Abstract

Corrections are pointed out to results reported by Chen et al.[J. Opt. Soc. Am. A 28, 1307 (2011)] pertaining to the Wigner distribution functions of two- and three-dimensional accelerating (bending) Airy beams.

© 2011 Optical Society of America

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References

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  1. R.-P. Chen, H.-P. Zheng, and C.-Q. Dai, “Wigner distribution function of an Airy beam,” J. Opt. Soc. Am. A 28, 1307-1311(2011).
    [CrossRef]
  2. I. M. Besieris and A. M. Shaarawi, “Accelerating Airy wave packets in the presence of quadratic and cubic dispersion,” Phys. Rev. E 78, 046605 (2008).
    [CrossRef]
  3. O. Vallée and M. Soares, Airy Functions and Applications to Physics (World Scientific, 2004), pp. 57-58.

2011 (1)

2008 (1)

I. M. Besieris and A. M. Shaarawi, “Accelerating Airy wave packets in the presence of quadratic and cubic dispersion,” Phys. Rev. E 78, 046605 (2008).
[CrossRef]

Besieris, I. M.

I. M. Besieris and A. M. Shaarawi, “Accelerating Airy wave packets in the presence of quadratic and cubic dispersion,” Phys. Rev. E 78, 046605 (2008).
[CrossRef]

Chen, R.-P.

Dai, C.-Q.

Shaarawi, A. M.

I. M. Besieris and A. M. Shaarawi, “Accelerating Airy wave packets in the presence of quadratic and cubic dispersion,” Phys. Rev. E 78, 046605 (2008).
[CrossRef]

Soares, M.

O. Vallée and M. Soares, Airy Functions and Applications to Physics (World Scientific, 2004), pp. 57-58.

Vallée, O.

O. Vallée and M. Soares, Airy Functions and Applications to Physics (World Scientific, 2004), pp. 57-58.

Zheng, H.-P.

J. Opt. Soc. Am. A (1)

Phys. Rev. E (1)

I. M. Besieris and A. M. Shaarawi, “Accelerating Airy wave packets in the presence of quadratic and cubic dispersion,” Phys. Rev. E 78, 046605 (2008).
[CrossRef]

Other (1)

O. Vallée and M. Soares, Airy Functions and Applications to Physics (World Scientific, 2004), pp. 57-58.

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Equations (7)

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W ( X , P , Z ) = 2 2 / 3 e 2 a ( X P Z ) Ai [ 2 2 / 3 ( X P Z + P 2 ) ]
Z W ( X , P , Z ) + P X W ( X , P , Z ) = 0 .
W 0 ( X , P ) = d X e i X P φ 0 * ( X X 2 ) φ 0 ( X + X 2 ) = e 2 a X d X e i X P Ai ( X X 2 ) Ai ( X + X 2 ) = 2 e 2 a X d X e i 2 X P Ai ( X X ) Ai ( X + X ) .
W 0 ( X , P ) = 2 2 / 3 e 2 a X Ai [ 2 2 / 3 ( X + P 2 ) ] .
W ( X , P , Z ) = W 0 ( X , P ) | X X P Z .
W ( X , Y , P X , P Y , Z ) = 2 2 / 3 e 2 a ( X P X Z ) Ai [ 2 2 / 3 ( X P X Z + P X 2 ) ] × 2 2 / 3 e 2 a ( Y P Y Z ) Ai [ 2 2 / 3 ( Y P Y Z + P Y 2 ) ]
Z W ( X , Y , P X , P Y , Z ) + P X X W ( X , Y , P X , P Y , Z ) + P Y Y W ( X , Y , P X , P Y , Z ) = 0 .

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