Abstract

By making use of the recently found expression for finite-energy 2D paraxial Airy beam, three types of ultrashort Airy pulses have been derived and numerically simulated. They differ in frequency dependences of their parameters and exhibit different spatial profiles and propagation features.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. A. Siviloglou and D. N. Christodoulides, "Accelerating finite energy Airy beams," Opt. Lett. 32, 979-981 (2007).
    [CrossRef] [PubMed]
  2. I. M. Besieris and A. M. Shaarawi, "A note on an accelerating finite energy Airy beam," Opt. Lett. 32, 2447-2449 (2007).
    [CrossRef] [PubMed]
  3. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, "Observation of accelerating Airy beams," Phys. Rev. Lett. 99, 213901 (2007).
    [CrossRef]
  4. M. V. Berry and N. L. Balazs, "Nonspreading wave packets," Am. J. Phys. 47, 264-267 (1979).
    [CrossRef]
  5. H. E. Hernandez-Figueroa, M. Zamboni-Rached, and E.  Recami, eds., Localized Waves: Theory and Applications, (J. Wiley, New York, 2008).
    [CrossRef]
  6. P. Saari and K. Reivelt, "Generation and classification of localized waves by Lorentz transformations in Fourier space," Phys. Rev. E 69, 036612 (2004).
    [CrossRef]
  7. Z. L. Horváth and Zs. Bor, "Reshaping of femtosecond pulses by the Gouy phase shift," Phys. Rev. E 60, 2337-2345 (1999).
    [CrossRef]
  8. S. Feng and H. G. Winful, "Spatiotemporal structure of isodiffracting ultrashort electromagnetic pulses," Phys. Rev. E 61, 862-873 (2000).
    [CrossRef]
  9. P. Saari, "Evolution of subcycle pulses in nonparaxial Gaussian beams," Opt. Express 8, 590-598 (2001).
    [CrossRef] [PubMed]
  10. P. Saari, "Relativistic Doppler effect, aberration and Gouy effect on localized waves," Special Issue on "Anomalies and Strange Behavior in Physics: Challenging the Conventional," Atti della Fondazione Giorgio Ronchi 58, 729-754 (2003).
  11. C. J. R. Sheppard, "Bessel pulse beams and focus wave modes," J. Opt. Soc. Am. A 18, 2594-2600 (2001).
    [CrossRef]
  12. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, "Ballistic dynamics of Airy beams," Opt. Lett. 33, 207-209 (2008).
    [CrossRef] [PubMed]
  13. M. A. Porras, "Pulsed light beams in vacuum with superluminal and negative group velocities," Phys. Rev. E 67, 066604 (2003).
    [CrossRef]
  14. A. Sezginer, "A general formulation of focus wave modes," J. Appl. Phys. 57, 678-683 (1985).
    [CrossRef]
  15. I. M. Besieris, A. M. Shaarawi, and R.W. Ziolkowski, "Nondispersive accelerating wave packets," Am. J. Phys. 62, 519-521 (1994).
    [CrossRef]

2008

2007

2004

P. Saari and K. Reivelt, "Generation and classification of localized waves by Lorentz transformations in Fourier space," Phys. Rev. E 69, 036612 (2004).
[CrossRef]

2003

P. Saari, "Relativistic Doppler effect, aberration and Gouy effect on localized waves," Special Issue on "Anomalies and Strange Behavior in Physics: Challenging the Conventional," Atti della Fondazione Giorgio Ronchi 58, 729-754 (2003).

M. A. Porras, "Pulsed light beams in vacuum with superluminal and negative group velocities," Phys. Rev. E 67, 066604 (2003).
[CrossRef]

2001

2000

S. Feng and H. G. Winful, "Spatiotemporal structure of isodiffracting ultrashort electromagnetic pulses," Phys. Rev. E 61, 862-873 (2000).
[CrossRef]

1999

Z. L. Horváth and Zs. Bor, "Reshaping of femtosecond pulses by the Gouy phase shift," Phys. Rev. E 60, 2337-2345 (1999).
[CrossRef]

1994

I. M. Besieris, A. M. Shaarawi, and R.W. Ziolkowski, "Nondispersive accelerating wave packets," Am. J. Phys. 62, 519-521 (1994).
[CrossRef]

1985

A. Sezginer, "A general formulation of focus wave modes," J. Appl. Phys. 57, 678-683 (1985).
[CrossRef]

1979

M. V. Berry and N. L. Balazs, "Nonspreading wave packets," Am. J. Phys. 47, 264-267 (1979).
[CrossRef]

Balazs, N. L.

M. V. Berry and N. L. Balazs, "Nonspreading wave packets," Am. J. Phys. 47, 264-267 (1979).
[CrossRef]

Berry, M. V.

M. V. Berry and N. L. Balazs, "Nonspreading wave packets," Am. J. Phys. 47, 264-267 (1979).
[CrossRef]

Besieris, I. M.

I. M. Besieris and A. M. Shaarawi, "A note on an accelerating finite energy Airy beam," Opt. Lett. 32, 2447-2449 (2007).
[CrossRef] [PubMed]

I. M. Besieris, A. M. Shaarawi, and R.W. Ziolkowski, "Nondispersive accelerating wave packets," Am. J. Phys. 62, 519-521 (1994).
[CrossRef]

Bor, Zs.

Z. L. Horváth and Zs. Bor, "Reshaping of femtosecond pulses by the Gouy phase shift," Phys. Rev. E 60, 2337-2345 (1999).
[CrossRef]

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.

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]

Feng, S.

S. Feng and H. G. Winful, "Spatiotemporal structure of isodiffracting ultrashort electromagnetic pulses," Phys. Rev. E 61, 862-873 (2000).
[CrossRef]

Horváth, Z. L.

Z. L. Horváth and Zs. Bor, "Reshaping of femtosecond pulses by the Gouy phase shift," Phys. Rev. E 60, 2337-2345 (1999).
[CrossRef]

Porras, M. A.

M. A. Porras, "Pulsed light beams in vacuum with superluminal and negative group velocities," Phys. Rev. E 67, 066604 (2003).
[CrossRef]

Reivelt, K.

P. Saari and K. Reivelt, "Generation and classification of localized waves by Lorentz transformations in Fourier space," Phys. Rev. E 69, 036612 (2004).
[CrossRef]

Saari, P.

P. Saari and K. Reivelt, "Generation and classification of localized waves by Lorentz transformations in Fourier space," Phys. Rev. E 69, 036612 (2004).
[CrossRef]

P. Saari, "Relativistic Doppler effect, aberration and Gouy effect on localized waves," Special Issue on "Anomalies and Strange Behavior in Physics: Challenging the Conventional," Atti della Fondazione Giorgio Ronchi 58, 729-754 (2003).

P. Saari, "Evolution of subcycle pulses in nonparaxial Gaussian beams," Opt. Express 8, 590-598 (2001).
[CrossRef] [PubMed]

Sezginer, A.

A. Sezginer, "A general formulation of focus wave modes," J. Appl. Phys. 57, 678-683 (1985).
[CrossRef]

Shaarawi, A. M.

I. M. Besieris and A. M. Shaarawi, "A note on an accelerating finite energy Airy beam," Opt. Lett. 32, 2447-2449 (2007).
[CrossRef] [PubMed]

I. M. Besieris, A. M. Shaarawi, and R.W. Ziolkowski, "Nondispersive accelerating wave packets," Am. J. Phys. 62, 519-521 (1994).
[CrossRef]

Sheppard, C. J. R.

Siviloglou, G. A.

Winful, H. G.

S. Feng and H. G. Winful, "Spatiotemporal structure of isodiffracting ultrashort electromagnetic pulses," Phys. Rev. E 61, 862-873 (2000).
[CrossRef]

Ziolkowski, R.W.

I. M. Besieris, A. M. Shaarawi, and R.W. Ziolkowski, "Nondispersive accelerating wave packets," Am. J. Phys. 62, 519-521 (1994).
[CrossRef]

Am. J. Phys.

M. V. Berry and N. L. Balazs, "Nonspreading wave packets," Am. J. Phys. 47, 264-267 (1979).
[CrossRef]

Am. J. Phys.

I. M. Besieris, A. M. Shaarawi, and R.W. Ziolkowski, "Nondispersive accelerating wave packets," Am. J. Phys. 62, 519-521 (1994).
[CrossRef]

Atti della Fondazione Giorgio Ronchi

P. Saari, "Relativistic Doppler effect, aberration and Gouy effect on localized waves," Special Issue on "Anomalies and Strange Behavior in Physics: Challenging the Conventional," Atti della Fondazione Giorgio Ronchi 58, 729-754 (2003).

J. Appl. Phys.

A. Sezginer, "A general formulation of focus wave modes," J. Appl. Phys. 57, 678-683 (1985).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Express

Opt. Lett.

Phys. Rev. E

M. A. Porras, "Pulsed light beams in vacuum with superluminal and negative group velocities," Phys. Rev. E 67, 066604 (2003).
[CrossRef]

P. Saari and K. Reivelt, "Generation and classification of localized waves by Lorentz transformations in Fourier space," Phys. Rev. E 69, 036612 (2004).
[CrossRef]

Z. L. Horváth and Zs. Bor, "Reshaping of femtosecond pulses by the Gouy phase shift," Phys. Rev. E 60, 2337-2345 (1999).
[CrossRef]

S. Feng and H. G. Winful, "Spatiotemporal structure of isodiffracting ultrashort electromagnetic pulses," Phys. Rev. E 61, 862-873 (2000).
[CrossRef]

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]

Other

H. E. Hernandez-Figueroa, M. Zamboni-Rached, and E.  Recami, eds., Localized Waves: Theory and Applications, (J. Wiley, New York, 2008).
[CrossRef]

Supplementary Material (4)

» Media 1: MOV (645 KB)     
» Media 2: MOV (1437 KB)     
» Media 3: MOV (1606 KB)     
» Media 4: MOV (1253 KB)     

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1.

A sum of frames taken at instants ct=6 cm, ct=45 cm, and ct=84 cm of the animated plot (0.6 MB) of profiles of a type I narrowband Airy pulse which have been computed as modulus squared of the wavefunction given by Eqs. (1), (2). The plot can be also considered as a snapshot of three sequential pulses separated by an interval ct=39 cm. The full width at 1/e level of the spectrum is 2×105 times smaller than the carrier frequency k 0=105 cm-1. Correspondingly, the pulsewidth (intensity FWHM) is 1/3 ns. Other parameters are given in the text. Pseudocolor scale – from dark blue (zero level) up to red (peak value).[Media 1]

Fig. 2.
Fig. 2.

The frame t=0 of the animated plot (1.4 MB) showing the modulus of the wavefunction of a type I wideband Airy pulse. Despite wavelengths of the monochromatic constituents of the pulse vary in a wide range the pulse Airy profile at z=0 is not smeared out, since the lateral scale x 0 is identical for all constituents in the case of type I pulse. Intensity temporal FWHM is 8 fs. [Media 2]

Fig. 3.
Fig. 3.

The frame t=0 of the animated plot (1.6 MB) of the modulus of the wavefunction of a type II wideband Airy pulse. The Airy profile is partially smeared out already at z=0 and replaced by a X-like branches, since the lateral scale x 0 varies strongly – x 0 is proportional to wavelength of a constituent of the type II pulse. Intensity temporal FWHM of the main lobe is 8 fs. [Media 3]

Fig. 4.
Fig. 4.

The frame t=0 of the animated plot (1.2 MB) of the modulus of the wavefunction of a type III wideband Airy pulse. Intensity temporal FWHM of the main lobe is 8 fs. [Media 4]

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

Ψ ( x , z , t ) = 0 d k S ( k ) Φ ( x , z , k ) exp [ i k ( z c t ) ] ,
Φ ( x , z , k ) = Ai [ x x 0 ( z 2 z 0 ) 2 + i a z z 0 ] exp [ a x x 0 a 2 ( z z 0 ) 2 + i φ ( x , z , k ) ] ,
φ ( x , z , k ) = x 2 x 0 z z 0 1 12 ( z z 0 ) 3 + a 2 2 z z 0 .

Metrics