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In 1979, Berry and Balazs [M V Berry and N L Balazs 1979 Am. J. Phys. 47 264] obtained a strict solution of the Schrödinger 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 Schrödinger 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.
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Keywords:
- Airy beam /
- non-diffraction /
- self-acceleration /
- numerical simulation
[1] Berry M V, Balazs N L 1979 Am. J. Phys. 47 264
[2] Siviloglou G A, Broky J, Dogariu A, Christodoulides D N 2007 Phys. Rev. Lett. 99 213901
[3] Siviloglou G A, Christodoulides D N 2007 Opt. Lett. 32 979
[4] Broky J, Siviloglou G A, Dogariu A, Christodoulides D N 2008 Opt. Express 16 12880
[5] Li L, Li T, Wang S M, Zhang C, Zhu S N 2011 Phys. Rev. Lett. 107 126804
[6] Baumgartl J, Mazilu M, Dholakia K 2008 Nat. Photon. 2 675
[7] Polynkin P, Kolesik M, Moloney J V, Siviloglou G A, Christodoulides D N 2009 Science 324 229
[8] Gu Y L, Gbur G 2010 Opt. Lett. 35 3456
[9] Cheng H, Zang W P, Tian J G 2011 Acta Opt. Sin. 31 s100405 (in Chinese) [程化, 臧维平, 田建国 2011 光学学报 31 s100405]
[10] Kaminer I, Bekenstein R, Nemirovsky J, Segev M 2012 Phys. Rev. Lett. 108 163901
[11] Zheng H P 2012 High Power Laser and Particle Beams 24 65 (in Chinese) [郑红平 2012 强激光与粒子束 24 65]
[12] Ehrenfest P 1927 Z. Physik. 45 455
[13] Besieris I M, Shaarawi A M 2007 Opt. Lett. 32 2447
[14] Zhou M S, Ma J C, Zhang C, Qin Y Q 2012 Opt. Express 20 1264
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[1] Berry M V, Balazs N L 1979 Am. J. Phys. 47 264
[2] Siviloglou G A, Broky J, Dogariu A, Christodoulides D N 2007 Phys. Rev. Lett. 99 213901
[3] Siviloglou G A, Christodoulides D N 2007 Opt. Lett. 32 979
[4] Broky J, Siviloglou G A, Dogariu A, Christodoulides D N 2008 Opt. Express 16 12880
[5] Li L, Li T, Wang S M, Zhang C, Zhu S N 2011 Phys. Rev. Lett. 107 126804
[6] Baumgartl J, Mazilu M, Dholakia K 2008 Nat. Photon. 2 675
[7] Polynkin P, Kolesik M, Moloney J V, Siviloglou G A, Christodoulides D N 2009 Science 324 229
[8] Gu Y L, Gbur G 2010 Opt. Lett. 35 3456
[9] Cheng H, Zang W P, Tian J G 2011 Acta Opt. Sin. 31 s100405 (in Chinese) [程化, 臧维平, 田建国 2011 光学学报 31 s100405]
[10] Kaminer I, Bekenstein R, Nemirovsky J, Segev M 2012 Phys. Rev. Lett. 108 163901
[11] Zheng H P 2012 High Power Laser and Particle Beams 24 65 (in Chinese) [郑红平 2012 强激光与粒子束 24 65]
[12] Ehrenfest P 1927 Z. Physik. 45 455
[13] Besieris I M, Shaarawi A M 2007 Opt. Lett. 32 2447
[14] Zhou M S, Ma J C, Zhang C, Qin Y Q 2012 Opt. Express 20 1264
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