Abstract

We investigate the acceleration dynamics of quasi-diffraction-free Airy beams in both one- and two-dimensional configurations. We show that this class of finite energy waves can retain their intensity features over several diffraction lengths. The possibility of other physical realizations involving spatiotemporal Airy wave packets is also considered.

© 2007 Optical Society of America

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References

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  1. J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
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  2. J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
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  4. M. A. Bandres, J. C. Gutiérrez-Vega, and S. Chávez-Cerda, Opt. Lett. 29, 44 (2004).
    [CrossRef] [PubMed]
  5. J. Lu and J. F. Greenleaf, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19 (1992).
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  6. D. N. Christodoulides, N. K. Efremidis, P. Di Trapani, and B. A. Malomed, Opt. Lett. 29, 1446 (2004).
    [CrossRef] [PubMed]
  7. O. Manela, M. Segev, and D. N. Christodoulides, Opt. Lett. 30, 2611 (2005).
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  8. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005).
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    [CrossRef]
  10. M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
    [CrossRef]
  11. D. M. Greenberger, Am. J. Phys. 48, 256 (1980).
    [CrossRef]
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    [CrossRef] [PubMed]
  14. M. Miyagi and S. Nishida, Appl. Opt. 18, 678 (1979).
    [CrossRef] [PubMed]
  15. A. M. Weiner, Rev. Sci. Instrum. 71, 1929 (2000).
    [CrossRef]

2005

2004

2000

1996

1992

J. Lu and J. F. Greenleaf, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19 (1992).
[CrossRef] [PubMed]

1987

J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

1980

D. M. Greenberger, Am. J. Phys. 48, 256 (1980).
[CrossRef]

1979

M. Miyagi and S. Nishida, Appl. Opt. 18, 678 (1979).
[CrossRef] [PubMed]

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1972).

Balazs, N. L.

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Bandres, M. A.

Berry, M. V.

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Chávez-Cerda, S.

Christodoulides, D. N.

Coskun, T. H.

Di Trapani, P.

Durnin, J.

J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Efremidis, N. K.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005).

Gori, F.

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

Greenberger, D. M.

D. M. Greenberger, Am. J. Phys. 48, 256 (1980).
[CrossRef]

Greenleaf, J. F.

J. Lu and J. F. Greenleaf, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19 (1992).
[CrossRef] [PubMed]

Guattari, G.

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

Gutiérrez-Vega, J. C.

Iturbe-Castillo, M. D.

Lu, J.

J. Lu and J. F. Greenleaf, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19 (1992).
[CrossRef] [PubMed]

Malomed, B. A.

Manela, O.

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Miyagi, M.

Nishida, S.

Padovani, C.

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

Segev, M.

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1972).

Weiner, A. M.

A. M. Weiner, Rev. Sci. Instrum. 71, 1929 (2000).
[CrossRef]

Am. J. Phys.

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

D. M. Greenberger, Am. J. Phys. 48, 256 (1980).
[CrossRef]

Appl. Opt.

IEEE Trans. Ultrason. Ferroelectr. Freq. Control

J. Lu and J. F. Greenleaf, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19 (1992).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

Opt. Commun.

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Rev. Sci. Instrum.

A. M. Weiner, Rev. Sci. Instrum. 71, 1929 (2000).
[CrossRef]

Other

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1972).

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005).

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Figures (4)

Fig. 1
Fig. 1

(a) Normalized field profile and (b) normalized intensity profile of a finite energy Airy beam when a = 0.1 .

Fig. 2
Fig. 2

(a) Propagation dynamics of a finite energy Airy beam as a function of distance. (b) Cross-sections of the normalized beam intensity at (i) z = 0 cm , (ii) 31.4 cm , (iii) 62.8 cm , (iv) 94.3 cm , and (v) 125.7 cm .

Fig. 3
Fig. 3

Two-dimensional finite energy Airy beam (a) at the input z = 0 cm and (b) after propagating z = 50 cm .

Fig. 4
Fig. 4

Isosurface intensity contour plot for a spatiotemporal Airy–Gauss–Bessel wave packet (with a = 0.15 , w 0 = 9 ) (a) at the input Z = 0 and (b) after a normalized propagation distance of Z = 3 . The arrow depicts the direction of acceleration.

Equations (6)

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i ϕ ξ + 1 2 2 ϕ s 2 = 0 .
ϕ ( s , ξ = 0 ) = A i ( s ) exp ( a s ) ,
Φ 0 ( k ) = exp ( a k 2 ) exp ( i 3 ( k 3 3 a 2 k i a 3 ) ) .
d s ϕ ( s , ξ = 0 ) 2 = 1 8 π a exp ( 2 a 3 3 ) .
ϕ ( ξ , s ) = A i [ s ( ξ 2 ) 2 + i a ξ ] exp ( a s ( a ξ 2 2 ) i ( ξ 3 12 ) + i ( a 2 ξ 2 ) + i ( s ξ 2 ) ) .
i ψ Z + 1 2 ( 2 ψ X 2 + 2 ψ Y 2 + 2 ψ T 2 ) = 0 ,

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