Abstract

We present measurements of the impulse response of a circular phase diffraction grating in dependence of the field point location behind it. These measurements were carried out using a white-light spectral interferometry set-up, which employs photonic crystal fibers in both the signal and reference arms, and achieves a few micron spatial and almost one-wave-cycle temporal resolution. Our study shows that the grating as a simple and robust single-element optical device (i) suppresses the material-induced spread of ultrashort pulses, (ii) thereby generates the Airy–Bessel light bullets, and (iii) enables temporal focusing of the pulses at the prescribed propagation depth.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Baker, I. A. Walmsley, J. W. G. Tisch, and J. P. Marangos, “Femtosecond to attosecond light pulses from a molecular modulator,” Nat. Photonics 5, 664–671 (2011).
    [CrossRef]
  2. B. Piglosiewicz, D. Sadiq, M. Mascheck, S. Schmidt, M. Silies, P. Vasa, and C. Lienau, “Ultrasmall bullets of light—focusing few-cycle light pulses to the diffraction limit,” Opt. Express 19, 14451–14463 (2011).
    [CrossRef] [PubMed]
  3. T. Kobayashi, J. Liu, and K. Okamura, “Applications of parametric processes to high-quality multicolour ultrashort pulses, pulse cleaning and cep stable sub-3fs pulse,” J. Phys. B. 45, 074005 (2012).
    [CrossRef]
  4. A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” New J. Phys. 9, 242 (2007).
    [CrossRef]
  5. R. Trebino, “Measuring the seemingly immeasurable,” Nat. Photonics 5, 189–192 (2011).
    [CrossRef]
  6. I. A. Walmsley and C. Dorrer, “Characterization of ultrashort electromagnetic pulses,” Adv. Opt. Photon. 1, 308–437 (2009).
    [CrossRef]
  7. E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. 5, 454–458 (1969).
    [CrossRef]
  8. P. Saari, J. Aaviksoo, A. Freiberg, and K. Timpmann, “Elimination of excess pulse broadening at high spectral resolution of picosecond duration light emission,” Opt. Commun. 39, 94–98 (1981).
    [CrossRef]
  9. R. Imhof and D. Birch, “Distortion of Gaussian pulses by a diffraction grating,” Opt. Commun. 42, 83–86 (1982).
    [CrossRef]
  10. J. Dyson, “Circular and spiral diffraction gratings,” Proc. R. Soc. Lond. A 248, 93–106 (1958).
    [CrossRef]
  11. 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, 310–312 (1997).
    [CrossRef] [PubMed]
  12. M. Clerici, D. Faccio, E. Rubino, A. Lotti, A. Couairon, and P. D. Trapani, “Space–time focusing of Bessel-like pulses,” Opt. Lett. 35, 3267–3269 (2010).
    [CrossRef] [PubMed]
  13. A. M. Shaarawi and I. M. Besieris, “On the superluminal propagation of X-shaped localized waves,” J. Phys. A. 33, 7227–7254 (2000).
    [CrossRef]
  14. P. Saari and K. Reivelt, “Evidence of X-shaped propagation-invariant localized light waves,” Phys. Rev. Lett. 79, 4135–4138 (1997).
    [CrossRef]
  15. 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, 2276–2278 (2009).
    [CrossRef] [PubMed]
  16. O. Mendoza-Yero, B. Alonso, O. Varela, G. Mínguez-Vega, Í. J. Sola, J. Lancis, V. Climent, and L. Roso, “Spatio-temporal characterization of ultrashort pulses diffracted by circularly symmetric hard-edge apertures: theory and experiment,” Opt. Express 18, 20900–20911 (2010).
    [CrossRef] [PubMed]
  17. M. Lõhmus, P. Bowlan, P. Piksarv, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort optical pulses from circularly symmetric binary phase gratings,” Opt. Lett 37, 1238–1240 (2012).
    [CrossRef] [PubMed]
  18. S. Akturk, X. Gu, P. Bowlan, and R. Trebino, “Spatio-temporal couplings in ultrashort laser pulses,” J. Opt. 12, 093001 (2010).
    [CrossRef]
  19. 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, 11892–11900 (2006).
    [CrossRef] [PubMed]
  20. P. Bowlan, P. Gabolde, M. A. Coughlan, R. Trebino, and R. J. Levis, “Measuring the spatiotemporal electric field of ultrashort pulses with high spatial and spectral resolution,” J. Opt. Soc. Am. B 25, A81–A92 (2008).
    [CrossRef]
  21. B. Alonso, Í. J. Sola, Ó. Varela, J. Hernández-Toro, C. Méndez, J. S. Román, A. Zaïr, and L. Roso, “Spatiotemporal amplitude-and-phase reconstruction by fourier-transform of interference spectra of high-complex-beams,” J. Opt. Soc. Am. B 27, 933–940 (2010).
    [CrossRef]
  22. T. Witting, F. Frank, C. A. Arrell, W. A. Okell, J. P. Marangos, and J. W. G. Tisch, “Characterization of high-intensity sub-4-fs laser pulses using spatially encoded spectral shearing interferometry,” Opt. Lett. 36, 1680–1682 (2011).
    [CrossRef] [PubMed]
  23. H. Valtna-Lukner, P. Bowlan, M. Lõhmus, P. Piksarv, R. Trebino, and P. Saari, “Direct spatiotemporal measurements of accelerating ultrashort Bessel-type light bullets,” Opt. Express 17, 14948–14955 (2009).
    [CrossRef] [PubMed]
  24. P. Saari, P. Bowlan, H. Valtna-Lukner, M. Lõhmus, P. Piksarv, and R. Trebino, “Basic diffraction phenomena in time domain,” Opt. Express 18, 11083–11088 (2010).
    [CrossRef] [PubMed]
  25. P. Piksarv, P. Bowlan, M. Lõhmus, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort Gaussian pulses within the framework of boundary diffraction wave theory,” J. Opt. 14, 015701 (2012).
    [CrossRef]
  26. Z. Liu and D. Fan, “Propagation of pulsed zeroth-order Bessel beams,” J. Mod. Opt. 45, 17–21 (1998).
    [CrossRef]
  27. W. Hu and H. Guo, “Ultrashort pulsed Bessel beams and spatially induced group-velocity dispersion,” J. Opt. Soc. Am. A 19, 49–53 (2002).
    [CrossRef]
  28. M. A. Porras, “Diffraction effects in few-cycle optical pulses,” Phys. Rev. E 65, 026606 (2002).
    [CrossRef]
  29. V. Jarutis, R. Paškauskas, and A. Stabinis, “Focusing of Laguerre–Gaussian beams by axicon,” Opt. Commun. 184, 105–112 (2000).
    [CrossRef]
  30. D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test (SPIE, 2003).
  31. A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
    [CrossRef]
  32. Z. Ren, H. Jin, Y. Shi, J. Xu, W. Zhou, and H. Wang, “Spatially induced spatiotemporally nonspreading airy–bessel wave packets,” J. Opt. Soc. Am. A 29, 848–853 (2012).
    [CrossRef]
  33. J. Piasecki, P. Colombeau, M. Vampouille, C. Froehly, and J. A. Arnaud, “Nouvelle méthode de mesure de la réponse impulsionnelle des fibres optiques,” Appl. Opt. 19, 3749–3755 (1980).
    [CrossRef] [PubMed]
  34. C. Sainz, J. E. Calatroni, and G. Tribillon, “Refractometry of liquid samples with spectrally resolved white light interferometry,” Meas. Sci. Technol. 1, 356–361 (1990).
    [CrossRef]
  35. A. P. Kovács, K. Osvay, Z. Bor, and R. Szipöcs, “Group-delay measurement on laser mirrors by spectrally resolved white-light interferometry,” Opt. Lett. 20, 788–790 (1995).
    [CrossRef] [PubMed]
  36. A. Börzsönyi, A. Kovács, M. Görbe, and K. Osvay, “Advances and limitations of phase dispersion measurement by spectrally and spatially resolved interferometry,” Opt. Commun. 281, 3051–3061 (2008).
    [CrossRef]
  37. N. Abramson, “Light-in-flight recording by holography,” Opt. Lett. 3, 121–123 (1978).
    [CrossRef] [PubMed]
  38. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
    [CrossRef] [PubMed]
  39. M. Roy, P. Svahn, L. Cherel, and C. J. R. Sheppard, “Geometric phase-shifting for low-coherence interference microscopy,” Opt. Laser Eng. 37, 631–641 (2002).
    [CrossRef]
  40. M. Akiba, K. P. Chan, and N. Tanno, “Full-field optical coherence tomography by two-dimensional heterodyne detection with a pair of CCD cameras,” Opt. Lett. 28, 816–818 (2003).
    [CrossRef] [PubMed]
  41. J. C. Knight, “Photonic crystal fibres,” Nature 424, 847–851 (2003).
    [CrossRef] [PubMed]
  42. J. Cohen, P. Bowlan, V. Chauhan, P. Vaughan, and R. Trebino, “Measuring extremely complex pulses with time-bandwidth products exceeding 65,000 using multiple-delay crossed-beam spectral interferometry,” Opt. Express 18, 24451–24460 (2010).
    [CrossRef] [PubMed]
  43. P. Bowlan and R. Trebino, “Using phase diversity for the measurement of the complete spatiotemporal electric field of ultrashort laser pulses,” J. Opt. Soc. Am. B 29, 244–248 (2012).
    [CrossRef]

2012 (5)

T. Kobayashi, J. Liu, and K. Okamura, “Applications of parametric processes to high-quality multicolour ultrashort pulses, pulse cleaning and cep stable sub-3fs pulse,” J. Phys. B. 45, 074005 (2012).
[CrossRef]

M. Lõhmus, P. Bowlan, P. Piksarv, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort optical pulses from circularly symmetric binary phase gratings,” Opt. Lett 37, 1238–1240 (2012).
[CrossRef] [PubMed]

P. Piksarv, P. Bowlan, M. Lõhmus, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort Gaussian pulses within the framework of boundary diffraction wave theory,” J. Opt. 14, 015701 (2012).
[CrossRef]

Z. Ren, H. Jin, Y. Shi, J. Xu, W. Zhou, and H. Wang, “Spatially induced spatiotemporally nonspreading airy–bessel wave packets,” J. Opt. Soc. Am. A 29, 848–853 (2012).
[CrossRef]

P. Bowlan and R. Trebino, “Using phase diversity for the measurement of the complete spatiotemporal electric field of ultrashort laser pulses,” J. Opt. Soc. Am. B 29, 244–248 (2012).
[CrossRef]

2011 (4)

2010 (7)

S. Akturk, X. Gu, P. Bowlan, and R. Trebino, “Spatio-temporal couplings in ultrashort laser pulses,” J. Opt. 12, 093001 (2010).
[CrossRef]

O. Mendoza-Yero, B. Alonso, O. Varela, G. Mínguez-Vega, Í. J. Sola, J. Lancis, V. Climent, and L. Roso, “Spatio-temporal characterization of ultrashort pulses diffracted by circularly symmetric hard-edge apertures: theory and experiment,” Opt. Express 18, 20900–20911 (2010).
[CrossRef] [PubMed]

M. Clerici, D. Faccio, E. Rubino, A. Lotti, A. Couairon, and P. D. Trapani, “Space–time focusing of Bessel-like pulses,” Opt. Lett. 35, 3267–3269 (2010).
[CrossRef] [PubMed]

B. Alonso, Í. J. Sola, Ó. Varela, J. Hernández-Toro, C. Méndez, J. S. Román, A. Zaïr, and L. Roso, “Spatiotemporal amplitude-and-phase reconstruction by fourier-transform of interference spectra of high-complex-beams,” J. Opt. Soc. Am. B 27, 933–940 (2010).
[CrossRef]

P. Saari, P. Bowlan, H. Valtna-Lukner, M. Lõhmus, P. Piksarv, and R. Trebino, “Basic diffraction phenomena in time domain,” Opt. Express 18, 11083–11088 (2010).
[CrossRef] [PubMed]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
[CrossRef]

J. Cohen, P. Bowlan, V. Chauhan, P. Vaughan, and R. Trebino, “Measuring extremely complex pulses with time-bandwidth products exceeding 65,000 using multiple-delay crossed-beam spectral interferometry,” Opt. Express 18, 24451–24460 (2010).
[CrossRef] [PubMed]

2009 (3)

2008 (2)

P. Bowlan, P. Gabolde, M. A. Coughlan, R. Trebino, and R. J. Levis, “Measuring the spatiotemporal electric field of ultrashort pulses with high spatial and spectral resolution,” J. Opt. Soc. Am. B 25, A81–A92 (2008).
[CrossRef]

A. Börzsönyi, A. Kovács, M. Görbe, and K. Osvay, “Advances and limitations of phase dispersion measurement by spectrally and spatially resolved interferometry,” Opt. Commun. 281, 3051–3061 (2008).
[CrossRef]

2007 (1)

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” New J. Phys. 9, 242 (2007).
[CrossRef]

2006 (1)

2003 (2)

2002 (3)

M. Roy, P. Svahn, L. Cherel, and C. J. R. Sheppard, “Geometric phase-shifting for low-coherence interference microscopy,” Opt. Laser Eng. 37, 631–641 (2002).
[CrossRef]

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

M. A. Porras, “Diffraction effects in few-cycle optical pulses,” Phys. Rev. E 65, 026606 (2002).
[CrossRef]

2000 (2)

V. Jarutis, R. Paškauskas, and A. Stabinis, “Focusing of Laguerre–Gaussian beams by axicon,” Opt. Commun. 184, 105–112 (2000).
[CrossRef]

A. M. Shaarawi and I. M. Besieris, “On the superluminal propagation of X-shaped localized waves,” J. Phys. A. 33, 7227–7254 (2000).
[CrossRef]

1998 (1)

Z. Liu and D. Fan, “Propagation of pulsed zeroth-order Bessel beams,” J. Mod. Opt. 45, 17–21 (1998).
[CrossRef]

1997 (2)

1995 (1)

1991 (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

1990 (1)

C. Sainz, J. E. Calatroni, and G. Tribillon, “Refractometry of liquid samples with spectrally resolved white light interferometry,” Meas. Sci. Technol. 1, 356–361 (1990).
[CrossRef]

1982 (1)

R. Imhof and D. Birch, “Distortion of Gaussian pulses by a diffraction grating,” Opt. Commun. 42, 83–86 (1982).
[CrossRef]

1981 (1)

P. Saari, J. Aaviksoo, A. Freiberg, and K. Timpmann, “Elimination of excess pulse broadening at high spectral resolution of picosecond duration light emission,” Opt. Commun. 39, 94–98 (1981).
[CrossRef]

1980 (1)

1978 (1)

1969 (1)

E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. 5, 454–458 (1969).
[CrossRef]

1958 (1)

J. Dyson, “Circular and spiral diffraction gratings,” Proc. R. Soc. Lond. A 248, 93–106 (1958).
[CrossRef]

Aaviksoo, J.

P. Saari, J. Aaviksoo, A. Freiberg, and K. Timpmann, “Elimination of excess pulse broadening at high spectral resolution of picosecond duration light emission,” Opt. Commun. 39, 94–98 (1981).
[CrossRef]

Abramson, N.

Akiba, M.

Akturk, S.

Alonso, B.

Apolonski, A.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” New J. Phys. 9, 242 (2007).
[CrossRef]

Arnaud, J. A.

Arrell, C. A.

Baker, S.

S. Baker, I. A. Walmsley, J. W. G. Tisch, and J. P. Marangos, “Femtosecond to attosecond light pulses from a molecular modulator,” Nat. Photonics 5, 664–671 (2011).
[CrossRef]

Besieris, I. M.

A. M. Shaarawi and I. M. Besieris, “On the superluminal propagation of X-shaped localized waves,” J. Phys. A. 33, 7227–7254 (2000).
[CrossRef]

Birch, D.

R. Imhof and D. Birch, “Distortion of Gaussian pulses by a diffraction grating,” Opt. Commun. 42, 83–86 (1982).
[CrossRef]

Bor, Z.

Börzsönyi, A.

A. Börzsönyi, A. Kovács, M. Görbe, and K. Osvay, “Advances and limitations of phase dispersion measurement by spectrally and spatially resolved interferometry,” Opt. Commun. 281, 3051–3061 (2008).
[CrossRef]

Bowlan, P.

M. Lõhmus, P. Bowlan, P. Piksarv, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort optical pulses from circularly symmetric binary phase gratings,” Opt. Lett 37, 1238–1240 (2012).
[CrossRef] [PubMed]

P. Piksarv, P. Bowlan, M. Lõhmus, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort Gaussian pulses within the framework of boundary diffraction wave theory,” J. Opt. 14, 015701 (2012).
[CrossRef]

P. Bowlan and R. Trebino, “Using phase diversity for the measurement of the complete spatiotemporal electric field of ultrashort laser pulses,” J. Opt. Soc. Am. B 29, 244–248 (2012).
[CrossRef]

J. Cohen, P. Bowlan, V. Chauhan, P. Vaughan, and R. Trebino, “Measuring extremely complex pulses with time-bandwidth products exceeding 65,000 using multiple-delay crossed-beam spectral interferometry,” Opt. Express 18, 24451–24460 (2010).
[CrossRef] [PubMed]

S. Akturk, X. Gu, P. Bowlan, and R. Trebino, “Spatio-temporal couplings in ultrashort laser pulses,” J. Opt. 12, 093001 (2010).
[CrossRef]

P. Saari, P. Bowlan, H. Valtna-Lukner, M. Lõhmus, P. Piksarv, and R. Trebino, “Basic diffraction phenomena in time domain,” Opt. Express 18, 11083–11088 (2010).
[CrossRef] [PubMed]

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, 2276–2278 (2009).
[CrossRef] [PubMed]

H. Valtna-Lukner, P. Bowlan, M. Lõhmus, P. Piksarv, R. Trebino, and P. Saari, “Direct spatiotemporal measurements of accelerating ultrashort Bessel-type light bullets,” Opt. Express 17, 14948–14955 (2009).
[CrossRef] [PubMed]

P. Bowlan, P. Gabolde, M. A. Coughlan, R. Trebino, and R. J. Levis, “Measuring the spatiotemporal electric field of ultrashort pulses with high spatial and spectral resolution,” J. Opt. Soc. Am. B 25, A81–A92 (2008).
[CrossRef]

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, 11892–11900 (2006).
[CrossRef] [PubMed]

Calatroni, J. E.

C. Sainz, J. E. Calatroni, and G. Tribillon, “Refractometry of liquid samples with spectrally resolved white light interferometry,” Meas. Sci. Technol. 1, 356–361 (1990).
[CrossRef]

Cavalieri, A. L.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” New J. Phys. 9, 242 (2007).
[CrossRef]

Chan, K. P.

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Chauhan, V.

Cherel, L.

M. Roy, P. Svahn, L. Cherel, and C. J. R. Sheppard, “Geometric phase-shifting for low-coherence interference microscopy,” Opt. Laser Eng. 37, 631–641 (2002).
[CrossRef]

Chong, A.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
[CrossRef]

Christodoulides, D. N.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
[CrossRef]

Clerici, M.

Climent, V.

Cohen, J.

Colombeau, P.

Couairon, A.

Coughlan, M. A.

Dorrer, C.

Dyson, J.

J. Dyson, “Circular and spiral diffraction gratings,” Proc. R. Soc. Lond. A 248, 93–106 (1958).
[CrossRef]

Faccio, D.

Fan, D.

Z. Liu and D. Fan, “Propagation of pulsed zeroth-order Bessel beams,” J. Mod. Opt. 45, 17–21 (1998).
[CrossRef]

Fieß, M.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” New J. Phys. 9, 242 (2007).
[CrossRef]

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Frank, F.

Freiberg, A.

P. Saari, J. Aaviksoo, A. Freiberg, and K. Timpmann, “Elimination of excess pulse broadening at high spectral resolution of picosecond duration light emission,” Opt. Commun. 39, 94–98 (1981).
[CrossRef]

Froehly, C.

Fujimoto, J. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Gabolde, P.

Görbe, M.

A. Börzsönyi, A. Kovács, M. Görbe, and K. Osvay, “Advances and limitations of phase dispersion measurement by spectrally and spatially resolved interferometry,” Opt. Commun. 281, 3051–3061 (2008).
[CrossRef]

Goulielmakis, E.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” New J. Phys. 9, 242 (2007).
[CrossRef]

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Gu, X.

S. Akturk, X. Gu, P. Bowlan, and R. Trebino, “Spatio-temporal couplings in ultrashort laser pulses,” J. Opt. 12, 093001 (2010).
[CrossRef]

Guo, H.

Hee, M. R.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Helml, W.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” New J. Phys. 9, 242 (2007).
[CrossRef]

Hernández-Toro, J.

Horvath, B.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” New J. Phys. 9, 242 (2007).
[CrossRef]

Hu, W.

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Imhof, R.

R. Imhof and D. Birch, “Distortion of Gaussian pulses by a diffraction grating,” Opt. Commun. 42, 83–86 (1982).
[CrossRef]

Jarutis, V.

V. Jarutis, R. Paškauskas, and A. Stabinis, “Focusing of Laguerre–Gaussian beams by axicon,” Opt. Commun. 184, 105–112 (2000).
[CrossRef]

Jin, H.

Kathman, A. D.

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test (SPIE, 2003).

Kienberger, R.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” New J. Phys. 9, 242 (2007).
[CrossRef]

Knight, J. C.

J. C. Knight, “Photonic crystal fibres,” Nature 424, 847–851 (2003).
[CrossRef] [PubMed]

Kobayashi, T.

T. Kobayashi, J. Liu, and K. Okamura, “Applications of parametric processes to high-quality multicolour ultrashort pulses, pulse cleaning and cep stable sub-3fs pulse,” J. Phys. B. 45, 074005 (2012).
[CrossRef]

Kovács, A.

A. Börzsönyi, A. Kovács, M. Görbe, and K. Osvay, “Advances and limitations of phase dispersion measurement by spectrally and spatially resolved interferometry,” Opt. Commun. 281, 3051–3061 (2008).
[CrossRef]

Kovács, A. P.

Krausz, F.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” New J. Phys. 9, 242 (2007).
[CrossRef]

Lancis, J.

Levis, R. J.

Lienau, C.

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Liu, J.

T. Kobayashi, J. Liu, and K. Okamura, “Applications of parametric processes to high-quality multicolour ultrashort pulses, pulse cleaning and cep stable sub-3fs pulse,” J. Phys. B. 45, 074005 (2012).
[CrossRef]

Liu, Z.

Z. Liu and D. Fan, “Propagation of pulsed zeroth-order Bessel beams,” J. Mod. Opt. 45, 17–21 (1998).
[CrossRef]

Lõhmus, M.

Lotti, A.

Marangos, J. P.

Mascheck, M.

McGresham, K.

Méndez, C.

Mendoza-Yero, O.

Mínguez-Vega, G.

O’Shea, D. C.

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test (SPIE, 2003).

Okamura, K.

T. Kobayashi, J. Liu, and K. Okamura, “Applications of parametric processes to high-quality multicolour ultrashort pulses, pulse cleaning and cep stable sub-3fs pulse,” J. Phys. B. 45, 074005 (2012).
[CrossRef]

Okell, W. A.

Osvay, K.

A. Börzsönyi, A. Kovács, M. Görbe, and K. Osvay, “Advances and limitations of phase dispersion measurement by spectrally and spatially resolved interferometry,” Opt. Commun. 281, 3051–3061 (2008).
[CrossRef]

A. P. Kovács, K. Osvay, Z. Bor, and R. Szipöcs, “Group-delay measurement on laser mirrors by spectrally resolved white-light interferometry,” Opt. Lett. 20, 788–790 (1995).
[CrossRef] [PubMed]

Paškauskas, R.

V. Jarutis, R. Paškauskas, and A. Stabinis, “Focusing of Laguerre–Gaussian beams by axicon,” Opt. Commun. 184, 105–112 (2000).
[CrossRef]

Pervak, V.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” New J. Phys. 9, 242 (2007).
[CrossRef]

Piasecki, J.

Piglosiewicz, B.

Piksarv, P.

Porras, M. A.

M. A. Porras, “Diffraction effects in few-cycle optical pulses,” Phys. Rev. E 65, 026606 (2002).
[CrossRef]

Prather, D. W.

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test (SPIE, 2003).

Puliafito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Rätsep, M.

Reivelt, K.

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

Ren, Z.

Renninger, W. H.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
[CrossRef]

Román, J. S.

Roso, L.

Roy, M.

M. Roy, P. Svahn, L. Cherel, and C. J. R. Sheppard, “Geometric phase-shifting for low-coherence interference microscopy,” Opt. Laser Eng. 37, 631–641 (2002).
[CrossRef]

Rubino, E.

Saari, P.

P. Piksarv, P. Bowlan, M. Lõhmus, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort Gaussian pulses within the framework of boundary diffraction wave theory,” J. Opt. 14, 015701 (2012).
[CrossRef]

M. Lõhmus, P. Bowlan, P. Piksarv, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort optical pulses from circularly symmetric binary phase gratings,” Opt. Lett 37, 1238–1240 (2012).
[CrossRef] [PubMed]

P. Saari, P. Bowlan, H. Valtna-Lukner, M. Lõhmus, P. Piksarv, and R. Trebino, “Basic diffraction phenomena in time domain,” Opt. Express 18, 11083–11088 (2010).
[CrossRef] [PubMed]

H. Valtna-Lukner, P. Bowlan, M. Lõhmus, P. Piksarv, R. Trebino, and P. Saari, “Direct spatiotemporal measurements of accelerating ultrashort Bessel-type light bullets,” Opt. Express 17, 14948–14955 (2009).
[CrossRef] [PubMed]

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, 2276–2278 (2009).
[CrossRef] [PubMed]

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, 310–312 (1997).
[CrossRef] [PubMed]

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

P. Saari, J. Aaviksoo, A. Freiberg, and K. Timpmann, “Elimination of excess pulse broadening at high spectral resolution of picosecond duration light emission,” Opt. Commun. 39, 94–98 (1981).
[CrossRef]

Sadiq, D.

Sainz, C.

C. Sainz, J. E. Calatroni, and G. Tribillon, “Refractometry of liquid samples with spectrally resolved white light interferometry,” Meas. Sci. Technol. 1, 356–361 (1990).
[CrossRef]

Schmidt, S.

Schultze, M.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” New J. Phys. 9, 242 (2007).
[CrossRef]

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Shaarawi, A. M.

A. M. Shaarawi and I. M. Besieris, “On the superluminal propagation of X-shaped localized waves,” J. Phys. A. 33, 7227–7254 (2000).
[CrossRef]

Sheppard, C. J. R.

M. Roy, P. Svahn, L. Cherel, and C. J. R. Sheppard, “Geometric phase-shifting for low-coherence interference microscopy,” Opt. Laser Eng. 37, 631–641 (2002).
[CrossRef]

Shi, Y.

Shreenath, A.

Silies, M.

Sola, Í. J.

Sõnajalg, H.

Stabinis, A.

V. Jarutis, R. Paškauskas, and A. Stabinis, “Focusing of Laguerre–Gaussian beams by axicon,” Opt. Commun. 184, 105–112 (2000).
[CrossRef]

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Suleski, T. J.

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test (SPIE, 2003).

Svahn, P.

M. Roy, P. Svahn, L. Cherel, and C. J. R. Sheppard, “Geometric phase-shifting for low-coherence interference microscopy,” Opt. Laser Eng. 37, 631–641 (2002).
[CrossRef]

Swanson, E. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Szipöcs, R.

Tanno, N.

Timpmann, K.

P. Saari, J. Aaviksoo, A. Freiberg, and K. Timpmann, “Elimination of excess pulse broadening at high spectral resolution of picosecond duration light emission,” Opt. Commun. 39, 94–98 (1981).
[CrossRef]

Tisch, J. W. G.

Trapani, P. D.

Treacy, E. B.

E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. 5, 454–458 (1969).
[CrossRef]

Trebino, R.

M. Lõhmus, P. Bowlan, P. Piksarv, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort optical pulses from circularly symmetric binary phase gratings,” Opt. Lett 37, 1238–1240 (2012).
[CrossRef] [PubMed]

P. Piksarv, P. Bowlan, M. Lõhmus, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort Gaussian pulses within the framework of boundary diffraction wave theory,” J. Opt. 14, 015701 (2012).
[CrossRef]

P. Bowlan and R. Trebino, “Using phase diversity for the measurement of the complete spatiotemporal electric field of ultrashort laser pulses,” J. Opt. Soc. Am. B 29, 244–248 (2012).
[CrossRef]

R. Trebino, “Measuring the seemingly immeasurable,” Nat. Photonics 5, 189–192 (2011).
[CrossRef]

S. Akturk, X. Gu, P. Bowlan, and R. Trebino, “Spatio-temporal couplings in ultrashort laser pulses,” J. Opt. 12, 093001 (2010).
[CrossRef]

P. Saari, P. Bowlan, H. Valtna-Lukner, M. Lõhmus, P. Piksarv, and R. Trebino, “Basic diffraction phenomena in time domain,” Opt. Express 18, 11083–11088 (2010).
[CrossRef] [PubMed]

J. Cohen, P. Bowlan, V. Chauhan, P. Vaughan, and R. Trebino, “Measuring extremely complex pulses with time-bandwidth products exceeding 65,000 using multiple-delay crossed-beam spectral interferometry,” Opt. Express 18, 24451–24460 (2010).
[CrossRef] [PubMed]

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, 2276–2278 (2009).
[CrossRef] [PubMed]

H. Valtna-Lukner, P. Bowlan, M. Lõhmus, P. Piksarv, R. Trebino, and P. Saari, “Direct spatiotemporal measurements of accelerating ultrashort Bessel-type light bullets,” Opt. Express 17, 14948–14955 (2009).
[CrossRef] [PubMed]

P. Bowlan, P. Gabolde, M. A. Coughlan, R. Trebino, and R. J. Levis, “Measuring the spatiotemporal electric field of ultrashort pulses with high spatial and spectral resolution,” J. Opt. Soc. Am. B 25, A81–A92 (2008).
[CrossRef]

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, 11892–11900 (2006).
[CrossRef] [PubMed]

Tribillon, G.

C. Sainz, J. E. Calatroni, and G. Tribillon, “Refractometry of liquid samples with spectrally resolved white light interferometry,” Meas. Sci. Technol. 1, 356–361 (1990).
[CrossRef]

Uiberacker, M.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” New J. Phys. 9, 242 (2007).
[CrossRef]

Valtna-Lukner, H.

Vampouille, M.

Varela, O.

Varela, Ó.

Vasa, P.

Vaughan, P.

Veisz, L.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” New J. Phys. 9, 242 (2007).
[CrossRef]

Walmsley, I. A.

S. Baker, I. A. Walmsley, J. W. G. Tisch, and J. P. Marangos, “Femtosecond to attosecond light pulses from a molecular modulator,” Nat. Photonics 5, 664–671 (2011).
[CrossRef]

I. A. Walmsley and C. Dorrer, “Characterization of ultrashort electromagnetic pulses,” Adv. Opt. Photon. 1, 308–437 (2009).
[CrossRef]

Wang, H.

Wise, F. W.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
[CrossRef]

Witting, T.

Xu, J.

Yakovlev, V. S.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” New J. Phys. 9, 242 (2007).
[CrossRef]

Zaïr, A.

Zhou, W.

Adv. Opt. Photon. (1)

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. 5, 454–458 (1969).
[CrossRef]

J. Mod. Opt. (1)

Z. Liu and D. Fan, “Propagation of pulsed zeroth-order Bessel beams,” J. Mod. Opt. 45, 17–21 (1998).
[CrossRef]

J. Opt. (2)

S. Akturk, X. Gu, P. Bowlan, and R. Trebino, “Spatio-temporal couplings in ultrashort laser pulses,” J. Opt. 12, 093001 (2010).
[CrossRef]

P. Piksarv, P. Bowlan, M. Lõhmus, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort Gaussian pulses within the framework of boundary diffraction wave theory,” J. Opt. 14, 015701 (2012).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (3)

J. Phys. A. (1)

A. M. Shaarawi and I. M. Besieris, “On the superluminal propagation of X-shaped localized waves,” J. Phys. A. 33, 7227–7254 (2000).
[CrossRef]

J. Phys. B. (1)

T. Kobayashi, J. Liu, and K. Okamura, “Applications of parametric processes to high-quality multicolour ultrashort pulses, pulse cleaning and cep stable sub-3fs pulse,” J. Phys. B. 45, 074005 (2012).
[CrossRef]

Meas. Sci. Technol. (1)

C. Sainz, J. E. Calatroni, and G. Tribillon, “Refractometry of liquid samples with spectrally resolved white light interferometry,” Meas. Sci. Technol. 1, 356–361 (1990).
[CrossRef]

Nat. Photonics (3)

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
[CrossRef]

S. Baker, I. A. Walmsley, J. W. G. Tisch, and J. P. Marangos, “Femtosecond to attosecond light pulses from a molecular modulator,” Nat. Photonics 5, 664–671 (2011).
[CrossRef]

R. Trebino, “Measuring the seemingly immeasurable,” Nat. Photonics 5, 189–192 (2011).
[CrossRef]

Nature (1)

J. C. Knight, “Photonic crystal fibres,” Nature 424, 847–851 (2003).
[CrossRef] [PubMed]

New J. Phys. (1)

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” New J. Phys. 9, 242 (2007).
[CrossRef]

Opt. Commun. (4)

P. Saari, J. Aaviksoo, A. Freiberg, and K. Timpmann, “Elimination of excess pulse broadening at high spectral resolution of picosecond duration light emission,” Opt. Commun. 39, 94–98 (1981).
[CrossRef]

R. Imhof and D. Birch, “Distortion of Gaussian pulses by a diffraction grating,” Opt. Commun. 42, 83–86 (1982).
[CrossRef]

V. Jarutis, R. Paškauskas, and A. Stabinis, “Focusing of Laguerre–Gaussian beams by axicon,” Opt. Commun. 184, 105–112 (2000).
[CrossRef]

A. Börzsönyi, A. Kovács, M. Görbe, and K. Osvay, “Advances and limitations of phase dispersion measurement by spectrally and spatially resolved interferometry,” Opt. Commun. 281, 3051–3061 (2008).
[CrossRef]

Opt. Express (6)

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, 11892–11900 (2006).
[CrossRef] [PubMed]

H. Valtna-Lukner, P. Bowlan, M. Lõhmus, P. Piksarv, R. Trebino, and P. Saari, “Direct spatiotemporal measurements of accelerating ultrashort Bessel-type light bullets,” Opt. Express 17, 14948–14955 (2009).
[CrossRef] [PubMed]

P. Saari, P. Bowlan, H. Valtna-Lukner, M. Lõhmus, P. Piksarv, and R. Trebino, “Basic diffraction phenomena in time domain,” Opt. Express 18, 11083–11088 (2010).
[CrossRef] [PubMed]

B. Piglosiewicz, D. Sadiq, M. Mascheck, S. Schmidt, M. Silies, P. Vasa, and C. Lienau, “Ultrasmall bullets of light—focusing few-cycle light pulses to the diffraction limit,” Opt. Express 19, 14451–14463 (2011).
[CrossRef] [PubMed]

O. Mendoza-Yero, B. Alonso, O. Varela, G. Mínguez-Vega, Í. J. Sola, J. Lancis, V. Climent, and L. Roso, “Spatio-temporal characterization of ultrashort pulses diffracted by circularly symmetric hard-edge apertures: theory and experiment,” Opt. Express 18, 20900–20911 (2010).
[CrossRef] [PubMed]

J. Cohen, P. Bowlan, V. Chauhan, P. Vaughan, and R. Trebino, “Measuring extremely complex pulses with time-bandwidth products exceeding 65,000 using multiple-delay crossed-beam spectral interferometry,” Opt. Express 18, 24451–24460 (2010).
[CrossRef] [PubMed]

Opt. Laser Eng. (1)

M. Roy, P. Svahn, L. Cherel, and C. J. R. Sheppard, “Geometric phase-shifting for low-coherence interference microscopy,” Opt. Laser Eng. 37, 631–641 (2002).
[CrossRef]

Opt. Lett (1)

M. Lõhmus, P. Bowlan, P. Piksarv, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort optical pulses from circularly symmetric binary phase gratings,” Opt. Lett 37, 1238–1240 (2012).
[CrossRef] [PubMed]

Opt. Lett. (7)

Phys. Rev. E (1)

M. A. Porras, “Diffraction effects in few-cycle optical pulses,” Phys. Rev. E 65, 026606 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

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

Proc. R. Soc. Lond. A (1)

J. Dyson, “Circular and spiral diffraction gratings,” Proc. R. Soc. Lond. A 248, 93–106 (1958).
[CrossRef]

Science (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Other (1)

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test (SPIE, 2003).

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 (5)

Fig. 1
Fig. 1

The axial evolution of pulsed Bessel beam. Evaluation of Eq. (1) with different initial phase φ0 (ω) : (a) an uniform phase, i.e. no initial chirp, (b) a phase corresponding to a propagation through a fused silica sample with a thickness of 0.92mm, and (c) 1.57mm. Color shows the amplitude of the electric field, temporal position t = 0fs corresponds to a plane wave traveling at c.

Fig. 2
Fig. 2

Experimental set-up. The beam from the laser L is expanded by a reflective beam expander BE and then sampled into the reference arm of the interferometer by an UV fused silica window BS1, directed by mirror M1 through a beam splitter dispersion compensation plate BS2 and a variable delay line D, and focused by a spherical mirror SM1 into photonic crystal fiber PCF1. On the measurement arm the light is directed with mirrors M2–4 onto circularly symmetric diffraction grating G and the resulting field is sampled by the fiber PCF2. The output of the fibers is placed on the entrance slit of an imaging spectrometer with a few mm separation, so that light enters the spectrometer under a small angle 2θ perpendicular to the frequency axis ω. Spectrometer consists of a spherical mirror SM2, reflecting half-prism P, uncoated FS cylindrical lens CL and a CCD camera. Spatial interference pattern on the CCD camera is processed to retrieve the spectral phase and amplitude information of the field correlation function. Optical fibers allow effortless redesign of measurement set-up while keeping the most alignment-critical part—the spectrometer—intact.

Fig. 3
Fig. 3

Instrument function of the set-up. Left: typical spectral intensity and phase response with a linear spectral phase component subtracted, and right: temporal intensity and phase. The blue dots on the right mark data points, and the light blue line is spline interpolation revealing a FWHM of 3.8fs of the instrument function.

Fig. 4
Fig. 4

Temporal focusing of the pulsed Bessel beam. Temporally broadened pulse shortens and thereupon spreads out again after propagating through the circularly symmetric phase grating with a substrate thickness of 0.92mm. Top row: results of measurements performed at different propagation depths; bottom row: simulation based on Eq. (1). Color shows the amplitude of the electric field. Temporal origin t = 0fs on the horizontal axis corresponds to a plane wave front traveling at c and its position relative to the measured pulse reveals subluminal velocity of the latter (cf. the superluminality of the Bessel-X pulse [14, 15]). Vertical axis shows the scan through the radial coordinate revealing the propagation of the pulsed Bessel beam with no lateral spread. At the closest distance the pulse corresponding to the 3rd diffraction order with a fringe spacing of 3.3μm was clearly resolved.

Fig. 5
Fig. 5

Measured on-axis intensities of pulsed Bessel beams. (a) Pulsed Bessel beam generated by circularly symmetric binary phase grating with dispersion compensated grating substrate. Initial pulse with a measured FWHM of 4.1fs broadens to 91.7fs over 10cm of propagation length. (b) Partially dispersion-compensated grating substrate: 27.8fs pulse focuses to 5.1fs and then broadens to a duration of 52.7fs. (c) Dispersion-uncompensated grating substrate: 44.8fs pulse achieves a minimum duration of 6.1fs by the end of its propagation length. Vertical scale shows normalized intensity In (z,t), color shows relative maximum intensity within a given measurement series. Pulses with the shortest temporal duration for each series have been highlighted with red border line and in the temporal focal region (series “b” and “c”) they exhibit a quasi-Airy profile. The latter is formed by a residual uncompensated cubic phase (cf. theoretical analysis of this effect in Ref. [32]).

Equations (6)

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

Ψ P B B ( ρ , z , t ) J 0 ( k ρ ) d ω A ( ω , z ) e i φ 0 ( ω ) e i k z z e i ω t ,
A ( ω , z ) S 0 ( ω ) I 0 ( ω , z ) η ( ω ) ,
I 0 k 2 c ω z exp [ 2 ( k c ω z w ) 2 ] .
η ( ω ) = | κ sinc ( κ m ) + ( 1 κ ) sinc ( ( 1 κ ) m ) e i π m e i ϕ ( ω , δ ) | 2 ,
E ( r , t ) = 0 h ( r , t ) E 0 ( t t ) d t ,
K ( r , τ ) = 0 h ( r , t ) E 0 ( t t ) d t E 0 ( t τ ) = = 0 h ( r , t ) E 0 ( t t ) E 0 ( t τ ) d t = = const × h ( r , τ ) ,

Metrics