Abstract

We measure the spatiotemporal field of ultrashort pulses with complex spatiotemporal profiles using the linear-optical, interferometric pulse-measurement technique SEA TADPOLE. Accelerating and decelerating ultrashort, localized, nonspreading Bessel-X wavepackets were generated from a ~27 fs duration Ti:Sapphire oscillator pulse using a combination of an axicon and a convex or concave lens. The wavefields are measured with ~5 μm spatial and ~15 fs temporal resolutions. Our experimental results are in good agreement with theoretical calculations and numerical simulations.

© 2009 OSA

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  1. H. E. Hernández-Figueroa, M. Zamboni-Rached, and E. Recami, eds., Localized Waves: Theory and Applications (New Jersey: John Wiley & Sons Ltd, 2008).
  2. P. Saari and K. Reivelt, “Evidence of X-Shaped propagation-invariant localized light waves,” Phys. Rev. Lett. 79(21), 4135–4138 (1997).
    [CrossRef]
  3. H. Sõnajalg, M. Rätsep, and P. Saari, “Demonstration of the Bessel-X pulse propagating with strong lateral and longitudinal localization in a dispersive medium,” Opt. Lett. 22(5), 310–312 (1997).
    [CrossRef] [PubMed]
  4. K. Reivelt and P. Saari, “Experimental demonstration of realizability of optical focus wave modes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5), 056611 (2002).
    [CrossRef]
  5. 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(7), 073901–073904 (2002).
    [CrossRef] [PubMed]
  6. R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piche´, G. Rousseau, and M. Fortin, “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67(6), 063820–063825 (2003).
    [CrossRef]
  7. F. Bonaretti, D. Faccio, M. Clerici, J. Biegert, and P. Di Trapani, “Spatiotemporal amplitude and phase retrieval of Bessel-X pulses using a Hartmann-Shack sensor,” Opt. Express 17(12), 9804–9809 (2009).
    [CrossRef] [PubMed]
  8. P. Bowlan, H. Valtna-Lukner, M. Lõhmus, P. Piksarv, P. Saari, and R. Trebino, “Measuring the spatiotemporal field of ultrashort Bessel-X pulses,” Opt. Lett. 34(15), 2276–2278 (2009).
    [CrossRef] [PubMed]
  9. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901–213904 (2007).
    [CrossRef]
  10. P. Saari, “Laterally accelerating airy pulses,” Opt. Express 16(14), 10303–10308 (2008).
    [CrossRef] [PubMed]
  11. P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
    [CrossRef] [PubMed]
  12. Z. L. Horváth and Z. Bor, “Diffraction of short pulses with boundary diffraction wave theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(2), 026601–026611 (2001).
    [CrossRef] [PubMed]
  13. P. Bowlan, U. Fuchs, R. Trebino, and U. D. Zeitner, “Measuring the spatiotemporal electric field of tightly focused ultrashort pulses with sub-micron spatial resolution,” Opt. Express 16(18), 13663–13675 (2008).
    [CrossRef] [PubMed]
  14. P. Bowlan, M. Lohmus, P. Piksarv, H. Valtna-Lukner, P. Saari, and R. Trebino, Measuring the spatio-temporal field of diffracting ultrashort pulses,” arXiv:0905.4381 (2009).
  15. M. Clerici, D. Faccio, A. Lotti, E. Rubino, O. Jedrkiewicz, J. Biegert, and P. Di Trapani, “Finite-energy, accelerating Bessel pulses,” Opt. Express 16(24), 19807–19811 (2008).
    [CrossRef] [PubMed]
  16. P. Bowlan, P. Gabolde, A. Shreenath, K. McGresham, R. Trebino, and S. Akturk, “Crossed-beam spectral interferometry: a simple, high-spectral-resolution method for completely characterizing complex ultrashort pulses in real time,” Opt. Express 14(24), 11892–11900 (2006).
    [CrossRef] [PubMed]
  17. P. Bowlan, P. Gabolde, and R. Trebino, “Directly measuring the spatio-temporal electric field of focusing ultrashort pulses,” Opt. Express 15(16), 10219–10230 (2007).
    [CrossRef] [PubMed]
  18. S. Akturk, B. Zhou, B. Pasquiou, M. Franco, and A. Mysyrowicz, “Intensity distribution around the focal regions of real axicons,” Opt. Commun. 281(17), 4240–4244 (2008).
    [CrossRef]
  19. D. Abdollahpour, P. Panagiotopoulos, M. Turconi, O. Jedrkiewicz, D. Faccio, P. Di Trapani, A. Couairon, D. Papazoglou, and S. Tzortzakis, “Long spatio-temporally stationary filaments in air using short pulse UV laser Bessel beams,” Opt. Express 17(7), 5052–5057 (2009).
    [CrossRef] [PubMed]
  20. J.-M. Manceau, A. Averchi, F. Bonaretti, D. Faccio, P. Di Trapani, A. Couairon, and S. Tzortzakis, “Terahertz pulse emission optimization from tailored femtosecond laser pulse filamentation in air,” Opt. Lett. 34(14), 2165–2167 (2009).
    [CrossRef] [PubMed]

2009

2008

2007

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901–213904 (2007).
[CrossRef]

P. Bowlan, P. Gabolde, and R. Trebino, “Directly measuring the spatio-temporal electric field of focusing ultrashort pulses,” Opt. Express 15(16), 10219–10230 (2007).
[CrossRef] [PubMed]

2006

2003

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piche´, G. Rousseau, and M. Fortin, “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67(6), 063820–063825 (2003).
[CrossRef]

2002

K. Reivelt and P. Saari, “Experimental demonstration of realizability of optical focus wave modes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5), 056611 (2002).
[CrossRef]

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(7), 073901–073904 (2002).
[CrossRef] [PubMed]

2001

Z. L. Horváth and Z. Bor, “Diffraction of short pulses with boundary diffraction wave theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(2), 026601–026611 (2001).
[CrossRef] [PubMed]

1997

Abdollahpour, D.

Akturk, S.

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(7), 073901–073904 (2002).
[CrossRef] [PubMed]

Averchi, A.

Biegert, J.

Bonaretti, F.

Bor, Z.

Z. L. Horváth and Z. Bor, “Diffraction of short pulses with boundary diffraction wave theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(2), 026601–026611 (2001).
[CrossRef] [PubMed]

Bowlan, P.

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901–213904 (2007).
[CrossRef]

Christodoulides, D. N.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901–213904 (2007).
[CrossRef]

Clerici, M.

Couairon, A.

Di Trapani, P.

Dogariu, A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901–213904 (2007).
[CrossRef]

Faccio, D.

Fortin, M.

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piche´, G. Rousseau, and M. Fortin, “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67(6), 063820–063825 (2003).
[CrossRef]

Franco, M.

S. Akturk, B. Zhou, B. Pasquiou, M. Franco, and A. Mysyrowicz, “Intensity distribution around the focal regions of real axicons,” Opt. Commun. 281(17), 4240–4244 (2008).
[CrossRef]

Fuchs, U.

Gabolde, P.

Griebner, U.

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piche´, G. Rousseau, and M. Fortin, “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67(6), 063820–063825 (2003).
[CrossRef]

Grunwald, R.

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piche´, G. Rousseau, and M. Fortin, “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67(6), 063820–063825 (2003).
[CrossRef]

Horváth, Z. L.

Z. L. Horváth and Z. Bor, “Diffraction of short pulses with boundary diffraction wave theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(2), 026601–026611 (2001).
[CrossRef] [PubMed]

Jedrkiewicz, O.

Kebbel, V.

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piche´, G. Rousseau, and M. Fortin, “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67(6), 063820–063825 (2003).
[CrossRef]

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(7), 073901–073904 (2002).
[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,” Science 324(5924), 229–232 (2009).
[CrossRef] [PubMed]

Kummrow, A.

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piche´, G. Rousseau, and M. Fortin, “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67(6), 063820–063825 (2003).
[CrossRef]

Lõhmus, M.

Lotti, A.

Manceau, J.-M.

McGresham, K.

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(7), 073901–073904 (2002).
[CrossRef] [PubMed]

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(5924), 229–232 (2009).
[CrossRef] [PubMed]

Mysyrowicz, A.

S. Akturk, B. Zhou, B. Pasquiou, M. Franco, and A. Mysyrowicz, “Intensity distribution around the focal regions of real axicons,” Opt. Commun. 281(17), 4240–4244 (2008).
[CrossRef]

Neumann, U.

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piche´, G. Rousseau, and M. Fortin, “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67(6), 063820–063825 (2003).
[CrossRef]

Nibbering, E. T. J.

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piche´, G. Rousseau, and M. Fortin, “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67(6), 063820–063825 (2003).
[CrossRef]

Panagiotopoulos, P.

Papazoglou, D.

Pasquiou, B.

S. Akturk, B. Zhou, B. Pasquiou, M. Franco, and A. Mysyrowicz, “Intensity distribution around the focal regions of real axicons,” Opt. Commun. 281(17), 4240–4244 (2008).
[CrossRef]

Piche´, M.

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piche´, G. Rousseau, and M. Fortin, “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67(6), 063820–063825 (2003).
[CrossRef]

Piksarv, P.

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(5924), 229–232 (2009).
[CrossRef] [PubMed]

Rätsep, M.

Reivelt, K.

K. Reivelt and P. Saari, “Experimental demonstration of realizability of optical focus wave modes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5), 056611 (2002).
[CrossRef]

P. Saari and K. Reivelt, “Evidence of X-Shaped propagation-invariant localized light waves,” Phys. Rev. Lett. 79(21), 4135–4138 (1997).
[CrossRef]

Rini, M.

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piche´, G. Rousseau, and M. Fortin, “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67(6), 063820–063825 (2003).
[CrossRef]

Rousseau, G.

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piche´, G. Rousseau, and M. Fortin, “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67(6), 063820–063825 (2003).
[CrossRef]

Rubino, E.

Saari, P.

Shreenath, A.

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(5924), 229–232 (2009).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901–213904 (2007).
[CrossRef]

Sõnajalg, H.

Trebino, R.

Turconi, M.

Tzortzakis, S.

Valtna-Lukner, H.

Zeitner, U. D.

Zhou, B.

S. Akturk, B. Zhou, B. Pasquiou, M. Franco, and A. Mysyrowicz, “Intensity distribution around the focal regions of real axicons,” Opt. Commun. 281(17), 4240–4244 (2008).
[CrossRef]

Opt. Commun.

S. Akturk, B. Zhou, B. Pasquiou, M. Franco, and A. Mysyrowicz, “Intensity distribution around the focal regions of real axicons,” Opt. Commun. 281(17), 4240–4244 (2008).
[CrossRef]

Opt. Express

P. Bowlan, P. Gabolde, A. Shreenath, K. McGresham, R. Trebino, and S. Akturk, “Crossed-beam spectral interferometry: a simple, high-spectral-resolution method for completely characterizing complex ultrashort pulses in real time,” Opt. Express 14(24), 11892–11900 (2006).
[CrossRef] [PubMed]

P. Bowlan, P. Gabolde, and R. Trebino, “Directly measuring the spatio-temporal electric field of focusing ultrashort pulses,” Opt. Express 15(16), 10219–10230 (2007).
[CrossRef] [PubMed]

P. Saari, “Laterally accelerating airy pulses,” Opt. Express 16(14), 10303–10308 (2008).
[CrossRef] [PubMed]

P. Bowlan, U. Fuchs, R. Trebino, and U. D. Zeitner, “Measuring the spatiotemporal electric field of tightly focused ultrashort pulses with sub-micron spatial resolution,” Opt. Express 16(18), 13663–13675 (2008).
[CrossRef] [PubMed]

M. Clerici, D. Faccio, A. Lotti, E. Rubino, O. Jedrkiewicz, J. Biegert, and P. Di Trapani, “Finite-energy, accelerating Bessel pulses,” Opt. Express 16(24), 19807–19811 (2008).
[CrossRef] [PubMed]

D. Abdollahpour, P. Panagiotopoulos, M. Turconi, O. Jedrkiewicz, D. Faccio, P. Di Trapani, A. Couairon, D. Papazoglou, and S. Tzortzakis, “Long spatio-temporally stationary filaments in air using short pulse UV laser Bessel beams,” Opt. Express 17(7), 5052–5057 (2009).
[CrossRef] [PubMed]

F. Bonaretti, D. Faccio, M. Clerici, J. Biegert, and P. Di Trapani, “Spatiotemporal amplitude and phase retrieval of Bessel-X pulses using a Hartmann-Shack sensor,” Opt. Express 17(12), 9804–9809 (2009).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. A

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piche´, G. Rousseau, and M. Fortin, “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67(6), 063820–063825 (2003).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

K. Reivelt and P. Saari, “Experimental demonstration of realizability of optical focus wave modes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5), 056611 (2002).
[CrossRef]

Z. L. Horváth and Z. Bor, “Diffraction of short pulses with boundary diffraction wave theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(2), 026601–026611 (2001).
[CrossRef] [PubMed]

Phys. Rev. Lett.

P. Saari and K. Reivelt, “Evidence of X-Shaped propagation-invariant localized light waves,” Phys. Rev. Lett. 79(21), 4135–4138 (1997).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901–213904 (2007).
[CrossRef]

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(7), 073901–073904 (2002).
[CrossRef] [PubMed]

Science

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[CrossRef] [PubMed]

Other

P. Bowlan, M. Lohmus, P. Piksarv, H. Valtna-Lukner, P. Saari, and R. Trebino, Measuring the spatio-temporal field of diffracting ultrashort pulses,” arXiv:0905.4381 (2009).

H. E. Hernández-Figueroa, M. Zamboni-Rached, and E. Recami, eds., Localized Waves: Theory and Applications (New Jersey: John Wiley & Sons Ltd, 2008).

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Figures (5)

Fig. 1
Fig. 1

Schematic of the formation of accelerating pulses from a plane-wave pulse moving to the right with velocity c. The red strips depict the pulses’ intensity profiles in space at four different times. The conical surface of the axicon transforms the plane-wave pulse into a Bessel-X pulse, and the convex lens then yields the accelerating pulse. (In the actual experiments, the positions of the axicon and lens were interchanged, but this does not influence the results.) The inset plots show the expected intensity vs. x and t for three different positions z.

Fig. 2
Fig. 2

Comparison of the measured and calculated spatiotemporal profiles of the electric field amplitude of an accelerating Bessel pulse at three positions along the propagation axis (z). The color bar indicates the amplitude scale normalized separately for each plot. The white bar emphasizes t = 0, which is where the pulse would be located if it were propagating at c.

Fig. 4
Fig. 4

Experimentally determined (points) and theoretically predicted (solid curves) temporal shifts (in femtoseconds) of the accelerating/decelerating Bessel pulses in respect of the reference pulse. z is the propagation distance.

Fig. 3
Fig. 3

Comparison of measured and calculated spatiotemporal profiles of the electric field amplitude of decelerating Bessel pulse at three positions along the propagation axis z.

Fig. 5
Fig. 5

Comparison of experimentally and theoretically calculated group velocities for accelerating and decelerating Bessel pulses. The measured group velocities for the accelerating Bessel pulses are marked with blue crosses, and, for decelerating pulses, with red circles. The error bars show the standard deviations from the mean value. The solid lines show the theoretically predicted dependences. At the position z = 0, the theoretical curves for both pulses coincide because the same axicon was used to generate them.

Equations (3)

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

Ψ(ρ,z,t)=0dωG(ωω0)J0[ωcρsinθ(z)]exp{iωc[zcosθ(z)ct]},
Ψsph(ρ,z,t)0dω0dφraωG(ωω0)exp{iωc[ρ2+ra22raρcosφ+z2ct]}ρ2+ra22raρcosφ+z2.
vg(z)=c/1[λ0/ΛB(z)]2.

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