物理学报Issue(4)：173-176,4.DOI:10.7498/aps.62.044205
关于Airy光束衍射及自加速性质的研究
Research on diffraction and self-acceleration of Airy beam∗
摘要
Abstract
In 1979, Berry and Balazs [M V Berry and N L Balazs 1979 Am. J. Phys. 47 264] obtained a strict solution of the Schr¨odinger equation with Airy function used as the initial condition, and described the wave function represented by such solution as the Airy wave-packets. They discovered that infinite Airy wave-packet has unique properties such as non-spreading and free acceleration, proving that it is the only nontrivial non-spreading solution of the time-dependent Schr¨odinger equation in one dimension. However, the observing of the finite Airy beam seems to be more meaningful since wave-packets in reality is inevitably band limited. A certain form of finite Airy beam was investigated by Siviloglou et al. in 2007 [Siviloglou G A, Broky J, Dogariu A, Christodoulides D N 2007 Phys. Rev. Lett. 99 213901;Siviloglou G A, Christodoulides D N 2007 Opt. Lett. 32 979]. They noted that the Airy wave packet still exhibits its most exotic feature, i.e., its trend toward free acceleration. While in the present paper we discuss the properties of Airy beam in a few steps further and propose several conclusions. On the one hand, a theoretic explanation is given to solve the matter of the centre of mass of infinite Airy beam. On the other hand, deeper research is conducted on the unique properties of finite Airy beam. Another form of finite Airy beam is discussed by reduction to absurdity, and its field distribution is put forward by numerical simulation. We find that the trajectory of the centroid holds its position, which means that the beam cannot accelerate freely as a whole. Ultimately, we have the conclusion that finite Airy beam can neither freely accelerate nor be non-diffractive.关键词
Airy光束/无衍射/自加速/数值模拟Key words
Airy beam/non-diffraction/self-acceleration/numerical simulation引用本文复制引用
乐阳阳,肖寒,王子潇,吴敏..关于Airy光束衍射及自加速性质的研究[J].物理学报,2013,(4):173-176,4.基金项目
国家自然科学基金(批准号:61275203)和四川省教育厅自然科学基金(批准号:10Zc031)资助的课题 （批准号:61275203）
