Abstract

We reexamine the Gouy phase in ballistic Airy beams (AiBs). A physical interpretation of our analysis is derived in terms of the local phase velocity and the Poynting vector streamlines. Recent experiments employing AiBs are consistent with our results. We provide an approach which potentially applies to any finite-energy paraxial wave field that lacks a beam axis.

© 2012 OSA

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  1. L. G. Gouy, “Sur une propriété nouvelle des ondes lumineuses,” Compt. Rendue Acad. Sci. (Paris)110, 1251–1253 (1890).
  2. S. Feng and H. G. Winful, “Physical origin of the Gouy phase shift,” Opt. Lett.26, 485–487 (2001).
    [CrossRef]
  3. T. D. Visser and E. Wolf, “The origin of the Gouy phase anomaly and its generalization to astigmatic wavefields,” Opt. Commun.283, 3371–3375 (2010).
    [CrossRef]
  4. R. W. Boyd, “Intuitive explanation of the phase anomaly of focused light beams,” J. Opt. Soc. Am.70, 877–880 (1980).
    [CrossRef]
  5. A. E. Siegman, Lasers (University Science Books, Mill Valley, 1986).
  6. G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the phase of few-cycle laser pulses,” Phys. Rev. Lett.91, 253004 (2003).
    [CrossRef]
  7. A. Apolonski, P. Dombi, G. Paulus, M. Kakehata, R. Holzwarth, T. Udem, C. Lemell, K. Torizuka, J. Burgdörfer, T. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett.92, 073902 (2004).
    [CrossRef] [PubMed]
  8. X. Pang, G. Gbur, and T. D. Visser, “The Gouy phase of Airy beams,” Opt. Lett.36, 2492–2494 (2011).
    [CrossRef] [PubMed]
  9. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett.32, 979–981 (2007).
    [CrossRef] [PubMed]
  10. M. A. Bandres, “Accelerating beams,” Opt. Lett.34, 3791–3793 (2009).
    [CrossRef] [PubMed]
  11. Y. Hu, G. Siviloglou, P. Zhang, N. Efremidis, D. Christodoulides, and Z. Chen, “Self-accelerating Airy beams: generation, control, and applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds. (Springer, 2012), vol. 170, pp. 1–46.
  12. J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Natura Photon.2, 675–678 (2008).
    [CrossRef]
  13. P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science324, 229–232 (2009).
    [CrossRef] [PubMed]
  14. A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics4, 103–106 (2010).
    [CrossRef]
  15. L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy Beam generated by in-plane diffraction,” Phys. Rev. Lett107, 1–4 (2011).
    [CrossRef]
  16. A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett107, 116802 (2011).
    [CrossRef] [PubMed]
  17. P. Zhang, S. Wang, Y. Liu, X. Yin, C. Lu, Z. Chen, and X. Zhang, “Plasmonic Airy beams with dynamically controlled trajectories,” Opt. Lett.36, 3191–3193 (2011).
    [CrossRef] [PubMed]
  18. W. Liu, D. N. Neshev, I. V. Shadrivov, A. E. Miroshnichenko, and Y. S. Kivshar, “Plasmonic Airy beam manipulation in linear optical potentials,” Opt. Lett.36, 1164–1166 (2011).
    [CrossRef] [PubMed]
  19. M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge University Press, 1999).
  20. H. I. Sztul and R. R. Alfano, “The Poynting vector and angular momentum of Airy beams,” Opt. Express16, 9411–9416 (2008).
    [CrossRef] [PubMed]
  21. M. A. Porras, C. J. Zapata-Rodríguez, and I. Gonzalo, “Gouy wave modes: undistorted pulse focalization in a dispersive medium,” Opt. Lett.32, 3287–3289 (2007).
    [CrossRef] [PubMed]
  22. C. J. Zapata-Rodríguez and M. A. Porras, “Controlling the carrier-envelope phase of few-cycle focused laser beams with a dispersive beam expander,” Opt. Express16, 22090–22098 (2008).
    [CrossRef] [PubMed]

2011 (5)

2010 (2)

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics4, 103–106 (2010).
[CrossRef]

T. D. Visser and E. Wolf, “The origin of the Gouy phase anomaly and its generalization to astigmatic wavefields,” Opt. Commun.283, 3371–3375 (2010).
[CrossRef]

2009 (2)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science324, 229–232 (2009).
[CrossRef] [PubMed]

M. A. Bandres, “Accelerating beams,” Opt. Lett.34, 3791–3793 (2009).
[CrossRef] [PubMed]

2008 (3)

2007 (2)

2004 (1)

A. Apolonski, P. Dombi, G. Paulus, M. Kakehata, R. Holzwarth, T. Udem, C. Lemell, K. Torizuka, J. Burgdörfer, T. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett.92, 073902 (2004).
[CrossRef] [PubMed]

2003 (1)

G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the phase of few-cycle laser pulses,” Phys. Rev. Lett.91, 253004 (2003).
[CrossRef]

2001 (1)

1980 (1)

1890 (1)

L. G. Gouy, “Sur une propriété nouvelle des ondes lumineuses,” Compt. Rendue Acad. Sci. (Paris)110, 1251–1253 (1890).

Alfano, R. R.

Apolonski, A.

A. Apolonski, P. Dombi, G. Paulus, M. Kakehata, R. Holzwarth, T. Udem, C. Lemell, K. Torizuka, J. Burgdörfer, T. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett.92, 073902 (2004).
[CrossRef] [PubMed]

Baltuska, A.

G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the phase of few-cycle laser pulses,” Phys. Rev. Lett.91, 253004 (2003).
[CrossRef]

Bandres, M. A.

Baumgartl, J.

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

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge University Press, 1999).

Boyd, R. W.

Burgdörfer, J.

A. Apolonski, P. Dombi, G. Paulus, M. Kakehata, R. Holzwarth, T. Udem, C. Lemell, K. Torizuka, J. Burgdörfer, T. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett.92, 073902 (2004).
[CrossRef] [PubMed]

Chen, Z.

P. Zhang, S. Wang, Y. Liu, X. Yin, C. Lu, Z. Chen, and X. Zhang, “Plasmonic Airy beams with dynamically controlled trajectories,” Opt. Lett.36, 3191–3193 (2011).
[CrossRef] [PubMed]

Y. Hu, G. Siviloglou, P. Zhang, N. Efremidis, D. Christodoulides, and Z. Chen, “Self-accelerating Airy beams: generation, control, and applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds. (Springer, 2012), vol. 170, pp. 1–46.

Chong, A.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics4, 103–106 (2010).
[CrossRef]

Christodoulides, D.

Y. Hu, G. Siviloglou, P. Zhang, N. Efremidis, D. Christodoulides, and Z. Chen, “Self-accelerating Airy beams: generation, control, and applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds. (Springer, 2012), vol. 170, pp. 1–46.

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. Photonics4, 103–106 (2010).
[CrossRef]

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science324, 229–232 (2009).
[CrossRef] [PubMed]

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

Dholakia, K.

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

Dombi, P.

A. Apolonski, P. Dombi, G. Paulus, M. Kakehata, R. Holzwarth, T. Udem, C. Lemell, K. Torizuka, J. Burgdörfer, T. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett.92, 073902 (2004).
[CrossRef] [PubMed]

Efremidis, N.

Y. Hu, G. Siviloglou, P. Zhang, N. Efremidis, D. Christodoulides, and Z. Chen, “Self-accelerating Airy beams: generation, control, and applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds. (Springer, 2012), vol. 170, pp. 1–46.

Feng, S.

Gbur, G.

Gonzalo, I.

Goulielmakis, E.

G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the phase of few-cycle laser pulses,” Phys. Rev. Lett.91, 253004 (2003).
[CrossRef]

Gouy, L. G.

L. G. Gouy, “Sur une propriété nouvelle des ondes lumineuses,” Compt. Rendue Acad. Sci. (Paris)110, 1251–1253 (1890).

Hänsch, T.

A. Apolonski, P. Dombi, G. Paulus, M. Kakehata, R. Holzwarth, T. Udem, C. Lemell, K. Torizuka, J. Burgdörfer, T. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett.92, 073902 (2004).
[CrossRef] [PubMed]

Holzwarth, R.

A. Apolonski, P. Dombi, G. Paulus, M. Kakehata, R. Holzwarth, T. Udem, C. Lemell, K. Torizuka, J. Burgdörfer, T. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett.92, 073902 (2004).
[CrossRef] [PubMed]

Hu, Y.

Y. Hu, G. Siviloglou, P. Zhang, N. Efremidis, D. Christodoulides, and Z. Chen, “Self-accelerating Airy beams: generation, control, and applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds. (Springer, 2012), vol. 170, pp. 1–46.

Janunts, N.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett107, 116802 (2011).
[CrossRef] [PubMed]

Kakehata, M.

A. Apolonski, P. Dombi, G. Paulus, M. Kakehata, R. Holzwarth, T. Udem, C. Lemell, K. Torizuka, J. Burgdörfer, T. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett.92, 073902 (2004).
[CrossRef] [PubMed]

Kivshar, Y. S.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett107, 116802 (2011).
[CrossRef] [PubMed]

W. Liu, D. N. Neshev, I. V. Shadrivov, A. E. Miroshnichenko, and Y. S. Kivshar, “Plasmonic Airy beam manipulation in linear optical potentials,” Opt. Lett.36, 1164–1166 (2011).
[CrossRef] [PubMed]

Klein, A. E.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett107, 116802 (2011).
[CrossRef] [PubMed]

Kolesik, M.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science324, 229–232 (2009).
[CrossRef] [PubMed]

Krausz, F.

A. Apolonski, P. Dombi, G. Paulus, M. Kakehata, R. Holzwarth, T. Udem, C. Lemell, K. Torizuka, J. Burgdörfer, T. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett.92, 073902 (2004).
[CrossRef] [PubMed]

G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the phase of few-cycle laser pulses,” Phys. Rev. Lett.91, 253004 (2003).
[CrossRef]

Lemell, C.

A. Apolonski, P. Dombi, G. Paulus, M. Kakehata, R. Holzwarth, T. Udem, C. Lemell, K. Torizuka, J. Burgdörfer, T. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett.92, 073902 (2004).
[CrossRef] [PubMed]

Lezius, M.

G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the phase of few-cycle laser pulses,” Phys. Rev. Lett.91, 253004 (2003).
[CrossRef]

Li, L.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy Beam generated by in-plane diffraction,” Phys. Rev. Lett107, 1–4 (2011).
[CrossRef]

Li, T.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy Beam generated by in-plane diffraction,” Phys. Rev. Lett107, 1–4 (2011).
[CrossRef]

Lindner, F.

G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the phase of few-cycle laser pulses,” Phys. Rev. Lett.91, 253004 (2003).
[CrossRef]

Liu, W.

Liu, Y.

Lu, C.

Mazilu, M.

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

Minovich, A.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett107, 116802 (2011).
[CrossRef] [PubMed]

Miroshnichenko, A. E.

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,” Science324, 229–232 (2009).
[CrossRef] [PubMed]

Neshev, D. N.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett107, 116802 (2011).
[CrossRef] [PubMed]

W. Liu, D. N. Neshev, I. V. Shadrivov, A. E. Miroshnichenko, and Y. S. Kivshar, “Plasmonic Airy beam manipulation in linear optical potentials,” Opt. Lett.36, 1164–1166 (2011).
[CrossRef] [PubMed]

Pang, X.

Paulus, G.

A. Apolonski, P. Dombi, G. Paulus, M. Kakehata, R. Holzwarth, T. Udem, C. Lemell, K. Torizuka, J. Burgdörfer, T. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett.92, 073902 (2004).
[CrossRef] [PubMed]

Paulus, G. G.

G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the phase of few-cycle laser pulses,” Phys. Rev. Lett.91, 253004 (2003).
[CrossRef]

Pertsch, T.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett107, 116802 (2011).
[CrossRef] [PubMed]

Polynkin, P.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science324, 229–232 (2009).
[CrossRef] [PubMed]

Porras, M. A.

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. Photonics4, 103–106 (2010).
[CrossRef]

Shadrivov, I. V.

Siegman, A. E.

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

Siviloglou, G.

Y. Hu, G. Siviloglou, P. Zhang, N. Efremidis, D. Christodoulides, and Z. Chen, “Self-accelerating Airy beams: generation, control, and applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds. (Springer, 2012), vol. 170, pp. 1–46.

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,” Science324, 229–232 (2009).
[CrossRef] [PubMed]

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

Sztul, H. I.

Torizuka, K.

A. Apolonski, P. Dombi, G. Paulus, M. Kakehata, R. Holzwarth, T. Udem, C. Lemell, K. Torizuka, J. Burgdörfer, T. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett.92, 073902 (2004).
[CrossRef] [PubMed]

Udem, T.

A. Apolonski, P. Dombi, G. Paulus, M. Kakehata, R. Holzwarth, T. Udem, C. Lemell, K. Torizuka, J. Burgdörfer, T. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett.92, 073902 (2004).
[CrossRef] [PubMed]

Visser, T. D.

X. Pang, G. Gbur, and T. D. Visser, “The Gouy phase of Airy beams,” Opt. Lett.36, 2492–2494 (2011).
[CrossRef] [PubMed]

T. D. Visser and E. Wolf, “The origin of the Gouy phase anomaly and its generalization to astigmatic wavefields,” Opt. Commun.283, 3371–3375 (2010).
[CrossRef]

Walther, H.

G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the phase of few-cycle laser pulses,” Phys. Rev. Lett.91, 253004 (2003).
[CrossRef]

Wang, S.

Wang, S. M.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy Beam generated by in-plane diffraction,” Phys. Rev. Lett107, 1–4 (2011).
[CrossRef]

Winful, H. G.

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. Photonics4, 103–106 (2010).
[CrossRef]

Wolf, E.

T. D. Visser and E. Wolf, “The origin of the Gouy phase anomaly and its generalization to astigmatic wavefields,” Opt. Commun.283, 3371–3375 (2010).
[CrossRef]

M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge University Press, 1999).

Yin, X.

Zapata-Rodríguez, C. J.

Zhang, C.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy Beam generated by in-plane diffraction,” Phys. Rev. Lett107, 1–4 (2011).
[CrossRef]

Zhang, P.

P. Zhang, S. Wang, Y. Liu, X. Yin, C. Lu, Z. Chen, and X. Zhang, “Plasmonic Airy beams with dynamically controlled trajectories,” Opt. Lett.36, 3191–3193 (2011).
[CrossRef] [PubMed]

Y. Hu, G. Siviloglou, P. Zhang, N. Efremidis, D. Christodoulides, and Z. Chen, “Self-accelerating Airy beams: generation, control, and applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds. (Springer, 2012), vol. 170, pp. 1–46.

Zhang, X.

Zhu, S. N.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy Beam generated by in-plane diffraction,” Phys. Rev. Lett107, 1–4 (2011).
[CrossRef]

Compt. Rendue Acad. Sci. (Paris) (1)

L. G. Gouy, “Sur une propriété nouvelle des ondes lumineuses,” Compt. Rendue Acad. Sci. (Paris)110, 1251–1253 (1890).

J. Opt. Soc. Am. (1)

Nat. Photonics (1)

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics4, 103–106 (2010).
[CrossRef]

Natura Photon. (1)

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

Opt. Commun. (1)

T. D. Visser and E. Wolf, “The origin of the Gouy phase anomaly and its generalization to astigmatic wavefields,” Opt. Commun.283, 3371–3375 (2010).
[CrossRef]

Opt. Express (2)

Opt. Lett. (7)

Phys. Rev. Lett (2)

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy Beam generated by in-plane diffraction,” Phys. Rev. Lett107, 1–4 (2011).
[CrossRef]

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett107, 116802 (2011).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the phase of few-cycle laser pulses,” Phys. Rev. Lett.91, 253004 (2003).
[CrossRef]

A. Apolonski, P. Dombi, G. Paulus, M. Kakehata, R. Holzwarth, T. Udem, C. Lemell, K. Torizuka, J. Burgdörfer, T. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett.92, 073902 (2004).
[CrossRef] [PubMed]

Science (1)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science324, 229–232 (2009).
[CrossRef] [PubMed]

Other (3)

M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge University Press, 1999).

Y. Hu, G. Siviloglou, P. Zhang, N. Efremidis, D. Christodoulides, and Z. Chen, “Self-accelerating Airy beams: generation, control, and applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds. (Springer, 2012), vol. 170, pp. 1–46.

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

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Figures (3)

Fig. 1
Fig. 1

(a) |u| and (c) ϕ for an AiB with a = 0.1. The parabolic curves (4) are drawn in the near field (b) and (d) in dashed lines. In the far field, the numbered straight trajectories of light rays satisfy Eq. (3).

Fig. 2
Fig. 2

(a) GP for k = {0, ±0.41, ±1.00, ±1.52}. The curves are displaced by π/2 from one to another, with increasing k down upward. The numbers code agrees with that applied in Fig. 1. (b) Geometrical interpretation of the GP in terms of the local wave vector k⃗PW of a plane wave and that k⃗i of a paraxial beam.

Fig. 3
Fig. 3

Spatial distribution of κ and several PSLs for the AiB of Fig. 1. (c) Plots of κ over the numbered contours also representing asymptotes of the PSLs.

Equations (7)

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u ( s , ζ ) = A i ( s ζ 2 / 4 + i a ζ ) exp ( a s a ζ 2 / 2 ) × exp ( i s ζ / 2 + i a 2 ζ / 2 i ζ 3 / 12 ) ,
u ˜ ( k ) = exp ( a k 2 + a 3 / 3 i a 2 k + i k 3 / 3 ) .
k 2 k ζ + s a 2 = 0 .
s = a 2 ( 3 π m / 2 ) 2 / 3 + ( ζ / 2 ) 2 , for m 0 .
φ G ( ζ ) = C Δ k d r ,
d s d ζ = ζ 2 + Im A i ( s ζ 2 / 4 + i a ζ ) A i ( s ζ 2 / 4 + i a ζ ) ,
κ = ζ ϕ + ( s ϕ ) 2 / 2 .

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