explore the FSE in optics,the propagation of light beams in the framework of the FSE has been investigated extensively.Also,the beams described by special functions,such as Airy beam,Gaussian beam and Bessel beam,were paid much attention due to their novel properties and potential applications in the related physical fields.However,among the investigations,the propagation dynamics of Airy beam in the framework of the FSE with a combined potential was rarely involved.In the paper,based on the FSE with a combined potential consisted of periodic potential and linear potential,the optical Bloch oscillation and Zener tunneling of Airy beam are studied by numerical simulation.It is found that under the condition of weak transverse force,the initial incident Airy beam first reaches the edge of Brillouin region due to the refractive index gradient,and then be reflected to the center of Brillouin region due to the Bragg reflection,at which the total internal reflection of the beam occurs.This eventually leads to periodic oscillation of the Airy beam alternating between Bragg reflection and total internal reflection,i.e.,optical Bloch oscillation.Different from the propagation in free space and uniform space,the Airy beam with Bloch oscillation can well maintain the Airy shape even after propagating for a long distance.It is related to the energy band structure of the system,i.e.,with the decrease of the Lévy index,the energy band width and oscillation amplitude decrease.In this case,the Lévy index can not only change the energy band structure of the fractional system,but also effectively control the optical Bloch oscillation.Furthermore,increasing the linear potential transverse force would lead the appearance of optical Zener tunneling at the edge of Brillouin region,but the decreasing of the Lévy index could suppress this phenomenon effectively.
作者
高燕雄
王艳
王栋栋
李禄
GAO Yan-xiong;WANG Yan;WANG Dong-dong;LI Lu(Institute of Theoretical Physics,Shanxi University,Taiyuan 030006,China;College of Physics and Electronic Engitwering,Shanxi University,Taiyuan 030006,China)
出处
《量子光学学报》
北大核心
2021年第4期319-326,共8页
Journal of Quantum Optics
基金
国家自然科学基金(11705108,61078079)。
