Abstract

Spatio-spectral and spatio-temporal transfer and intensity propagation of truncated ultrashort-pulsed Bessel-Gauss beams were investigated. Extended needle-shaped focal zones were generated using a compact setup with a reflective small-angle axicon and self-apodized truncation by an adapted aperture. Spectral maps of Bessel-Gauss beams were analyzed on the basis of higher order statistical moments. Compared to focused pulsed Gaussian beams with their spectrally dependent propagation, an ultrabroadband spatio-spectral transfer function was detected over Rayleigh ranges exceeding 10 cm. These results indicate favorable pseudo-nondiffracting characteristics not only from the point of view of spatial propagation but also with respect to the spectral and temporal stability.

©2008 Optical Society of America

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2007 (1)

2006 (2)

G. Stibenz and G. Steinmeyer, “Optimizing spectral phase interferometry for direct electric-field reconstruction,” Rev. Sci. Instrum. 77, 073105 (2006).
[Crossref]

G. Steinmeyer and G. Stibenz, “Generation of sub-4-fs pulses via compression of a white-light continuum using only chirped mirrors,” Appl. Phys. B 82, 175–81 (2006).
[Crossref]

2005 (1)

2004 (3)

K. Reivelt and P. Saari, “Bessel-Gauss pulse as an appropriate mathematical model for optically realizable localized waves,” Opt. Lett. 29, 1176–1178 (2004).
[Crossref] [PubMed]

R. Grunwald, U. Neumann, G. Stibenz, S. Langer, G. Steinmeyer, V. Kebbel, J.-L. Néron, and M. Piché, “Truncated ultrashort-pulse small-angle Bessel beams,” Photonics North 2004, Sept. 27–29, Ottawa, Canada, Proc. SPIE 5579, 724–735 (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 (3)

E. Recami, M. Zamboni-Rached, K. Z. Nóbrega, C. A. Dartora, and H. E. Hernández Figueroa, “On the localized superluminal solutions to the Maxwell equations,” IEEE J. Sel. Top. Quantum Electron. 9, 59–73 (2003).
[Crossref]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[Crossref] [PubMed]

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piché, G. Rousseau, and M. Fortin, “Generation and characterization of spatially and temporally localized few-cycle optical wavepackets,” Phys. Rev. A 67, 063820 (2003).
[Crossref]

2002 (4)

M. Nisoli, E. Priori, G. Sansone, S. Stagira, G. Cerullo, S. De Silvestri, C. Altucci, R. Bruzzese, C. de Lisio, P. Villoresi, L. Poletto, M. Pascolini, and G. Tondello, “High-brightness high-order harmonic generation by truncated Bessel beams in the sub-10-fs regime,” Phys. Rev. Lett. 88, 033902 (2002).
[Crossref] [PubMed]

J.-F. Fortin, G. Rousseau, N. McCarthy, and M. Piché, “Generation of quasi-Bessel beams and femtosecond optical X-waves with conical mirrors,” Proc. SPIE 4833, 876–884 (2002).
[Crossref]

W. Hu and H. Guo, “Ultrashort-pulsed Bessel beams and spatially induced group-velocity,” J. Opt. Soc. Am. A 19, 49–53 (2002).
[Crossref]

C. Dorrer, E. M. Kosik, and I. A. Walmsley, “Direct space-time characterization of the electric fields of ultrashort optical pulses,” Opt. Lett. 27, 548–550 (2002).
[Crossref]

2001 (1)

2000 (1)

M. A. Porras, R. Borghi, and M. Santarsiero, “Few-optical-cycle Bessel-Gauss pulsed beams in free space,” Phys. Rev. E 62, 5729–5730 (2000).
[Crossref]

1999 (2)

M. Piché, G. Rousseau, C. Varin, and N. McCarthy, “Conical wave packets: their propagation speed and their longitudinal fields,” Proc. SPIE 3611, 332–343 (1999).
[Crossref]

C. F. R. Caron and R. M. Potvliege, “Free-space propagation of ultrashort pulses: space-time couplings in Gaussian pulse beams,” J. Mod. Opt. 46, 1881–1891 (1999).
[Crossref]

1998 (6)

M. A. Porras, “Ultrashort pulsed Gaussian light beams,” Phys. Rev. E 58, 1086–1093 (1998).
[Crossref]

G. P. Agrawal, “Spectrum-induced changes in diffraction of pulsed optical beams,” Opt. Commun. 157, 52–56 (1998).
[Crossref]

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207–211 (1998).
[Crossref]

Z. Y. Liu and D. Y. Fan, “Propagation of pulsed zeroth order Bessel beams,” J. Mod. Opt. 45, 17–22 (1998).
[Crossref]

A. E. Kaplan, “Diffraction-induced transformation of near-cycle and sub-cycle pulses,” J. Opt. Soc. Am. B 15, 951–956 (1998).
[Crossref]

S. Feng, H. G. Winful, and R. W. Hellwarth, “Gouy shift and temporal reshaping of focused single-cycle electromagnetic pulses,” Opt. Lett. 23, 385–387 (1998).
[Crossref]

1997 (4)

D. You and P. H. Bucksbaum, “Propagation of half-cycle far infrared pulses,” J. Opt. Soc. Am. B 14, 1651–1655 (1997).
[Crossref]

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

C. J. R. Sheppard and X. Gan, “Free-space propagation of femto-second light pulses,” Opt. Commun 133, 1–6 (1997).
[Crossref]

Z. Wang, Z. Zhang, Z. Xu, and Q. Lin, “Space-time profiles of the ultrashort pulsed Gaussian beam,” IEEE J. Quantum Electron. 33, 566–573 (1997).
[Crossref]

1996 (1)

1992 (2)

R. W. Ziolkowski and J. P. Judkins, “Propagation characteristics of ultrawide-bandwidth pulsed Gaussian beams,” J. Opt. Soc. Am. A 9, 2021 (1992).
[Crossref]

J. Y. Lu and J. F. Greenleaf, “Experimental verification of nondiffracting X-waves,” IEEE Trans. Ultrason. Ferrelec. Freq. Cont. 39, 19–31 (1992).
[Crossref]

1991 (2)

1987 (2)

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[Crossref]

1983 (1)

J. N. Brittingham, J. Appl. Phys. 54, “Focus wave modes in homogeneous Maxwell equations: transverse electric mode,” 1179–1189 (1983).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, “Spectrum-induced changes in diffraction of pulsed optical beams,” Opt. Commun. 157, 52–56 (1998).
[Crossref]

Altucci, C.

M. Nisoli, E. Priori, G. Sansone, S. Stagira, G. Cerullo, S. De Silvestri, C. Altucci, R. Bruzzese, C. de Lisio, P. Villoresi, L. Poletto, M. Pascolini, and G. Tondello, “High-brightness high-order harmonic generation by truncated Bessel beams in the sub-10-fs regime,” Phys. Rev. Lett. 88, 033902 (2002).
[Crossref] [PubMed]

Bock, M.

R. Grunwald, S. Huferath, M. Bock, U. Neumann, and S. Langer, “Angular tolerance of Shack-Hartmann wavefront sensors with microaxicons,” Opt. Lett. 32, 1533–1535 (2007).
[Crossref] [PubMed]

M. Bock, “Spatio-spectral diagnostics of ultrashort laser pulses by means of statistical moments,” Photonik International, 104–107 (2007).

R. Grunwald, U. Neumann, U. Griebner, G. Steinmeyer, G. Stibenz, M. Bock, and V. Kebbel, Self-reconstruction of pulsed optical X-waves, in Localized Waves, Theory and experiments, M. Zamboni-Rached, E. Recami, and H. E. Hernández-Figueroa, eds., (Wiley & Sons, New York, 2007), (in press).

Borghi, R.

M. A. Porras, R. Borghi, and M. Santarsiero, “Few-optical-cycle Bessel-Gauss pulsed beams in free space,” Phys. Rev. E 62, 5729–5730 (2000).
[Crossref]

Bouchal, Z.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207–211 (1998).
[Crossref]

Brittingham, J. N.

J. N. Brittingham, J. Appl. Phys. 54, “Focus wave modes in homogeneous Maxwell equations: transverse electric mode,” 1179–1189 (1983).
[Crossref]

Brown, C. T. A.

Bruzzese, R.

M. Nisoli, E. Priori, G. Sansone, S. Stagira, G. Cerullo, S. De Silvestri, C. Altucci, R. Bruzzese, C. de Lisio, P. Villoresi, L. Poletto, M. Pascolini, and G. Tondello, “High-brightness high-order harmonic generation by truncated Bessel beams in the sub-10-fs regime,” Phys. Rev. Lett. 88, 033902 (2002).
[Crossref] [PubMed]

Bucksbaum, P. H.

Caron, C. F. R.

C. F. R. Caron and R. M. Potvliege, “Free-space propagation of ultrashort pulses: space-time couplings in Gaussian pulse beams,” J. Mod. Opt. 46, 1881–1891 (1999).
[Crossref]

Cerullo, G.

M. Nisoli, E. Priori, G. Sansone, S. Stagira, G. Cerullo, S. De Silvestri, C. Altucci, R. Bruzzese, C. de Lisio, P. Villoresi, L. Poletto, M. Pascolini, and G. Tondello, “High-brightness high-order harmonic generation by truncated Bessel beams in the sub-10-fs regime,” Phys. Rev. Lett. 88, 033902 (2002).
[Crossref] [PubMed]

Chlup, M.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207–211 (1998).
[Crossref]

Conti, C.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[Crossref] [PubMed]

Dartora, C. A.

E. Recami, M. Zamboni-Rached, K. Z. Nóbrega, C. A. Dartora, and H. E. Hernández Figueroa, “On the localized superluminal solutions to the Maxwell equations,” IEEE J. Sel. Top. Quantum Electron. 9, 59–73 (2003).
[Crossref]

de Lisio, C.

M. Nisoli, E. Priori, G. Sansone, S. Stagira, G. Cerullo, S. De Silvestri, C. Altucci, R. Bruzzese, C. de Lisio, P. Villoresi, L. Poletto, M. Pascolini, and G. Tondello, “High-brightness high-order harmonic generation by truncated Bessel beams in the sub-10-fs regime,” Phys. Rev. Lett. 88, 033902 (2002).
[Crossref] [PubMed]

De Silvestri, S.

M. Nisoli, E. Priori, G. Sansone, S. Stagira, G. Cerullo, S. De Silvestri, C. Altucci, R. Bruzzese, C. de Lisio, P. Villoresi, L. Poletto, M. Pascolini, and G. Tondello, “High-brightness high-order harmonic generation by truncated Bessel beams in the sub-10-fs regime,” Phys. Rev. Lett. 88, 033902 (2002).
[Crossref] [PubMed]

Dholakia, K.

Di Trapani, P.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[Crossref] [PubMed]

Dopazo, J. Román

Dorrer, C.

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

Fan, D. Y.

Z. Y. Liu and D. Y. Fan, “Propagation of pulsed zeroth order Bessel beams,” J. Mod. Opt. 45, 17–22 (1998).
[Crossref]

Feng, S.

Figueroa, H. E. Hernández

E. Recami, M. Zamboni-Rached, K. Z. Nóbrega, C. A. Dartora, and H. E. Hernández Figueroa, “On the localized superluminal solutions to the Maxwell equations,” IEEE J. Sel. Top. Quantum Electron. 9, 59–73 (2003).
[Crossref]

Fischer, P.

Fortin, J.-F.

J.-F. Fortin, G. Rousseau, N. McCarthy, and M. Piché, “Generation of quasi-Bessel beams and femtosecond optical X-waves with conical mirrors,” Proc. SPIE 4833, 876–884 (2002).
[Crossref]

Fortin, M.

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piché, G. Rousseau, and M. Fortin, “Generation and characterization of spatially and temporally localized few-cycle optical wavepackets,” Phys. Rev. A 67, 063820 (2003).
[Crossref]

R. Grunwald, U. Griebner, U. Neumann, A. Kummrow, E. T. J. Nibbering, M. Rini, M. Piché, G. Rousseau, M. Fortin, N. McCarthy, and V. Kebbel, “Generation of ultrashort-pulse nondiffracting beams and X-waves with thin-film axicons,” in Ultrafast Phenomena XIII, Springer Ser. Chem. Phys. 71, R. D. Miller, M. M. Murnane, N. F. Scherer, and A. M. Weiner, eds., (Springer, Berlin, 2003) pp. 247–249.

Gan, X.

C. J. R. Sheppard and X. Gan, “Free-space propagation of femto-second light pulses,” Opt. Commun 133, 1–6 (1997).
[Crossref]

Gómez-Reino, C.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw Hill, New York, 1996), p. 60.

Gori, F.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[Crossref]

Greenleaf, J. F.

J. Y. Lu and J. F. Greenleaf, “Experimental verification of nondiffracting X-waves,” IEEE Trans. Ultrason. Ferrelec. Freq. Cont. 39, 19–31 (1992).
[Crossref]

Griebner, U.

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piché, G. Rousseau, and M. Fortin, “Generation and characterization of spatially and temporally localized few-cycle optical wavepackets,” Phys. Rev. A 67, 063820 (2003).
[Crossref]

R. Grunwald, U. Griebner, U. Neumann, A. Kummrow, E. T. J. Nibbering, M. Rini, M. Piché, G. Rousseau, M. Fortin, N. McCarthy, and V. Kebbel, “Generation of ultrashort-pulse nondiffracting beams and X-waves with thin-film axicons,” in Ultrafast Phenomena XIII, Springer Ser. Chem. Phys. 71, R. D. Miller, M. M. Murnane, N. F. Scherer, and A. M. Weiner, eds., (Springer, Berlin, 2003) pp. 247–249.

R. Grunwald, U. Neumann, U. Griebner, G. Steinmeyer, G. Stibenz, M. Bock, and V. Kebbel, Self-reconstruction of pulsed optical X-waves, in Localized Waves, Theory and experiments, M. Zamboni-Rached, E. Recami, and H. E. Hernández-Figueroa, eds., (Wiley & Sons, New York, 2007), (in press).

Grunwald, R.

R. Grunwald, S. Huferath, M. Bock, U. Neumann, and S. Langer, “Angular tolerance of Shack-Hartmann wavefront sensors with microaxicons,” Opt. Lett. 32, 1533–1535 (2007).
[Crossref] [PubMed]

R. Grunwald, U. Neumann, G. Stibenz, S. Langer, G. Steinmeyer, V. Kebbel, J.-L. Néron, and M. Piché, “Truncated ultrashort-pulse small-angle Bessel beams,” Photonics North 2004, Sept. 27–29, Ottawa, Canada, Proc. SPIE 5579, 724–735 (2004).

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piché, G. Rousseau, and M. Fortin, “Generation and characterization of spatially and temporally localized few-cycle optical wavepackets,” Phys. Rev. A 67, 063820 (2003).
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R. Grunwald, U. Neumann, U. Griebner, G. Steinmeyer, G. Stibenz, M. Bock, and V. Kebbel, Self-reconstruction of pulsed optical X-waves, in Localized Waves, Theory and experiments, M. Zamboni-Rached, E. Recami, and H. E. Hernández-Figueroa, eds., (Wiley & Sons, New York, 2007), (in press).

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P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
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Kaplan, A. E.

Kebbel, V.

R. Grunwald, U. Neumann, G. Stibenz, S. Langer, G. Steinmeyer, V. Kebbel, J.-L. Néron, and M. Piché, “Truncated ultrashort-pulse small-angle Bessel beams,” Photonics North 2004, Sept. 27–29, Ottawa, Canada, Proc. SPIE 5579, 724–735 (2004).

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piché, G. Rousseau, and M. Fortin, “Generation and characterization of spatially and temporally localized few-cycle optical wavepackets,” Phys. Rev. A 67, 063820 (2003).
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V. Kebbel, “Untersuchungen zur Erzeugung und Propagation ultrakurzer optischer Bessel-Impulse,” Doctoral thesis, University Bremen, 2004 (in German).

R. Grunwald, U. Griebner, U. Neumann, A. Kummrow, E. T. J. Nibbering, M. Rini, M. Piché, G. Rousseau, M. Fortin, N. McCarthy, and V. Kebbel, “Generation of ultrashort-pulse nondiffracting beams and X-waves with thin-film axicons,” in Ultrafast Phenomena XIII, Springer Ser. Chem. Phys. 71, R. D. Miller, M. M. Murnane, N. F. Scherer, and A. M. Weiner, eds., (Springer, Berlin, 2003) pp. 247–249.

R. Grunwald, U. Neumann, U. Griebner, G. Steinmeyer, G. Stibenz, M. Bock, and V. Kebbel, Self-reconstruction of pulsed optical X-waves, in Localized Waves, Theory and experiments, M. Zamboni-Rached, E. Recami, and H. E. Hernández-Figueroa, eds., (Wiley & Sons, New York, 2007), (in press).

Kenney, C. S.

Kosik, E. M.

Kummrow, A.

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piché, G. Rousseau, and M. Fortin, “Generation and characterization of spatially and temporally localized few-cycle optical wavepackets,” Phys. Rev. A 67, 063820 (2003).
[Crossref]

R. Grunwald, U. Griebner, U. Neumann, A. Kummrow, E. T. J. Nibbering, M. Rini, M. Piché, G. Rousseau, M. Fortin, N. McCarthy, and V. Kebbel, “Generation of ultrashort-pulse nondiffracting beams and X-waves with thin-film axicons,” in Ultrafast Phenomena XIII, Springer Ser. Chem. Phys. 71, R. D. Miller, M. M. Murnane, N. F. Scherer, and A. M. Weiner, eds., (Springer, Berlin, 2003) pp. 247–249.

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R. Grunwald, S. Huferath, M. Bock, U. Neumann, and S. Langer, “Angular tolerance of Shack-Hartmann wavefront sensors with microaxicons,” Opt. Lett. 32, 1533–1535 (2007).
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R. Grunwald, U. Neumann, G. Stibenz, S. Langer, G. Steinmeyer, V. Kebbel, J.-L. Néron, and M. Piché, “Truncated ultrashort-pulse small-angle Bessel beams,” Photonics North 2004, Sept. 27–29, Ottawa, Canada, Proc. SPIE 5579, 724–735 (2004).

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Z. Wang, Z. Zhang, Z. Xu, and Q. Lin, “Space-time profiles of the ultrashort pulsed Gaussian beam,” IEEE J. Quantum Electron. 33, 566–573 (1997).
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J.-F. Fortin, G. Rousseau, N. McCarthy, and M. Piché, “Generation of quasi-Bessel beams and femtosecond optical X-waves with conical mirrors,” Proc. SPIE 4833, 876–884 (2002).
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M. Piché, G. Rousseau, C. Varin, and N. McCarthy, “Conical wave packets: their propagation speed and their longitudinal fields,” Proc. SPIE 3611, 332–343 (1999).
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R. Grunwald, U. Griebner, U. Neumann, A. Kummrow, E. T. J. Nibbering, M. Rini, M. Piché, G. Rousseau, M. Fortin, N. McCarthy, and V. Kebbel, “Generation of ultrashort-pulse nondiffracting beams and X-waves with thin-film axicons,” in Ultrafast Phenomena XIII, Springer Ser. Chem. Phys. 71, R. D. Miller, M. M. Murnane, N. F. Scherer, and A. M. Weiner, eds., (Springer, Berlin, 2003) pp. 247–249.

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Néron, J.-L.

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Neumann, U.

R. Grunwald, S. Huferath, M. Bock, U. Neumann, and S. Langer, “Angular tolerance of Shack-Hartmann wavefront sensors with microaxicons,” Opt. Lett. 32, 1533–1535 (2007).
[Crossref] [PubMed]

R. Grunwald, U. Neumann, G. Stibenz, S. Langer, G. Steinmeyer, V. Kebbel, J.-L. Néron, and M. Piché, “Truncated ultrashort-pulse small-angle Bessel beams,” Photonics North 2004, Sept. 27–29, Ottawa, Canada, Proc. SPIE 5579, 724–735 (2004).

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piché, G. Rousseau, and M. Fortin, “Generation and characterization of spatially and temporally localized few-cycle optical wavepackets,” Phys. Rev. A 67, 063820 (2003).
[Crossref]

R. Grunwald, U. Griebner, U. Neumann, A. Kummrow, E. T. J. Nibbering, M. Rini, M. Piché, G. Rousseau, M. Fortin, N. McCarthy, and V. Kebbel, “Generation of ultrashort-pulse nondiffracting beams and X-waves with thin-film axicons,” in Ultrafast Phenomena XIII, Springer Ser. Chem. Phys. 71, R. D. Miller, M. M. Murnane, N. F. Scherer, and A. M. Weiner, eds., (Springer, Berlin, 2003) pp. 247–249.

R. Grunwald, U. Neumann, U. Griebner, G. Steinmeyer, G. Stibenz, M. Bock, and V. Kebbel, Self-reconstruction of pulsed optical X-waves, in Localized Waves, Theory and experiments, M. Zamboni-Rached, E. Recami, and H. E. Hernández-Figueroa, eds., (Wiley & Sons, New York, 2007), (in press).

Nibbering, E. T. J.

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piché, G. Rousseau, and M. Fortin, “Generation and characterization of spatially and temporally localized few-cycle optical wavepackets,” Phys. Rev. A 67, 063820 (2003).
[Crossref]

R. Grunwald, U. Griebner, U. Neumann, A. Kummrow, E. T. J. Nibbering, M. Rini, M. Piché, G. Rousseau, M. Fortin, N. McCarthy, and V. Kebbel, “Generation of ultrashort-pulse nondiffracting beams and X-waves with thin-film axicons,” in Ultrafast Phenomena XIII, Springer Ser. Chem. Phys. 71, R. D. Miller, M. M. Murnane, N. F. Scherer, and A. M. Weiner, eds., (Springer, Berlin, 2003) pp. 247–249.

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M. Nisoli, E. Priori, G. Sansone, S. Stagira, G. Cerullo, S. De Silvestri, C. Altucci, R. Bruzzese, C. de Lisio, P. Villoresi, L. Poletto, M. Pascolini, and G. Tondello, “High-brightness high-order harmonic generation by truncated Bessel beams in the sub-10-fs regime,” Phys. Rev. Lett. 88, 033902 (2002).
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E. Recami, M. Zamboni-Rached, K. Z. Nóbrega, C. A. Dartora, and H. E. Hernández Figueroa, “On the localized superluminal solutions to the Maxwell equations,” IEEE J. Sel. Top. Quantum Electron. 9, 59–73 (2003).
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Padovani, C.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64, 491–495 (1987).
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M. Nisoli, E. Priori, G. Sansone, S. Stagira, G. Cerullo, S. De Silvestri, C. Altucci, R. Bruzzese, C. de Lisio, P. Villoresi, L. Poletto, M. Pascolini, and G. Tondello, “High-brightness high-order harmonic generation by truncated Bessel beams in the sub-10-fs regime,” Phys. Rev. Lett. 88, 033902 (2002).
[Crossref] [PubMed]

Piché, M.

R. Grunwald, U. Neumann, G. Stibenz, S. Langer, G. Steinmeyer, V. Kebbel, J.-L. Néron, and M. Piché, “Truncated ultrashort-pulse small-angle Bessel beams,” Photonics North 2004, Sept. 27–29, Ottawa, Canada, Proc. SPIE 5579, 724–735 (2004).

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piché, G. Rousseau, and M. Fortin, “Generation and characterization of spatially and temporally localized few-cycle optical wavepackets,” Phys. Rev. A 67, 063820 (2003).
[Crossref]

J.-F. Fortin, G. Rousseau, N. McCarthy, and M. Piché, “Generation of quasi-Bessel beams and femtosecond optical X-waves with conical mirrors,” Proc. SPIE 4833, 876–884 (2002).
[Crossref]

M. Piché, G. Rousseau, C. Varin, and N. McCarthy, “Conical wave packets: their propagation speed and their longitudinal fields,” Proc. SPIE 3611, 332–343 (1999).
[Crossref]

R. Grunwald, U. Griebner, U. Neumann, A. Kummrow, E. T. J. Nibbering, M. Rini, M. Piché, G. Rousseau, M. Fortin, N. McCarthy, and V. Kebbel, “Generation of ultrashort-pulse nondiffracting beams and X-waves with thin-film axicons,” in Ultrafast Phenomena XIII, Springer Ser. Chem. Phys. 71, R. D. Miller, M. M. Murnane, N. F. Scherer, and A. M. Weiner, eds., (Springer, Berlin, 2003) pp. 247–249.

Piskarskas, A.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[Crossref] [PubMed]

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M. Nisoli, E. Priori, G. Sansone, S. Stagira, G. Cerullo, S. De Silvestri, C. Altucci, R. Bruzzese, C. de Lisio, P. Villoresi, L. Poletto, M. Pascolini, and G. Tondello, “High-brightness high-order harmonic generation by truncated Bessel beams in the sub-10-fs regime,” Phys. Rev. Lett. 88, 033902 (2002).
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M. Nisoli, E. Priori, G. Sansone, S. Stagira, G. Cerullo, S. De Silvestri, C. Altucci, R. Bruzzese, C. de Lisio, P. Villoresi, L. Poletto, M. Pascolini, and G. Tondello, “High-brightness high-order harmonic generation by truncated Bessel beams in the sub-10-fs regime,” Phys. Rev. Lett. 88, 033902 (2002).
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E. Recami, M. Zamboni-Rached, K. Z. Nóbrega, C. A. Dartora, and H. E. Hernández Figueroa, “On the localized superluminal solutions to the Maxwell equations,” IEEE J. Sel. Top. Quantum Electron. 9, 59–73 (2003).
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K. Reivelt and P. Saari, “Bessel-Gauss pulse as an appropriate mathematical model for optically realizable localized waves,” Opt. Lett. 29, 1176–1178 (2004).
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R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piché, G. Rousseau, and M. Fortin, “Generation and characterization of spatially and temporally localized few-cycle optical wavepackets,” Phys. Rev. A 67, 063820 (2003).
[Crossref]

R. Grunwald, U. Griebner, U. Neumann, A. Kummrow, E. T. J. Nibbering, M. Rini, M. Piché, G. Rousseau, M. Fortin, N. McCarthy, and V. Kebbel, “Generation of ultrashort-pulse nondiffracting beams and X-waves with thin-film axicons,” in Ultrafast Phenomena XIII, Springer Ser. Chem. Phys. 71, R. D. Miller, M. M. Murnane, N. F. Scherer, and A. M. Weiner, eds., (Springer, Berlin, 2003) pp. 247–249.

Rousseau, G.

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piché, G. Rousseau, and M. Fortin, “Generation and characterization of spatially and temporally localized few-cycle optical wavepackets,” Phys. Rev. A 67, 063820 (2003).
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J.-F. Fortin, G. Rousseau, N. McCarthy, and M. Piché, “Generation of quasi-Bessel beams and femtosecond optical X-waves with conical mirrors,” Proc. SPIE 4833, 876–884 (2002).
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M. Piché, G. Rousseau, C. Varin, and N. McCarthy, “Conical wave packets: their propagation speed and their longitudinal fields,” Proc. SPIE 3611, 332–343 (1999).
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R. Grunwald, U. Griebner, U. Neumann, A. Kummrow, E. T. J. Nibbering, M. Rini, M. Piché, G. Rousseau, M. Fortin, N. McCarthy, and V. Kebbel, “Generation of ultrashort-pulse nondiffracting beams and X-waves with thin-film axicons,” in Ultrafast Phenomena XIII, Springer Ser. Chem. Phys. 71, R. D. Miller, M. M. Murnane, N. F. Scherer, and A. M. Weiner, eds., (Springer, Berlin, 2003) pp. 247–249.

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K. Reivelt and P. Saari, “Bessel-Gauss pulse as an appropriate mathematical model for optically realizable localized waves,” Opt. Lett. 29, 1176–1178 (2004).
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P. Saari and K. Reivelt, “Generation and classification of localized waves by Lorentz transformations in Fourier space,” Phys. Rev. E 69, 036612 (2004).
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P. Saari and K. Reivelt, “Evidence of X-shaped propagation-invariant localized light waves,” Phys. Rev. Lett. 79, 4135–4138 (1997).
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M. Nisoli, E. Priori, G. Sansone, S. Stagira, G. Cerullo, S. De Silvestri, C. Altucci, R. Bruzzese, C. de Lisio, P. Villoresi, L. Poletto, M. Pascolini, and G. Tondello, “High-brightness high-order harmonic generation by truncated Bessel beams in the sub-10-fs regime,” Phys. Rev. Lett. 88, 033902 (2002).
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M. A. Porras, R. Borghi, and M. Santarsiero, “Few-optical-cycle Bessel-Gauss pulsed beams in free space,” Phys. Rev. E 62, 5729–5730 (2000).
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R. Grunwald, U. Neumann, G. Stibenz, S. Langer, G. Steinmeyer, V. Kebbel, J.-L. Néron, and M. Piché, “Truncated ultrashort-pulse small-angle Bessel beams,” Photonics North 2004, Sept. 27–29, Ottawa, Canada, Proc. SPIE 5579, 724–735 (2004).

R. Grunwald, U. Neumann, U. Griebner, G. Steinmeyer, G. Stibenz, M. Bock, and V. Kebbel, Self-reconstruction of pulsed optical X-waves, in Localized Waves, Theory and experiments, M. Zamboni-Rached, E. Recami, and H. E. Hernández-Figueroa, eds., (Wiley & Sons, New York, 2007), (in press).

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G. Steinmeyer and G. Stibenz, “Generation of sub-4-fs pulses via compression of a white-light continuum using only chirped mirrors,” Appl. Phys. B 82, 175–81 (2006).
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G. Stibenz and G. Steinmeyer, “Optimizing spectral phase interferometry for direct electric-field reconstruction,” Rev. Sci. Instrum. 77, 073105 (2006).
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R. Grunwald, U. Neumann, G. Stibenz, S. Langer, G. Steinmeyer, V. Kebbel, J.-L. Néron, and M. Piché, “Truncated ultrashort-pulse small-angle Bessel beams,” Photonics North 2004, Sept. 27–29, Ottawa, Canada, Proc. SPIE 5579, 724–735 (2004).

R. Grunwald, U. Neumann, U. Griebner, G. Steinmeyer, G. Stibenz, M. Bock, and V. Kebbel, Self-reconstruction of pulsed optical X-waves, in Localized Waves, Theory and experiments, M. Zamboni-Rached, E. Recami, and H. E. Hernández-Figueroa, eds., (Wiley & Sons, New York, 2007), (in press).

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M. Nisoli, E. Priori, G. Sansone, S. Stagira, G. Cerullo, S. De Silvestri, C. Altucci, R. Bruzzese, C. de Lisio, P. Villoresi, L. Poletto, M. Pascolini, and G. Tondello, “High-brightness high-order harmonic generation by truncated Bessel beams in the sub-10-fs regime,” Phys. Rev. Lett. 88, 033902 (2002).
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P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
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P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
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P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
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M. Piché, G. Rousseau, C. Varin, and N. McCarthy, “Conical wave packets: their propagation speed and their longitudinal fields,” Proc. SPIE 3611, 332–343 (1999).
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M. Nisoli, E. Priori, G. Sansone, S. Stagira, G. Cerullo, S. De Silvestri, C. Altucci, R. Bruzzese, C. de Lisio, P. Villoresi, L. Poletto, M. Pascolini, and G. Tondello, “High-brightness high-order harmonic generation by truncated Bessel beams in the sub-10-fs regime,” Phys. Rev. Lett. 88, 033902 (2002).
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Z. Wang, Z. Zhang, Z. Xu, and Q. Lin, “Space-time profiles of the ultrashort pulsed Gaussian beam,” IEEE J. Quantum Electron. 33, 566–573 (1997).
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Zamboni-Rached, M.

E. Recami, M. Zamboni-Rached, K. Z. Nóbrega, C. A. Dartora, and H. E. Hernández Figueroa, “On the localized superluminal solutions to the Maxwell equations,” IEEE J. Sel. Top. Quantum Electron. 9, 59–73 (2003).
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Z. Wang, Z. Zhang, Z. Xu, and Q. Lin, “Space-time profiles of the ultrashort pulsed Gaussian beam,” IEEE J. Quantum Electron. 33, 566–573 (1997).
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G. Steinmeyer and G. Stibenz, “Generation of sub-4-fs pulses via compression of a white-light continuum using only chirped mirrors,” Appl. Phys. B 82, 175–81 (2006).
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R. Grunwald, U. Griebner, U. Neumann, A. Kummrow, E. T. J. Nibbering, M. Rini, M. Piché, G. Rousseau, M. Fortin, N. McCarthy, and V. Kebbel, “Generation of ultrashort-pulse nondiffracting beams and X-waves with thin-film axicons,” in Ultrafast Phenomena XIII, Springer Ser. Chem. Phys. 71, R. D. Miller, M. M. Murnane, N. F. Scherer, and A. M. Weiner, eds., (Springer, Berlin, 2003) pp. 247–249.

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M. Bock, “Spatio-spectral diagnostics of ultrashort laser pulses by means of statistical moments,” Photonik International, 104–107 (2007).

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Figures (12)

Fig. 1.
Fig. 1.

Principle of the self-apodized truncation of Bessel-like beams (schematically): (a) Transmitted Bessel-like intensity fringe pattern for an aperture diameter d large compared to the diameter of the first minimum 2r0 , (b) truncation of the intensity profile (radial cut) by an optimized aperture of d=2r0 , and (c) transmitted central lobe shaping a single-maximum beam (“needle beam”) without diffraction at the aperture rim.

Fig. 2.
Fig. 2.

Numerical simulations of time-integrated propagation of an untruncated pulsed Bessel-Gauss beam: (a) and (b) show the axial propagation in the r-z-plane for intensity and square root of amplitude, respectively. The propagation invariance can be recognized in corresponding radial cuts at different distances in (c)–(f). Dashed lines in (a) and (b) mark the positions of these planes of interest. zD , marks the position of the diaphragm in the subsequent simulation, cf. Fig. 3. Pulse duration and spectral distribution correspond to experimental parameters of a 10-fs Ti:sapphire laser oscillator. The calculations were performed on the basis of angular spectrum representation.

Fig. 3.
Fig. 3.

Simulated propagation of a pulsed Bessel-Gauss beam truncated by a diaphragm D with a diameter d=2rD located a few cm in front of the intensity maximum (a,b) and propagation of an idealized pulsed Gaussian beam of comparable waist radius w0 (c,d). The intensity representations in (a,c) show needle-like focal zones (notice the different scales for z and r). To enhance the visibility of details, the square root of field amplitudes is plotted in (b) and (d). Pulse duration and spectral distribution were assumed to be identical to Fig. 2. To obtain compatible spatial parameters, the second moments at the positions of maximum intensity of both types of focal zones were matched. The dashed line marks the position of the Gaussian beam waist.

Fig. 4.
Fig. 4.

Spectral distribution used for the numerical simulation of polychromatic pulsed BGB and Gaussian beams as shown in Figs. 3(a)–3(d). The FWHM bandwidth was about 120 nm.

Fig. 5.
Fig. 5.

Beam radii (standard deviation) of a truncated pulsed Bessel-Gaussian beam and a pulsed Gaussian beam with an idealized spectrum calculated from simulated near field intensity propagation and for time-integrated detection. In proximity of the diaphragm, the truncated pulsed BGB is less divergent compared to a Gaussian beam, which is why we refer to this interval as “nondiffracting zone”. However, towards the transition to the far field, i.e., well behind the Rayleigh range, the pulsed Gaussian beam displays a somewhat lower divergence.

Fig. 6.
Fig. 6.

Generation of pulsed Bessel-Gauss beams by conical axicons: (a) measured thickness profile of a thin-film axicon (total diameter 1 cm, Au-coated Cu structure, apex angle 0.027°, (b) Intensity distribution of the pulsed BGB (central lobe and first maximum) generated by illuminating the axicon with 10-fs Ti:sapphire laser pulses (spectral FWHM 120 nm, imaged plane at an axial distance z=87.5 cm from the axicon, field of view 1×1 mm2).

Fig. 7.
Fig. 7.

Experimental setup for the self-apodized truncation of a pulsed Bessel-Gauss beam generated by a thin-film axicon. (a) Spatio-spectral mapping by scanning with a fiber-based spectrometer, utilizing a 15 µm pinhole in proximity to the fiber. (b) 3D analysis of the beam propagation by microscopic imaging onto a CCD camera (schematically).

Fig. 8.
Fig. 8.

Radial cuts through the measured time integrated intensity propagation of a truncated pulsed Bessel-Gauss beam generated by a 10-fs Ti:sapphire laser pulse (diameter of diaphragm d=450 µm at a distance of 110 cm behind the axicon, FOV=960×960 µm2). The distance z-zD is the propagation distance relative to the truncating diaphragm.

Fig. 9.
Fig. 9.

Spatial propagation of a truncated pulsed Bessel-Gauss beam generated from a 10-fs Ti:sapphire laser pulse with a reflective axicon (axicon diameter 1 cm, conical angle 0.027°) for an axial position of the diaphragm at about z=110 cm. In agreement with the theoretical simulations, a needle-shaped propagation zone appears at a time-integrated detection with a CCD camera (Vosskuehler, 4 Megapixels). The plot shows a two-dimensional cut (r-z-plane) of a 3D propagation zone (normalized intensity represented by contour levels increasing in linear steps).

Fig. 10.
Fig. 10.

Spectral mapping of pulsed BGBs represented by two-dimensionally resolved spectral moments in planes perpendicular to the optical axis for the untruncated (a–d) and truncated beam (e–h), M1 =first order moments (a,e), M2 =second order moments (b,f), M3 =third order moments (c,g), M4 =fourth order moments (d,h). The spectra were detected with a time-integrating detector. The rim of the truncating diaphragms is schematically indicated by the red dashed circle in (a).

Fig. 11.
Fig. 11.

Temporal transfer of the ultrashort-pulsed BGB after self-apodized truncation proved by second order autocorrelation: noncollinear autocorrelation traces (normalized, after subtracting background and averaging positive and negative envelope functions) measured at two different distances from the diaphragm (z-zD =0 cm and z-zD =14.5 cm).

Fig. 12.
Fig. 12.

Spatio-spectral mapping of transversal cuts through the focal region of a pulsed Gaussian beam at a pulse duration of 10 fs) by a vertical scan of the spectrometer-fiber. Normalized spectra (color code) were measured at two different axial distances: (a) z=256 cm, (b) z=276 cm.

Equations (2)

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U ( r ) J 0 = k = 0 ( 1 ) k ( r 2 ) 2 k ( k ! ) 2 ,
U ( r , z , t ) = 0 S ( ω ) J 0 ( k ρ r ) exp [ i ( k z z ω t ) ] d ω ,

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