Abstract

We propose a new experimental technique, which allows for a complete characterization of ultrashort optical pulses both in space and in time. Combining the well-known Frequency-Resolved-Optical-Gating technique for the retrieval of the temporal profile of the pulse with a measurement of the near-field made with an Hartmann-Shack sensor, we are able to retrieve the spatiotemporal amplitude and phase profile of a Bessel-X pulse. By following the pulse evolution along the propagation direction we highlight the superluminal propagation of the pulse peak.

© 2009 Optical Society of America

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  1. R. V. Shack and B. C. Platt, "Lenticular Hartmann-screen," Opt.Science Center Newslett. 5, 15-16 (1971).
  2. C. P. Hauri, J. Biegert, U. Keller, B. Schaefer, K. Mann, and G. Marowski, "Validity of wavefront reconstruction and propagation of ultra-broadband pulses measured with a Hartmann-Shack sensor," Opt. Lett. 30, 1563-1565 (2005).
    [CrossRef] [PubMed]
  3. R. Trebino and D. J. Kane, "Using phase retrieval to measure the intensity and phase of ultrashort pulses: frequency-resolved optical gating," J. Opt. Soc. Am. A 10, 1101-1111 (1993).
    [CrossRef]
  4. P. Bowlan, P. Gabolde, A. Schreenath, K. McGresham, and R. Trebino, "Crossed-beam spectral interferometry: a simple, high-spectral-resolution method for completely characterizing complex ultrashort pulses in real time," Opt. Express 14, 11892-11900 (2006).
    [CrossRef] [PubMed]
  5. P. Bowlan, P. Gabolde, and R. Trebino, "Directly measuring the spatio-temporal electric field of focusing ultrashort pulses," Opt. Express 15, 10219-10230 (2007).
    [CrossRef] [PubMed]
  6. P. Gabolde and R. Trebino, "Single-shot measurement of the full spatiotemporal field of ultrashort pulses with multispectral digital holography," Opt. Express 14, 11460-11467 (2006).
    [CrossRef] [PubMed]
  7. A.S. Wyatt, I.A. Walmsley, G. Stibenz and G. Steinmeyer, "Sub-10 fs pulse characterization using spatially encoded arrangement for spectral phase interferometry for direct electric field reconstruction," Opt. Lett. 31, 1914-1916 (2006).
    [CrossRef] [PubMed]
  8. F. Bragheri, D. Faccio, F. Bonaretti, A. Lotti, M. Clerici, O. Jedrkiewicz, C. Liberale, S. Henin, L. Tartara, V. Degiorgio, and P. Di Trapani, "Complete retrieval of the field of ultrashort optical pulses using the angle-frequency spectrum," Opt. Lett. 33, 2952-2955 (2008).
    [CrossRef] [PubMed]
  9. P. Migdal, P. Fita, C. Radzewicz, and L. Mazurek, "Wavefront sensor with Fresnel zone plates for use in an undergraduate laboratory," Am. J. Phys. 76, 229-235 (2008).
    [CrossRef]
  10. H. E. Hernandez-Figueroa, M. Zamboni-Rached, and E. Recami, Eds. Localized Waves (Wiley-Interscience, 2008).
  11. E. Recami, "On localized "X-shaped" superluminal solutions to Maxwell equations," Phys. A 252, 586-610 (1998).
    [CrossRef]
  12. M. Zamboni-Rached, H. E. Hernández-Figueroa, and E. Recami, "Chirped optical X-shaped pulses in material media," J. Opt. Soc. A 21, 2455-2463 (2004).
    [CrossRef]
  13. M. Zamboni-Rached, "Analytical expressions for the longitudinal evolution of nondiffracting pulses truncated finite apertures," J. Opt. Soc. A 23, 2166-2176 (2006).
    [CrossRef]
  14. M. Zamboni-Rached, "Unidirectional decomposition method for obtaining exact localized wave solutions totally free of backward components," Phys. Rev. A 79, 013816 (2009).
    [CrossRef]
  15. P. Saari and K. Reivelt, "Evidence of X-shaped propagation-invariant localized light waves," Phys. Rev. Lett. 79, 4135-4138 (1997).
    [CrossRef]
  16. D. Mugnai, A. Ranfagni, and R. Ruggeri,"Observation of Superluminal Behaviors in Wave Propagation," Phys. Rev. Lett. 84, 4830-4833 (2000)
    [CrossRef] [PubMed]
  17. I. Alexeev, K. Y. Kim, and H. M. Milchberg,"Measurement of the Superluminal Group Velocity of an Ultrashort Bessel Beam Pulse," Phys. Rev. Lett. 88, 073901 (2002)
    [CrossRef] [PubMed]

2009 (1)

M. Zamboni-Rached, "Unidirectional decomposition method for obtaining exact localized wave solutions totally free of backward components," Phys. Rev. A 79, 013816 (2009).
[CrossRef]

2008 (2)

2007 (1)

2006 (4)

2005 (1)

2004 (1)

M. Zamboni-Rached, H. E. Hernández-Figueroa, and E. Recami, "Chirped optical X-shaped pulses in material media," J. Opt. Soc. A 21, 2455-2463 (2004).
[CrossRef]

2002 (1)

I. Alexeev, K. Y. Kim, and H. M. Milchberg,"Measurement of the Superluminal Group Velocity of an Ultrashort Bessel Beam Pulse," Phys. Rev. Lett. 88, 073901 (2002)
[CrossRef] [PubMed]

2000 (1)

D. Mugnai, A. Ranfagni, and R. Ruggeri,"Observation of Superluminal Behaviors in Wave Propagation," Phys. Rev. Lett. 84, 4830-4833 (2000)
[CrossRef] [PubMed]

1998 (1)

E. Recami, "On localized "X-shaped" superluminal solutions to Maxwell equations," Phys. A 252, 586-610 (1998).
[CrossRef]

1997 (1)

P. Saari and K. Reivelt, "Evidence of X-shaped propagation-invariant localized light waves," Phys. Rev. Lett. 79, 4135-4138 (1997).
[CrossRef]

1993 (1)

1971 (1)

R. V. Shack and B. C. Platt, "Lenticular Hartmann-screen," Opt.Science Center Newslett. 5, 15-16 (1971).

Alexeev, I.

I. Alexeev, K. Y. Kim, and H. M. Milchberg,"Measurement of the Superluminal Group Velocity of an Ultrashort Bessel Beam Pulse," Phys. Rev. Lett. 88, 073901 (2002)
[CrossRef] [PubMed]

Biegert, J.

Bonaretti, F.

Bowlan, P.

Bragheri, F.

Clerici, M.

Degiorgio, V.

Di Trapani, P.

Faccio, D.

Fita, P.

P. Migdal, P. Fita, C. Radzewicz, and L. Mazurek, "Wavefront sensor with Fresnel zone plates for use in an undergraduate laboratory," Am. J. Phys. 76, 229-235 (2008).
[CrossRef]

Gabolde, P.

Hauri, C. P.

Henin, S.

Hernández-Figueroa, H. E.

M. Zamboni-Rached, H. E. Hernández-Figueroa, and E. Recami, "Chirped optical X-shaped pulses in material media," J. Opt. Soc. A 21, 2455-2463 (2004).
[CrossRef]

Jedrkiewicz, O.

Kane, D. J.

Keller, U.

Kim, K. Y.

I. Alexeev, K. Y. Kim, and H. M. Milchberg,"Measurement of the Superluminal Group Velocity of an Ultrashort Bessel Beam Pulse," Phys. Rev. Lett. 88, 073901 (2002)
[CrossRef] [PubMed]

Liberale, C.

Lotti, A.

Mann, K.

Marowski, G.

Mazurek, L.

P. Migdal, P. Fita, C. Radzewicz, and L. Mazurek, "Wavefront sensor with Fresnel zone plates for use in an undergraduate laboratory," Am. J. Phys. 76, 229-235 (2008).
[CrossRef]

McGresham, K.

Migdal, P.

P. Migdal, P. Fita, C. Radzewicz, and L. Mazurek, "Wavefront sensor with Fresnel zone plates for use in an undergraduate laboratory," Am. J. Phys. 76, 229-235 (2008).
[CrossRef]

Milchberg, H. M.

I. Alexeev, K. Y. Kim, and H. M. Milchberg,"Measurement of the Superluminal Group Velocity of an Ultrashort Bessel Beam Pulse," Phys. Rev. Lett. 88, 073901 (2002)
[CrossRef] [PubMed]

Mugnai, D.

D. Mugnai, A. Ranfagni, and R. Ruggeri,"Observation of Superluminal Behaviors in Wave Propagation," Phys. Rev. Lett. 84, 4830-4833 (2000)
[CrossRef] [PubMed]

Platt, B. C.

R. V. Shack and B. C. Platt, "Lenticular Hartmann-screen," Opt.Science Center Newslett. 5, 15-16 (1971).

Radzewicz, C.

P. Migdal, P. Fita, C. Radzewicz, and L. Mazurek, "Wavefront sensor with Fresnel zone plates for use in an undergraduate laboratory," Am. J. Phys. 76, 229-235 (2008).
[CrossRef]

Ranfagni, A.

D. Mugnai, A. Ranfagni, and R. Ruggeri,"Observation of Superluminal Behaviors in Wave Propagation," Phys. Rev. Lett. 84, 4830-4833 (2000)
[CrossRef] [PubMed]

Recami, E.

M. Zamboni-Rached, H. E. Hernández-Figueroa, and E. Recami, "Chirped optical X-shaped pulses in material media," J. Opt. Soc. A 21, 2455-2463 (2004).
[CrossRef]

E. Recami, "On localized "X-shaped" superluminal solutions to Maxwell equations," Phys. A 252, 586-610 (1998).
[CrossRef]

Reivelt, K.

P. Saari and K. Reivelt, "Evidence of X-shaped propagation-invariant localized light waves," Phys. Rev. Lett. 79, 4135-4138 (1997).
[CrossRef]

Ruggeri, R.

D. Mugnai, A. Ranfagni, and R. Ruggeri,"Observation of Superluminal Behaviors in Wave Propagation," Phys. Rev. Lett. 84, 4830-4833 (2000)
[CrossRef] [PubMed]

Saari, P.

P. Saari and K. Reivelt, "Evidence of X-shaped propagation-invariant localized light waves," Phys. Rev. Lett. 79, 4135-4138 (1997).
[CrossRef]

Schaefer, B.

Schreenath, A.

Shack, R. V.

R. V. Shack and B. C. Platt, "Lenticular Hartmann-screen," Opt.Science Center Newslett. 5, 15-16 (1971).

Steinmeyer, G.

Stibenz, G.

Tartara, L.

Trebino, R.

Walmsley, I.A.

Wyatt, A.S.

Zamboni-Rached, M.

M. Zamboni-Rached, "Unidirectional decomposition method for obtaining exact localized wave solutions totally free of backward components," Phys. Rev. A 79, 013816 (2009).
[CrossRef]

M. Zamboni-Rached, "Analytical expressions for the longitudinal evolution of nondiffracting pulses truncated finite apertures," J. Opt. Soc. A 23, 2166-2176 (2006).
[CrossRef]

M. Zamboni-Rached, H. E. Hernández-Figueroa, and E. Recami, "Chirped optical X-shaped pulses in material media," J. Opt. Soc. A 21, 2455-2463 (2004).
[CrossRef]

Am. J. Phys. (1)

P. Migdal, P. Fita, C. Radzewicz, and L. Mazurek, "Wavefront sensor with Fresnel zone plates for use in an undergraduate laboratory," Am. J. Phys. 76, 229-235 (2008).
[CrossRef]

J. Opt. Soc. A (2)

M. Zamboni-Rached, H. E. Hernández-Figueroa, and E. Recami, "Chirped optical X-shaped pulses in material media," J. Opt. Soc. A 21, 2455-2463 (2004).
[CrossRef]

M. Zamboni-Rached, "Analytical expressions for the longitudinal evolution of nondiffracting pulses truncated finite apertures," J. Opt. Soc. A 23, 2166-2176 (2006).
[CrossRef]

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

Opt. Express (3)

Opt. Lett. (3)

Phys. A (1)

E. Recami, "On localized "X-shaped" superluminal solutions to Maxwell equations," Phys. A 252, 586-610 (1998).
[CrossRef]

Phys. Rev. A (1)

M. Zamboni-Rached, "Unidirectional decomposition method for obtaining exact localized wave solutions totally free of backward components," Phys. Rev. A 79, 013816 (2009).
[CrossRef]

Phys. Rev. Lett. (3)

P. Saari and K. Reivelt, "Evidence of X-shaped propagation-invariant localized light waves," Phys. Rev. Lett. 79, 4135-4138 (1997).
[CrossRef]

D. Mugnai, A. Ranfagni, and R. Ruggeri,"Observation of Superluminal Behaviors in Wave Propagation," Phys. Rev. Lett. 84, 4830-4833 (2000)
[CrossRef] [PubMed]

I. Alexeev, K. Y. Kim, and H. M. Milchberg,"Measurement of the Superluminal Group Velocity of an Ultrashort Bessel Beam Pulse," Phys. Rev. Lett. 88, 073901 (2002)
[CrossRef] [PubMed]

Science Center Newslett. (1)

R. V. Shack and B. C. Platt, "Lenticular Hartmann-screen," Opt.Science Center Newslett. 5, 15-16 (1971).

Other (1)

H. E. Hernandez-Figueroa, M. Zamboni-Rached, and E. Recami, Eds. Localized Waves (Wiley-Interscience, 2008).

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Figures (4)

Fig. 1.
Fig. 1.

Experimental layout of the experiment: z 0 indicates the distance between the axicon and the H-S sensor, d indicates the distance between the H-S sensor and the detector. The temporal characterization is performed by substituting the H-S sensor with a FROG setup.

Fig. 2.
Fig. 2.

(a) Experimental spectrogram. (b) Last spectrogram retrieved by the iterative algorithm. (c) Retrieved temporal pulse: intensity (continuous line) and phase (dashed line). The retrieved pulse duration is 33 fs FWHM.

Fig. 3.
Fig. 3.

Left hand side figures: H-S acquisition. Right hand side: corresponding retrieved phase. (a) Beginning of the Bessel zone: z 0=18 mm. (b) Middle of the Bessel zone: z 0=58 mm. (c) End of the Bessel zone: z 0=108 mm. In all figures, the converging front is shown in red circles and the diverging pulse front in blue spots.

Fig. 4.
Fig. 4.

Space-time evolution of the normalized intensity of the Bessel-X pulse during the propagation. The pulses are shown in the reference frame of the peak of the Bessel-X pulse. (a) z 0=18 mm. (b) z 0=48 mm. (c) z 0=78 mm. (d) z 0=108 mm. The inset in (c) shows the Bessel profile formed in the central zone of the pulse. The vertical axis spans from -40 µm to 40 µm and the horizontal axis spans from -40 fs to +40 fs.

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