Abstract

A new kind of Airy-related beam has been obtained from Airy transform for flat-topped Gaussian beams. It is proved in this paper that this beam also possesses an “Airy” profile, quasi-diffraction-free character and transverse accelerating character as the Airy beam generated from the fundamental Gaussian beams. The propagation dynamics of this beam can be modulated by varying N, i.e., the beam order of the flat-topped Gaussian beam.

© 2012 Optical Society of America

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  1. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
    [CrossRef]
  2. J. Kasparian and J. P. Wolf, “Laser beams take a curve,” Science 324, 194–195 (2009).
    [CrossRef]
  3. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33, 207–209 (2008).
    [CrossRef]
  4. J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16, 12880–12891 (2008).
    [CrossRef]
  5. J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photon. 2, 675–678 (2008).
    [CrossRef]
  6. P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
    [CrossRef]
  7. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32, 979–981 (2007).
    [CrossRef]
  8. J. E. Morris, M. Mazilu, J. Baumgartl, T. Cižmár, and K. Dholakia, “Propagation characteristics of Airy beams: dependence upon spatial coherence and wavelength,” Opt. Express 17, 13236–13245 (2009).
    [CrossRef]
  9. S. Barwick, “Reduced side-lobe Airy beams,” Opt. Lett. 36, 2827–2829 (2011).
    [CrossRef]
  10. M. I. Carvalho and M. Facão, “Propagation of Airy-related beams,” Opt. Express 18, 21938–21949 (2010).
    [CrossRef]
  11. A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photon. 4, 103–106 (2010).
    [CrossRef]
  12. N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35, 4045–4047 (2010).
    [CrossRef]
  13. H. T. Dai, Y. J. Liu, D. Luo, and X. W. Sun, “Propagation dynamics of an optical vortex imposed on an Airy beam,” Opt. Lett. 35, 4075–4077 (2010).
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  14. M. A. Bandres and J. C. Gutiérrez-Vega, “Airy-Gauss beams and their transformation by paraxial optical systems,” Opt. Express 15, 16719–16728 (2007).
    [CrossRef]
  15. D. V. Widder, “Airy transform,” Am. Math. Mon. 86, 271–277 (1979).
    [CrossRef]
  16. O. Vallée and M. Soares, Airy Functions and Applications to Physics (Imperial College, 2004).
  17. S. A. Collins, “Lens-system diffraction integral written in terms of matrix optics,” J. Opt. Soc. Am. 60, 1168–1177(1970).
    [CrossRef]
  18. Y. J. Li, “New expressions for flat-topped light beams,” Opt. Commun. 206, 225–234 (2002).
    [CrossRef]
  19. A. E. Siegman, Lasers (University Science Books, 1986).

2011

2010

2009

J. Kasparian and J. P. Wolf, “Laser beams take a curve,” Science 324, 194–195 (2009).
[CrossRef]

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
[CrossRef]

J. E. Morris, M. Mazilu, J. Baumgartl, T. Cižmár, and K. Dholakia, “Propagation characteristics of Airy beams: dependence upon spatial coherence and wavelength,” Opt. Express 17, 13236–13245 (2009).
[CrossRef]

2008

2007

2002

Y. J. Li, “New expressions for flat-topped light beams,” Opt. Commun. 206, 225–234 (2002).
[CrossRef]

1979

D. V. Widder, “Airy transform,” Am. Math. Mon. 86, 271–277 (1979).
[CrossRef]

1970

Bandres, M. A.

Barwick, S.

Baumgartl, J.

Broky, J.

Carvalho, M. I.

Chong, A.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photon. 4, 103–106 (2010).
[CrossRef]

Christodoulides, D. N.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photon. 4, 103–106 (2010).
[CrossRef]

N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35, 4045–4047 (2010).
[CrossRef]

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
[CrossRef]

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16, 12880–12891 (2008).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33, 207–209 (2008).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32, 979–981 (2007).
[CrossRef]

Cižmár, T.

Collins, S. A.

Dai, H. T.

Dholakia, K.

Dogariu, A.

Efremidis, N. K.

Facão, M.

Gutiérrez-Vega, J. C.

Kasparian, J.

J. Kasparian and J. P. Wolf, “Laser beams take a curve,” Science 324, 194–195 (2009).
[CrossRef]

Kolesik, M.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
[CrossRef]

Li, Y. J.

Y. J. Li, “New expressions for flat-topped light beams,” Opt. Commun. 206, 225–234 (2002).
[CrossRef]

Liu, Y. J.

Luo, D.

Mazilu, M.

Moloney, J. V.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
[CrossRef]

Morris, J. E.

Polynkin, P.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
[CrossRef]

Renninger, W. H.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photon. 4, 103–106 (2010).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, 1986).

Siviloglou, G. A.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
[CrossRef]

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16, 12880–12891 (2008).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33, 207–209 (2008).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32, 979–981 (2007).
[CrossRef]

Soares, M.

O. Vallée and M. Soares, Airy Functions and Applications to Physics (Imperial College, 2004).

Sun, X. W.

Vallée, O.

O. Vallée and M. Soares, Airy Functions and Applications to Physics (Imperial College, 2004).

Widder, D. V.

D. V. Widder, “Airy transform,” Am. Math. Mon. 86, 271–277 (1979).
[CrossRef]

Wise, F. W.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photon. 4, 103–106 (2010).
[CrossRef]

Wolf, J. P.

J. Kasparian and J. P. Wolf, “Laser beams take a curve,” Science 324, 194–195 (2009).
[CrossRef]

Am. Math. Mon.

D. V. Widder, “Airy transform,” Am. Math. Mon. 86, 271–277 (1979).
[CrossRef]

J. Opt. Soc. Am.

Nat. Photon.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photon. 4, 103–106 (2010).
[CrossRef]

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photon. 2, 675–678 (2008).
[CrossRef]

Opt. Commun.

Y. J. Li, “New expressions for flat-topped light beams,” Opt. Commun. 206, 225–234 (2002).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Science

J. Kasparian and J. P. Wolf, “Laser beams take a curve,” Science 324, 194–195 (2009).
[CrossRef]

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324, 229–232 (2009).
[CrossRef]

Other

A. E. Siegman, Lasers (University Science Books, 1986).

O. Vallée and M. Soares, Airy Functions and Applications to Physics (Imperial College, 2004).

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Figures (5)

Fig. 1.
Fig. 1.

Optical setup for Airy transform. f is the focal length of the lens. The SLM imposes the cubic phase modulation on the light beams.

Fig. 2.
Fig. 2.

Intensity cross sections of the input flat-topped Gaussian beams with different N and output Airy-related beams at different positions: (a) input beams with different power; (b) z=0; (c) z=0.2m; (d) z=0.4m; (e) z=0.6m; (f) z=1.6m; (g) z=1.8m; and (h) z=2.0m; The insets in (f)–(h) show the subsidiary peaks.

Fig. 3.
Fig. 3.

Changes of (a) peak intensity, (b) peak location, and (c) FWHM of the first lobe of the Airy-related beam generated from flat-topped Gaussian beam at z=0 with N.

Fig. 4.
Fig. 4.

Propagation dynamics of the Airy-related beams generated from the flat-topped Gaussian beams with (a) N=1, (b) N=4, and (c) N=10.

Fig. 5.
Fig. 5.

Trajectories of the first lobes of the Airy-related beam with different N.

Equations (9)

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g(x)=Aα(f(x))=πeα6/192|α|exp[14α3(x+116α3)]Ai[1α(x+116α3)].
Φ(x1,y1)=α3kx3+β3ky33(4kf+π),
U1(x1,y1)=e2ikfiλfU0(x0,y0)exp[ik(x1x0+y1y0)f]dx0dy0eiΦ(x1,y1),
UA(xA,yA)=e2ikfiλfU1(x1,y1)exp[ik(xAx1+yAy1)f]dx1dy1.
UA(xA,yA)=1|αβ|U0(x0,y0)Ai(xAx0α)Ai(yAy0β)dx0dy0.
E(x)=A0n=1N(1)n1N(Nn)exp(nx2w02),
E(x)=2πA0n=1N(1)n1anN(Nn)exp(2an33)Ai(xα+an2)exp(anxα),
Ep(xp,z)=ik2πzexp[ik2z(xp22xpxq+xq2)]Eq(xq)dxq,
Ep(x,z)=2A0n=1N(1)n1πanN(Nn)Ai[r(x)αξ24+ianξ]exp[anr(x)α+iξr(x)2αiξ312anξ22+ian2ξ2an33],

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