Abstract

We numerically investigate the possibility to generate freely accelerating or decelerating pulses. In particular it is shown that acceleration along the propagation direction z may be obtained by a purely spatial modulation of an input Gaussian pulse in the form of finite-energy Bessel pulses with a cone angle that varies along the radial coordinate. We discuss simple practical implementations of such accelerating Bessel beams.

© 2008 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. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, "Ballistic dynamics of airy beams," Opt. Lett. 33, 207-209 (2008).
    [CrossRef] [PubMed]
  3. G. A. Siviloglou and D. N. Christodoulides, "Accelerating finite energy airy beams," Opt. Lett. 32, 979-981 (2007).
    [CrossRef] [PubMed]
  4. P. Saari, "Laterally accelerating airy pulses," Opt. Express 16, 10303-10308 (2008)
    [CrossRef] [PubMed]
  5. J. Durnin, J. Miceli, and J. H. Eberly,"Diffraction-free beams," Phys. Rev. Lett. 58, 1499 (1987).
    [CrossRef] [PubMed]
  6. A. Averchi, D. Faccio, R. Berlasso, M. Kolesik, J. V. Moloney, A. Couairon, and P. Di Trapani, "Phase matching with pulsed bessel beams for high-order harmonic generation," Phys. Rev. A 77, 021802 (2008).
  7. V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature (London) 419, 145-147 (2002).
    [CrossRef]
  8. D. McGloin and K. Dholakia, "Bessel beams: diffraction in a new light," Contemp. Phys. 46, 15-28 (2005).
    [CrossRef]
  9. P. Saari and K. Reivelt, "Evidence of X-shaped propagation-invariant localized light waves," Phys. Rev. Lett. 79, 4135 (1997)
    [CrossRef]
  10. H. Sonajalg, M. Ratsep and P. Saari, "Demonstration of the Bessel-X pulse propagating with strong lateral and longitudinal localization in a dispersive medium," Opt. Lett. 22, 310-312 (1997)
    [CrossRef] [PubMed]
  11. Z. Liu and D. Fan, "Propagation of pulsed zeroth-order Bessel beams, " J. Mod. Opt. 45, 17-22 (1998).
    [CrossRef]
  12. S. Longhi, D. Janner and P. Laporta, "Propagating pulsed Bessel beams in periodic media," J. Opt. B 6, 477-481 (2004)
  13. C. J. Zapata-Rodriguez and M. A. Porras, "X-wave bullets with negative group velocity in vacuum," Opt. Lett. 31, 3532-3534 (2006).
    [CrossRef] [PubMed]
  14. M. Guizar-Sicairos and J. C. Gutierrez-Vega, "Computation of quasi-discrete hankel transforms of integer order for propagating optical wave fields," J. Opt. Soc. Am. A 21, 53-58 (2004).
    [CrossRef]
  15. M. Kempe and W. Rudolph, "Femtosecond pulses in the focal region of lenses," Phys. Rev. A 48, 4721 (1993).
  16. Z. Horvath and Z. Bor, "Diffraction of short pulses with boundary diffraction wave theory," Phys. Rev. E 63, 026601 (2001).
  17. U. Fuchs, U. D. Zeitner, and A. Tunnermann, "Ultra-short pulse propagation in complex optical systems," Opt. Express 13, 3852-3861 (2005).
    [CrossRef] [PubMed]
  18. D. Fischer, C. Harkrider, and D. Moore, "Design and manufacture of a gradient-index axicon," Appl. Opt. 39, 2687-2694 (2000).
    [CrossRef]
  19. M. Porras and P. Di Trapani, "Localized and stationary light wave modes in dispersive media," Phys. Rev. E 69, 066606 (2004).
  20. H. Sonajalg and P. Saari, "Suppression of temporal spread of ultrashort pulses in dispersive media by bessel beam generators," Opt. Lett. 21, 1162-1164 (1996).
    [CrossRef] [PubMed]

2008 (3)

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, "Ballistic dynamics of airy beams," Opt. Lett. 33, 207-209 (2008).
[CrossRef] [PubMed]

P. Saari, "Laterally accelerating airy pulses," Opt. Express 16, 10303-10308 (2008)
[CrossRef] [PubMed]

A. Averchi, D. Faccio, R. Berlasso, M. Kolesik, J. V. Moloney, A. Couairon, and P. Di Trapani, "Phase matching with pulsed bessel beams for high-order harmonic generation," Phys. Rev. A 77, 021802 (2008).

2007 (2)

G. A. Siviloglou and D. N. Christodoulides, "Accelerating finite energy airy beams," Opt. Lett. 32, 979-981 (2007).
[CrossRef] [PubMed]

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

2006 (1)

2005 (2)

2004 (3)

S. Longhi, D. Janner and P. Laporta, "Propagating pulsed Bessel beams in periodic media," J. Opt. B 6, 477-481 (2004)

M. Guizar-Sicairos and J. C. Gutierrez-Vega, "Computation of quasi-discrete hankel transforms of integer order for propagating optical wave fields," J. Opt. Soc. Am. A 21, 53-58 (2004).
[CrossRef]

M. Porras and P. Di Trapani, "Localized and stationary light wave modes in dispersive media," Phys. Rev. E 69, 066606 (2004).

2002 (1)

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature (London) 419, 145-147 (2002).
[CrossRef]

2001 (1)

Z. Horvath and Z. Bor, "Diffraction of short pulses with boundary diffraction wave theory," Phys. Rev. E 63, 026601 (2001).

2000 (1)

1998 (1)

Z. Liu and D. Fan, "Propagation of pulsed zeroth-order Bessel beams, " J. Mod. Opt. 45, 17-22 (1998).
[CrossRef]

1997 (2)

1996 (1)

1993 (1)

M. Kempe and W. Rudolph, "Femtosecond pulses in the focal region of lenses," Phys. Rev. A 48, 4721 (1993).

1987 (1)

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

Averchi, A.

A. Averchi, D. Faccio, R. Berlasso, M. Kolesik, J. V. Moloney, A. Couairon, and P. Di Trapani, "Phase matching with pulsed bessel beams for high-order harmonic generation," Phys. Rev. A 77, 021802 (2008).

Berlasso, R.

A. Averchi, D. Faccio, R. Berlasso, M. Kolesik, J. V. Moloney, A. Couairon, and P. Di Trapani, "Phase matching with pulsed bessel beams for high-order harmonic generation," Phys. Rev. A 77, 021802 (2008).

Bor, Z.

Z. Horvath and Z. Bor, "Diffraction of short pulses with boundary diffraction wave theory," Phys. Rev. E 63, 026601 (2001).

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, "Ballistic dynamics of airy beams," Opt. Lett. 33, 207-209 (2008).
[CrossRef] [PubMed]

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

Christodoulides, D. N.

Couairon, A.

A. Averchi, D. Faccio, R. Berlasso, M. Kolesik, J. V. Moloney, A. Couairon, and P. Di Trapani, "Phase matching with pulsed bessel beams for high-order harmonic generation," Phys. Rev. A 77, 021802 (2008).

Dholakia, K.

D. McGloin and K. Dholakia, "Bessel beams: diffraction in a new light," Contemp. Phys. 46, 15-28 (2005).
[CrossRef]

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature (London) 419, 145-147 (2002).
[CrossRef]

Di Trapani, P.

A. Averchi, D. Faccio, R. Berlasso, M. Kolesik, J. V. Moloney, A. Couairon, and P. Di Trapani, "Phase matching with pulsed bessel beams for high-order harmonic generation," Phys. Rev. A 77, 021802 (2008).

M. Porras and P. Di Trapani, "Localized and stationary light wave modes in dispersive media," Phys. Rev. E 69, 066606 (2004).

Dogariu, A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, "Ballistic dynamics of airy beams," Opt. Lett. 33, 207-209 (2008).
[CrossRef] [PubMed]

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

Durnin, J.

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

Eberly, J. H.

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

Faccio, D.

A. Averchi, D. Faccio, R. Berlasso, M. Kolesik, J. V. Moloney, A. Couairon, and P. Di Trapani, "Phase matching with pulsed bessel beams for high-order harmonic generation," Phys. Rev. A 77, 021802 (2008).

Fan, D.

Z. Liu and D. Fan, "Propagation of pulsed zeroth-order Bessel beams, " J. Mod. Opt. 45, 17-22 (1998).
[CrossRef]

Fischer, D.

Fuchs, U.

Garces-Chavez, V.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature (London) 419, 145-147 (2002).
[CrossRef]

Guizar-Sicairos, M.

Guti’errez-Vega, J. C.

Harkrider, C.

Horvath, Z.

Z. Horvath and Z. Bor, "Diffraction of short pulses with boundary diffraction wave theory," Phys. Rev. E 63, 026601 (2001).

Janner, D.

S. Longhi, D. Janner and P. Laporta, "Propagating pulsed Bessel beams in periodic media," J. Opt. B 6, 477-481 (2004)

Kempe, M.

M. Kempe and W. Rudolph, "Femtosecond pulses in the focal region of lenses," Phys. Rev. A 48, 4721 (1993).

Kolesik, M.

A. Averchi, D. Faccio, R. Berlasso, M. Kolesik, J. V. Moloney, A. Couairon, and P. Di Trapani, "Phase matching with pulsed bessel beams for high-order harmonic generation," Phys. Rev. A 77, 021802 (2008).

Laporta, P.

S. Longhi, D. Janner and P. Laporta, "Propagating pulsed Bessel beams in periodic media," J. Opt. B 6, 477-481 (2004)

Liu, Z.

Z. Liu and D. Fan, "Propagation of pulsed zeroth-order Bessel beams, " J. Mod. Opt. 45, 17-22 (1998).
[CrossRef]

Longhi, S.

S. Longhi, D. Janner and P. Laporta, "Propagating pulsed Bessel beams in periodic media," J. Opt. B 6, 477-481 (2004)

McGloin, D.

D. McGloin and K. Dholakia, "Bessel beams: diffraction in a new light," Contemp. Phys. 46, 15-28 (2005).
[CrossRef]

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature (London) 419, 145-147 (2002).
[CrossRef]

Melville, H.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature (London) 419, 145-147 (2002).
[CrossRef]

Miceli, J.

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

Moloney, J. V.

A. Averchi, D. Faccio, R. Berlasso, M. Kolesik, J. V. Moloney, A. Couairon, and P. Di Trapani, "Phase matching with pulsed bessel beams for high-order harmonic generation," Phys. Rev. A 77, 021802 (2008).

Moore, D.

Porras, M.

M. Porras and P. Di Trapani, "Localized and stationary light wave modes in dispersive media," Phys. Rev. E 69, 066606 (2004).

Porras, M. A.

Reivelt, K.

P. Saari and K. Reivelt, "Evidence of X-shaped propagation-invariant localized light waves," Phys. Rev. Lett. 79, 4135 (1997)
[CrossRef]

Rudolph, W.

M. Kempe and W. Rudolph, "Femtosecond pulses in the focal region of lenses," Phys. Rev. A 48, 4721 (1993).

Saari, P.

Sibbett, W.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature (London) 419, 145-147 (2002).
[CrossRef]

Siviloglou, G. A.

Sonajalg, H.

Tunnermann, A.

Zapata-Rodriguez, C. J.

Zeitner, U. D.

Appl. Opt. (1)

Contemp. Phys. (1)

D. McGloin and K. Dholakia, "Bessel beams: diffraction in a new light," Contemp. Phys. 46, 15-28 (2005).
[CrossRef]

J. Mod. Opt. (1)

Z. Liu and D. Fan, "Propagation of pulsed zeroth-order Bessel beams, " J. Mod. Opt. 45, 17-22 (1998).
[CrossRef]

J. Opt. B (1)

S. Longhi, D. Janner and P. Laporta, "Propagating pulsed Bessel beams in periodic media," J. Opt. B 6, 477-481 (2004)

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

Nature (London) (1)

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature (London) 419, 145-147 (2002).
[CrossRef]

Opt. Express (2)

Opt. Lett. (5)

Phys. Rev. A (2)

M. Kempe and W. Rudolph, "Femtosecond pulses in the focal region of lenses," Phys. Rev. A 48, 4721 (1993).

A. Averchi, D. Faccio, R. Berlasso, M. Kolesik, J. V. Moloney, A. Couairon, and P. Di Trapani, "Phase matching with pulsed bessel beams for high-order harmonic generation," Phys. Rev. A 77, 021802 (2008).

Phys. Rev. E (2)

Z. Horvath and Z. Bor, "Diffraction of short pulses with boundary diffraction wave theory," Phys. Rev. E 63, 026601 (2001).

M. Porras and P. Di Trapani, "Localized and stationary light wave modes in dispersive media," Phys. Rev. E 69, 066606 (2004).

Phys. Rev. Lett. (3)

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

P. Saari and K. Reivelt, "Evidence of X-shaped propagation-invariant localized light waves," Phys. Rev. Lett. 79, 4135 (1997)
[CrossRef]

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

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Figures (2)

Fig. 1.
Fig. 1.

(a) Ray-tracing of an annular-shaped input beam through a spherical lens. (b) On-axis group velocity of the pulse as a function of propagation distance for the propagation shown in (a). (c) Logarithmic spatio-temporal intensity profile evaluated at 3.2 cm from the lens output plane. The central wavelength of the pulse is 825 nm.

Fig. 2.
Fig. 2.

(a) Ray-tracing for the nonlinear axicon described in the text. (b) Group velocity of the pulse as a function of propagation distance for the linear acceleration condition (solid line) and for quadratic positive and negative correction (dashed green and red curve respectively). (c) Logarithmic spatio-temporal intensity profile evaluated at 1.5 cm from the axicon tip. The central wavelength of the pulse is 1.25 µm.

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