CAJ | 학술논문

对Airy光束的特性做进一步探讨,一方面对无限宽Airy光束的重心问题给出新的理论说明,另一方面着重对有限宽情形下的Airy光束的奇特性质进行探讨.文中采用反证法给出无衍射的讨论,同时结合数值模拟给出高斯函数及矩形函数限定下的有限宽Airy光束的场分布,并由此得到其重心位置的轨迹:重心位置是不变的,不可能整体自由加速.最终得到有限宽Airy光束既不可能在自由空间加速,也不可能是无衍射光束.
대Airy광속적특성주진일보탐토,일방면대무한관Airy광속적중심문제급출신적이론설명,령일방면착중대유한관정형하적Airy광속적기특성질진행탐토.문중채용반증법급출무연사적토론,동시결합수치모의급출고사함수급구형함수한정하적유한관Airy광속적장분포,병유차득도기중심위치적궤적:중심위치시불변적,불가능정체자유가속.최종득도유한관Airy광속기불가능재자유공간가속,야불가능시무연사광속.
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.