Abstract

The recently introduced concept of radially non-oscillating, temporally stable ultrashort-pulsed Bessel-like beams we referred to as needle beams is generalized to a particular class of highly localized wavepackets (HLWs). Spatio-temporally quasi-nondiffracting pulses propagating along extended zones are shaped from Ti:sapphire oscillator radiation with a spatial light modulator and characterized with spatially resolved second order autocorrelation. Few-cycle wavepackets tailored to resemble circular disks, rings and bars of light represent the closest approximation of linear-optical light bullets known so far. By combining multiple HLWs, complex pulsed nondiffracting patterns are obtained.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. Saari, “How small a packet of photons can be made?” Laser Phys.16(4), 556–561 (2006).
    [CrossRef]
  2. P. Saari, “Photon Localization Revisited,” in: Quantum Optics and Laser Experiments Sergiy Lyagushin Ed. (InTech - Open Access Publisher, Croatia, 2012), 49–66.
  3. P. Saari, M. Menert, and H. Valtna, “Photon localization barrier can be overcome,” Opt. Commun.246(4-6), 445–450 (2005).
    [CrossRef]
  4. 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. Express19(15), 14451–14463 (2011).
    [CrossRef] [PubMed]
  5. S. Trillo and W. Torruellas Eds, Spatial Dolitons (Springer, Berlin, 2001), pp. 73–74.
  6. Y. S, Kivshar and G. P. Agrawal, Optical solitons - From fibers to photonic crystals (Academic Press, Elsevier Science, Amsterdam, 2003), pp. 226–228.
  7. 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]
  8. 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(9), 093904 (2003).
    [CrossRef] [PubMed]
  9. P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater.5(2), 93–96 (2006).
    [CrossRef] [PubMed]
  10. J. A. Stratton, Electromagnetic Theory (McGraw Hill, New York, 1941), 356.
  11. J. Durnin, “Exact solution for nondiffracting beams I - The scalar theory,” J. Opt. Soc. Am. A4(4), 651–654 (1987).
    [CrossRef]
  12. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58(15), 1499–1501 (1987).
    [CrossRef] [PubMed]
  13. H. E. Hernández-Figueroa, M. Zamboni-Rached, and E. Recami, eds., Localized Waves, Theory and Experiments (Wiley & Sons, New York, 2008).
  14. Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun.151(4-6), 207–211 (1998).
    [CrossRef]
  15. P. Martelli, M. Tacca, A. Gatto, G. Moneta, and M. Martinelli, “Gouy phase shift in nondiffracting Bessel beams,” Opt. Express18(7), 7108–7120 (2010).
    [CrossRef] [PubMed]
  16. S. Chávez-Cerda, “A new approach to Bessel beams,” J. Mod. Opt.46, 923–930 (1999).
  17. K. Reivelt and P. Saari, “Bessel-Gauss pulse as an appropriate mathematical model for optically realizable localized waves,” Opt. Lett.29(11), 1176–1178 (2004).
    [CrossRef] [PubMed]
  18. 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] [PubMed]
  19. G. Scott, “Efficient generation of nearly diffraction-free beams using an axicon,” Opt. Eng.31(12), 2640–2646 (1992).
    [CrossRef]
  20. J. H. McLeod, “The axicon: A new type of optical element,” J. Opt. Soc. Am.44(8), 592–597 (1954).
    [CrossRef]
  21. J. Turunen, A. Vasara, and A. T. Friberg, “Holographic generation of diffraction-free beams,” Appl. Opt.27(19), 3959–3962 (1988).
    [CrossRef] [PubMed]
  22. J. Durnin, J. J. Miceli, and J. H. Eberly, “Comparison of Bessel and Gaussian beams,” Opt. Lett.13(2), 79–80 (1988).
    [CrossRef] [PubMed]
  23. P. L. Overfelt and C. S. Kenney, “Comparison of the propagation characteristics of Bessel, Bessel-Gauss, and Gaussian beams diffracted by a circular aperture,” J. Opt. Soc. Am. A8(5), 732–745 (1991).
    [CrossRef]
  24. R. M. Herman and T. A. Wiggins, “Bessel-like beams modulated by arbitrary radial functions,” J. Opt. Soc. Am. A17(6), 1021–1032 (2000).
    [CrossRef] [PubMed]
  25. R. M. Herman and T. A. Wiggins, “Apodization of diffractionless beams,” Appl. Opt.31(28), 5913–5915 (1992).
    [CrossRef] [PubMed]
  26. F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun.64(6), 491–495 (1987).
    [CrossRef]
  27. J. Arlt and M. J. Padgett, “Generation of a beam with a dark focus surrounded by regions of higher intensity: the optical bottle beam,” Opt. Lett.25(4), 191–193 (2000).
    [CrossRef] [PubMed]
  28. P. Saari and K. Reivelt, “Evidence of X-shaped propagation-invariant localized light waves,” Phys. Rev. Lett.79(21), 4135–4138 (1997).
    [CrossRef]
  29. R. Grunwald, U. Griebner, U. Neumann, A. Kummrow, E. T. J. Nibbering, M. Piché, G. Rousseau, M. Fortin, and V. Kebbel, “Generation of ultrashort-pulse nondiffracting beams and X-waves with thin-film axicons,” in: M. Murnane, N. F. Scherer, and A. M. Weiner (Eds.), Ultrafast Phenomena XIII (Springer-Verlag, New York, 2002) 247–249.
  30. 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. A67(6), 063820 (2003).
    [CrossRef]
  31. J. Y. Lu and J. F. Greenleaf, “Nondiffracting X waves. Exact solutions to free space scalar wave equation and their finite aperture realizations,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control39(1), 19–31 (1992).
    [CrossRef] [PubMed]
  32. J. Y. Lu and J. F. Greenleaf, “Experimental verification of nondiffracting X waves,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control39(3), 441–446 (1992).
    [CrossRef] [PubMed]
  33. M. Zamboni-Rached, E. Recami, and H. E. Hernández-Figueroa, “New localized Superluminal solutions to the wave equations with finite total energies and arbitrary frequencies,” Eur. Phys. J. D21(2), 217–228 (2002).
    [CrossRef]
  34. M. Zamboni-Rached, E. Recami, and H. E. Hernández-Figueroa, “Theory of 'frozen waves': modeling the shape of stationary wave fields,” J. Opt. Soc. Am. A22, 2465–2475 (2005).
  35. M. Z. Rached and E. Recami, “Subluminal wave bullets: Exact localized subluminal solutions to the wave equations,” Phys. Rev. A77(3), 033824 (2008).
    [CrossRef]
  36. M. Zamboni-Rached, “Unidirectional decomposition method for obtaining exact localized wave solutions totally free of backward components,” Phys. Rev. A79(1), 013816 (2009).
    [CrossRef]
  37. A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics4(2), 103–106 (2010).
    [CrossRef]
  38. D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett.105(25), 253901 (2010).
    [CrossRef] [PubMed]
  39. R. Grunwald, M. Bock, V. Kebbel, S. Huferath, U. Neumann, G. Steinmeyer, G. Stibenz, J.-L. Néron, and M. Piché, “Ultrashort-pulsed truncated polychromatic Bessel-Gauss beams,” Opt. Express16(2), 1077–1089 (2008).
    [CrossRef] [PubMed]
  40. R. Grunwald, Thin-film microoptics - new frontiers of spatio-temporal beam shaping (Elsevier, Amsterdam, 2007).
  41. M. Bock, S. K. Das, and R. Grunwald, “Programmable ultrashort-pulsed flying images,” Opt. Express17(9), 7465–7478 (2009).
    [CrossRef] [PubMed]
  42. P. Sprangle and B. Hafizi, “Comment on nondiffracting beams,” Phys. Rev. Lett.66(6), 837 (1991).
    [CrossRef] [PubMed]
  43. J. Durnin, J. J. Miceli, and J. H. Eberly, “Durnin, Miceli, and Eberly Reply,” Phys. Rev. Lett.66(6), 838 (1991).
    [CrossRef] [PubMed]
  44. M. Mansuripur, “The uncertainty principle in classical optics,” Opt. & Photon. News, Jan. 2002, 44–48 (2002).
  45. M. J. Bastiaans, “Uncertainty principle and informational entropy for partially coherent light,” J. Opt. Soc. Am. A3(8), 1243–1246 (1986).
    [CrossRef]
  46. P. Saari and K. Reivelt, “Evidence of X-shaped propagation-invariant localized light waves,” Phys. Rev. Lett.79(21), 4135–4138 (1997).
    [CrossRef]
  47. A. Siegman, “New developments in laser resonators,” Proc. SPIE1224, 2–14 (1990).
    [CrossRef]
  48. R. Borghi and M. Santarsiero, “M2 factor of Bessel-Gauss beams,” Opt. Lett.22(5), 262–264 (1997).
    [CrossRef] [PubMed]
  49. R. M. Herman and T. A. Wiggins, “Rayleigh range and the M2 factor for Bessel-Gauss beams,” Appl. Opt.37(16), 3398–3400 (1998).
    [CrossRef] [PubMed]
  50. S.-A. Amarande, “Beam propagation factor and the kurtosis parameter of flattened Gaussian beams,” Opt. Commun.129, 311–317 (1996).
  51. R. Grunwald and M. Bock, “Spatio-spectral analysis and encoding of ultrashort pulses with higher-order statistical moments,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper CThM2.
  52. M. Bock, S. K. Das, and R. Grunwald, “Adaptive shaping of complex pulsed nondiffracting light fields,” Proc. SPIE7716, 7950–7958 (2011).
  53. Z. Mei and D. Zhao, “Controllable dark-hollow beams and their propagation characteristics,” J. Opt. Soc. Am. A22(9), 1898–1902 (2005).
    [CrossRef] [PubMed]
  54. G. Rousseau, N. McCarthy, and M. Pichãé, “Description of pulse propagation in a dispersive medium by use of a pulse quality factor,” Opt. Lett.27(18), 1649–1651 (2002).
    [CrossRef] [PubMed]
  55. M. Piché and R. Grunwald, private communication. In the discussion, the product of M2 and P2 was considered to be used to describe the spatio-temporal beam properties of pulsed Bessel beams.
  56. B. Salik, J. Rosen, and A. Yariv, “Nondiffracting images under coherent illumination,” Opt. Lett.20(17), 1743–1745 (1995).
    [CrossRef] [PubMed]
  57. R. Grunwald, S. Huferath, M. Bock, U. Neumann, and S. Langer, “Angular tolerance of Shack-Hartmann wavefront sensors with microaxicons,” Opt. Lett.32(11), 1533–1535 (2007).
    [CrossRef] [PubMed]
  58. R. Grunwald, U. Neumann, U. Griebner, K. Reimann, G. Steinmeyer, and V. Kebbel, “Ultrashort-pulse wave-front autocorrelation,” Opt. Lett.28(23), 2399–2401 (2003).
    [CrossRef] [PubMed]
  59. M. Bock, S. K. Das, C. Fischer, M. Diehl, P. Börner, and R. Grunwald, “Reconfigurable wavefront sensor for ultrashort pulses,” Opt. Lett.37(7), 1154–1156 (2012).
    [CrossRef] [PubMed]
  60. R. Grunwald and M. Bock, “Spatially encoded localized wavepackets for ultrafast optical data transfer,” JEOS:RP (submitted to).
  61. M. Bock, S. K. Das, R. Grunwald, S. Osten, P. Staudt, and G. Stibenz, “Spectral and temporal response of liquid-crystal-on-silicon spatial light modulators,” Appl. Phys. Lett.92(15), 151105 (2008).
    [CrossRef]
  62. I. Golub, “Fresnel axicon,” Opt. Lett.31(12), 1890–1892 (2006).
    [CrossRef] [PubMed]
  63. R. Grunwald and M. Bock, “Programmable microoptics for ultrashort pulses,” Proc. SPIE7716, 77160P, 77160P-8 (2010).
    [CrossRef]
  64. M. Bouafia, A. Bencheikh, L. Bouamama, and H. Weber, “M2 quality factor as a key for mastering laser beam propagation,” Proc. SPIE5456, 130–140 (2004).
    [CrossRef]
  65. R. Grunwald and M. Bock, “Programmable micro-optics for ultrashort pulses,” SPIE Newsroom (2010). http://spie.org/x39625.xml?highlight=x2422&ArticleID=x39625 .

2012

2011

2010

R. Grunwald and M. Bock, “Programmable microoptics for ultrashort pulses,” Proc. SPIE7716, 77160P, 77160P-8 (2010).
[CrossRef]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics4(2), 103–106 (2010).
[CrossRef]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett.105(25), 253901 (2010).
[CrossRef] [PubMed]

P. Martelli, M. Tacca, A. Gatto, G. Moneta, and M. Martinelli, “Gouy phase shift in nondiffracting Bessel beams,” Opt. Express18(7), 7108–7120 (2010).
[CrossRef] [PubMed]

2009

M. Bock, S. K. Das, and R. Grunwald, “Programmable ultrashort-pulsed flying images,” Opt. Express17(9), 7465–7478 (2009).
[CrossRef] [PubMed]

M. Zamboni-Rached, “Unidirectional decomposition method for obtaining exact localized wave solutions totally free of backward components,” Phys. Rev. A79(1), 013816 (2009).
[CrossRef]

2008

M. Z. Rached and E. Recami, “Subluminal wave bullets: Exact localized subluminal solutions to the wave equations,” Phys. Rev. A77(3), 033824 (2008).
[CrossRef]

M. Bock, S. K. Das, R. Grunwald, S. Osten, P. Staudt, and G. Stibenz, “Spectral and temporal response of liquid-crystal-on-silicon spatial light modulators,” Appl. Phys. Lett.92(15), 151105 (2008).
[CrossRef]

R. Grunwald, M. Bock, V. Kebbel, S. Huferath, U. Neumann, G. Steinmeyer, G. Stibenz, J.-L. Néron, and M. Piché, “Ultrashort-pulsed truncated polychromatic Bessel-Gauss beams,” Opt. Express16(2), 1077–1089 (2008).
[CrossRef] [PubMed]

2007

2006

I. Golub, “Fresnel axicon,” Opt. Lett.31(12), 1890–1892 (2006).
[CrossRef] [PubMed]

P. Saari, “How small a packet of photons can be made?” Laser Phys.16(4), 556–561 (2006).
[CrossRef]

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater.5(2), 93–96 (2006).
[CrossRef] [PubMed]

2005

2004

K. Reivelt and P. Saari, “Bessel-Gauss pulse as an appropriate mathematical model for optically realizable localized waves,” Opt. Lett.29(11), 1176–1178 (2004).
[CrossRef] [PubMed]

M. Bouafia, A. Bencheikh, L. Bouamama, and H. Weber, “M2 quality factor as a key for mastering laser beam propagation,” Proc. SPIE5456, 130–140 (2004).
[CrossRef]

2003

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(9), 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. A67(6), 063820 (2003).
[CrossRef]

R. Grunwald, U. Neumann, U. Griebner, K. Reimann, G. Steinmeyer, and V. Kebbel, “Ultrashort-pulse wave-front autocorrelation,” Opt. Lett.28(23), 2399–2401 (2003).
[CrossRef] [PubMed]

2002

G. Rousseau, N. McCarthy, and M. Pichãé, “Description of pulse propagation in a dispersive medium by use of a pulse quality factor,” Opt. Lett.27(18), 1649–1651 (2002).
[CrossRef] [PubMed]

M. Zamboni-Rached, E. Recami, and H. E. Hernández-Figueroa, “New localized Superluminal solutions to the wave equations with finite total energies and arbitrary frequencies,” Eur. Phys. J. D21(2), 217–228 (2002).
[CrossRef]

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] [PubMed]

M. Mansuripur, “The uncertainty principle in classical optics,” Opt. & Photon. News, Jan. 2002, 44–48 (2002).

2000

1999

S. Chávez-Cerda, “A new approach to Bessel beams,” J. Mod. Opt.46, 923–930 (1999).

1998

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun.151(4-6), 207–211 (1998).
[CrossRef]

R. M. Herman and T. A. Wiggins, “Rayleigh range and the M2 factor for Bessel-Gauss beams,” Appl. Opt.37(16), 3398–3400 (1998).
[CrossRef] [PubMed]

1997

R. Borghi and M. Santarsiero, “M2 factor of Bessel-Gauss beams,” Opt. Lett.22(5), 262–264 (1997).
[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(5), 310–312 (1997).
[CrossRef] [PubMed]

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

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

1996

S.-A. Amarande, “Beam propagation factor and the kurtosis parameter of flattened Gaussian beams,” Opt. Commun.129, 311–317 (1996).

1995

1992

R. M. Herman and T. A. Wiggins, “Apodization of diffractionless beams,” Appl. Opt.31(28), 5913–5915 (1992).
[CrossRef] [PubMed]

J. Y. Lu and J. F. Greenleaf, “Nondiffracting X waves. Exact solutions to free space scalar wave equation and their finite aperture realizations,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control39(1), 19–31 (1992).
[CrossRef] [PubMed]

J. Y. Lu and J. F. Greenleaf, “Experimental verification of nondiffracting X waves,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control39(3), 441–446 (1992).
[CrossRef] [PubMed]

G. Scott, “Efficient generation of nearly diffraction-free beams using an axicon,” Opt. Eng.31(12), 2640–2646 (1992).
[CrossRef]

1991

P. Sprangle and B. Hafizi, “Comment on nondiffracting beams,” Phys. Rev. Lett.66(6), 837 (1991).
[CrossRef] [PubMed]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Durnin, Miceli, and Eberly Reply,” Phys. Rev. Lett.66(6), 838 (1991).
[CrossRef] [PubMed]

P. L. Overfelt and C. S. Kenney, “Comparison of the propagation characteristics of Bessel, Bessel-Gauss, and Gaussian beams diffracted by a circular aperture,” J. Opt. Soc. Am. A8(5), 732–745 (1991).
[CrossRef]

1990

A. Siegman, “New developments in laser resonators,” Proc. SPIE1224, 2–14 (1990).
[CrossRef]

1988

1987

J. Durnin, “Exact solution for nondiffracting beams I - The scalar theory,” J. Opt. Soc. Am. A4(4), 651–654 (1987).
[CrossRef]

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun.64(6), 491–495 (1987).
[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

1986

1954

Abdollahpour, D.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett.105(25), 253901 (2010).
[CrossRef] [PubMed]

Amarande, S.-A.

S.-A. Amarande, “Beam propagation factor and the kurtosis parameter of flattened Gaussian beams,” Opt. Commun.129, 311–317 (1996).

Arlt, J.

Bastiaans, M. J.

Bencheikh, A.

M. Bouafia, A. Bencheikh, L. Bouamama, and H. Weber, “M2 quality factor as a key for mastering laser beam propagation,” Proc. SPIE5456, 130–140 (2004).
[CrossRef]

Bock, M.

M. Bock, S. K. Das, C. Fischer, M. Diehl, P. Börner, and R. Grunwald, “Reconfigurable wavefront sensor for ultrashort pulses,” Opt. Lett.37(7), 1154–1156 (2012).
[CrossRef] [PubMed]

M. Bock, S. K. Das, and R. Grunwald, “Adaptive shaping of complex pulsed nondiffracting light fields,” Proc. SPIE7716, 7950–7958 (2011).

R. Grunwald and M. Bock, “Programmable microoptics for ultrashort pulses,” Proc. SPIE7716, 77160P, 77160P-8 (2010).
[CrossRef]

M. Bock, S. K. Das, and R. Grunwald, “Programmable ultrashort-pulsed flying images,” Opt. Express17(9), 7465–7478 (2009).
[CrossRef] [PubMed]

R. Grunwald, M. Bock, V. Kebbel, S. Huferath, U. Neumann, G. Steinmeyer, G. Stibenz, J.-L. Néron, and M. Piché, “Ultrashort-pulsed truncated polychromatic Bessel-Gauss beams,” Opt. Express16(2), 1077–1089 (2008).
[CrossRef] [PubMed]

M. Bock, S. K. Das, R. Grunwald, S. Osten, P. Staudt, and G. Stibenz, “Spectral and temporal response of liquid-crystal-on-silicon spatial light modulators,” Appl. Phys. Lett.92(15), 151105 (2008).
[CrossRef]

R. Grunwald, S. Huferath, M. Bock, U. Neumann, and S. Langer, “Angular tolerance of Shack-Hartmann wavefront sensors with microaxicons,” Opt. Lett.32(11), 1533–1535 (2007).
[CrossRef] [PubMed]

R. Grunwald and M. Bock, “Spatially encoded localized wavepackets for ultrafast optical data transfer,” JEOS:RP (submitted to).

Borghi, R.

Börner, P.

Bouafia, M.

M. Bouafia, A. Bencheikh, L. Bouamama, and H. Weber, “M2 quality factor as a key for mastering laser beam propagation,” Proc. SPIE5456, 130–140 (2004).
[CrossRef]

Bouamama, L.

M. Bouafia, A. Bencheikh, L. Bouamama, and H. Weber, “M2 quality factor as a key for mastering laser beam propagation,” Proc. SPIE5456, 130–140 (2004).
[CrossRef]

Bouchal, Z.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun.151(4-6), 207–211 (1998).
[CrossRef]

Chávez-Cerda, S.

S. Chávez-Cerda, “A new approach to Bessel beams,” J. Mod. Opt.46, 923–930 (1999).

Chlup, M.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun.151(4-6), 207–211 (1998).
[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. Photonics4(2), 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. Photonics4(2), 103–106 (2010).
[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(9), 093904 (2003).
[CrossRef] [PubMed]

Dahlem, M. S.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater.5(2), 93–96 (2006).
[CrossRef] [PubMed]

Das, S. K.

M. Bock, S. K. Das, C. Fischer, M. Diehl, P. Börner, and R. Grunwald, “Reconfigurable wavefront sensor for ultrashort pulses,” Opt. Lett.37(7), 1154–1156 (2012).
[CrossRef] [PubMed]

M. Bock, S. K. Das, and R. Grunwald, “Adaptive shaping of complex pulsed nondiffracting light fields,” Proc. SPIE7716, 7950–7958 (2011).

M. Bock, S. K. Das, and R. Grunwald, “Programmable ultrashort-pulsed flying images,” Opt. Express17(9), 7465–7478 (2009).
[CrossRef] [PubMed]

M. Bock, S. K. Das, R. Grunwald, S. Osten, P. Staudt, and G. Stibenz, “Spectral and temporal response of liquid-crystal-on-silicon spatial light modulators,” Appl. Phys. Lett.92(15), 151105 (2008).
[CrossRef]

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(9), 093904 (2003).
[CrossRef] [PubMed]

Diehl, M.

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Durnin, Miceli, and Eberly Reply,” Phys. Rev. Lett.66(6), 838 (1991).
[CrossRef] [PubMed]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Comparison of Bessel and Gaussian beams,” Opt. Lett.13(2), 79–80 (1988).
[CrossRef] [PubMed]

J. Durnin, “Exact solution for nondiffracting beams I - The scalar theory,” J. Opt. Soc. Am. A4(4), 651–654 (1987).
[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Durnin, Miceli, and Eberly Reply,” Phys. Rev. Lett.66(6), 838 (1991).
[CrossRef] [PubMed]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Comparison of Bessel and Gaussian beams,” Opt. Lett.13(2), 79–80 (1988).
[CrossRef] [PubMed]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

Fischer, C.

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. A67(6), 063820 (2003).
[CrossRef]

Friberg, A. T.

Gatto, A.

Golub, I.

Gori, F.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun.64(6), 491–495 (1987).
[CrossRef]

Greenleaf, J. F.

J. Y. Lu and J. F. Greenleaf, “Experimental verification of nondiffracting X waves,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control39(3), 441–446 (1992).
[CrossRef] [PubMed]

J. Y. Lu and J. F. Greenleaf, “Nondiffracting X waves. Exact solutions to free space scalar wave equation and their finite aperture realizations,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control39(1), 19–31 (1992).
[CrossRef] [PubMed]

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. A67(6), 063820 (2003).
[CrossRef]

R. Grunwald, U. Neumann, U. Griebner, K. Reimann, G. Steinmeyer, and V. Kebbel, “Ultrashort-pulse wave-front autocorrelation,” Opt. Lett.28(23), 2399–2401 (2003).
[CrossRef] [PubMed]

Grunwald, R.

M. Bock, S. K. Das, C. Fischer, M. Diehl, P. Börner, and R. Grunwald, “Reconfigurable wavefront sensor for ultrashort pulses,” Opt. Lett.37(7), 1154–1156 (2012).
[CrossRef] [PubMed]

M. Bock, S. K. Das, and R. Grunwald, “Adaptive shaping of complex pulsed nondiffracting light fields,” Proc. SPIE7716, 7950–7958 (2011).

R. Grunwald and M. Bock, “Programmable microoptics for ultrashort pulses,” Proc. SPIE7716, 77160P, 77160P-8 (2010).
[CrossRef]

M. Bock, S. K. Das, and R. Grunwald, “Programmable ultrashort-pulsed flying images,” Opt. Express17(9), 7465–7478 (2009).
[CrossRef] [PubMed]

R. Grunwald, M. Bock, V. Kebbel, S. Huferath, U. Neumann, G. Steinmeyer, G. Stibenz, J.-L. Néron, and M. Piché, “Ultrashort-pulsed truncated polychromatic Bessel-Gauss beams,” Opt. Express16(2), 1077–1089 (2008).
[CrossRef] [PubMed]

M. Bock, S. K. Das, R. Grunwald, S. Osten, P. Staudt, and G. Stibenz, “Spectral and temporal response of liquid-crystal-on-silicon spatial light modulators,” Appl. Phys. Lett.92(15), 151105 (2008).
[CrossRef]

R. Grunwald, S. Huferath, M. Bock, U. Neumann, and S. Langer, “Angular tolerance of Shack-Hartmann wavefront sensors with microaxicons,” Opt. Lett.32(11), 1533–1535 (2007).
[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. A67(6), 063820 (2003).
[CrossRef]

R. Grunwald, U. Neumann, U. Griebner, K. Reimann, G. Steinmeyer, and V. Kebbel, “Ultrashort-pulse wave-front autocorrelation,” Opt. Lett.28(23), 2399–2401 (2003).
[CrossRef] [PubMed]

R. Grunwald and M. Bock, “Spatially encoded localized wavepackets for ultrafast optical data transfer,” JEOS:RP (submitted to).

Guattari, G.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun.64(6), 491–495 (1987).
[CrossRef]

Hafizi, B.

P. Sprangle and B. Hafizi, “Comment on nondiffracting beams,” Phys. Rev. Lett.66(6), 837 (1991).
[CrossRef] [PubMed]

Herman, R. M.

Hernández-Figueroa, H. E.

M. Zamboni-Rached, E. Recami, and H. E. Hernández-Figueroa, “Theory of 'frozen waves': modeling the shape of stationary wave fields,” J. Opt. Soc. Am. A22, 2465–2475 (2005).

M. Zamboni-Rached, E. Recami, and H. E. Hernández-Figueroa, “New localized Superluminal solutions to the wave equations with finite total energies and arbitrary frequencies,” Eur. Phys. J. D21(2), 217–228 (2002).
[CrossRef]

Huferath, S.

Ibanescu, M.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater.5(2), 93–96 (2006).
[CrossRef] [PubMed]

Ippen, E. P.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater.5(2), 93–96 (2006).
[CrossRef] [PubMed]

Jedrkiewicz, O.

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(9), 093904 (2003).
[CrossRef] [PubMed]

Joannopoulos, J. D.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater.5(2), 93–96 (2006).
[CrossRef] [PubMed]

Kebbel, V.

Kenney, C. S.

Kolodziejski, L. A.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater.5(2), 93–96 (2006).
[CrossRef] [PubMed]

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. A67(6), 063820 (2003).
[CrossRef]

Langer, S.

Lienau, C.

Lu, J. Y.

J. Y. Lu and J. F. Greenleaf, “Experimental verification of nondiffracting X waves,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control39(3), 441–446 (1992).
[CrossRef] [PubMed]

J. Y. Lu and J. F. Greenleaf, “Nondiffracting X waves. Exact solutions to free space scalar wave equation and their finite aperture realizations,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control39(1), 19–31 (1992).
[CrossRef] [PubMed]

Mansuripur, M.

M. Mansuripur, “The uncertainty principle in classical optics,” Opt. & Photon. News, Jan. 2002, 44–48 (2002).

Martelli, P.

Martinelli, M.

Mascheck, M.

McCarthy, N.

McLeod, J. H.

Mei, Z.

Menert, M.

P. Saari, M. Menert, and H. Valtna, “Photon localization barrier can be overcome,” Opt. Commun.246(4-6), 445–450 (2005).
[CrossRef]

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Durnin, Miceli, and Eberly Reply,” Phys. Rev. Lett.66(6), 838 (1991).
[CrossRef] [PubMed]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Comparison of Bessel and Gaussian beams,” Opt. Lett.13(2), 79–80 (1988).
[CrossRef] [PubMed]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

Moneta, G.

Néron, J.-L.

Neumann, U.

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. A67(6), 063820 (2003).
[CrossRef]

Osten, S.

M. Bock, S. K. Das, R. Grunwald, S. Osten, P. Staudt, and G. Stibenz, “Spectral and temporal response of liquid-crystal-on-silicon spatial light modulators,” Appl. Phys. Lett.92(15), 151105 (2008).
[CrossRef]

Overfelt, P. L.

Padgett, M. J.

Padovani, C.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun.64(6), 491–495 (1987).
[CrossRef]

Papazoglou, D. G.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett.105(25), 253901 (2010).
[CrossRef] [PubMed]

Petrich, G. S.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater.5(2), 93–96 (2006).
[CrossRef] [PubMed]

Pichãé, M.

Piché, M.

R. Grunwald, M. Bock, V. Kebbel, S. Huferath, U. Neumann, G. Steinmeyer, G. Stibenz, J.-L. Néron, and M. Piché, “Ultrashort-pulsed truncated polychromatic Bessel-Gauss beams,” Opt. Express16(2), 1077–1089 (2008).
[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. A67(6), 063820 (2003).
[CrossRef]

Piglosiewicz, B.

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(9), 093904 (2003).
[CrossRef] [PubMed]

Rached, M. Z.

M. Z. Rached and E. Recami, “Subluminal wave bullets: Exact localized subluminal solutions to the wave equations,” Phys. Rev. A77(3), 033824 (2008).
[CrossRef]

Rakich, P. T.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater.5(2), 93–96 (2006).
[CrossRef] [PubMed]

Rätsep, M.

Recami, E.

M. Z. Rached and E. Recami, “Subluminal wave bullets: Exact localized subluminal solutions to the wave equations,” Phys. Rev. A77(3), 033824 (2008).
[CrossRef]

M. Zamboni-Rached, E. Recami, and H. E. Hernández-Figueroa, “Theory of 'frozen waves': modeling the shape of stationary wave fields,” J. Opt. Soc. Am. A22, 2465–2475 (2005).

M. Zamboni-Rached, E. Recami, and H. E. Hernández-Figueroa, “New localized Superluminal solutions to the wave equations with finite total energies and arbitrary frequencies,” Eur. Phys. J. D21(2), 217–228 (2002).
[CrossRef]

Reimann, K.

Reivelt, K.

K. Reivelt and P. Saari, “Bessel-Gauss pulse as an appropriate mathematical model for optically realizable localized waves,” Opt. Lett.29(11), 1176–1178 (2004).
[CrossRef] [PubMed]

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] [PubMed]

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

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

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. Photonics4(2), 103–106 (2010).
[CrossRef]

Rini, 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. A67(6), 063820 (2003).
[CrossRef]

Rosen, J.

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. A67(6), 063820 (2003).
[CrossRef]

G. Rousseau, N. McCarthy, and M. Pichãé, “Description of pulse propagation in a dispersive medium by use of a pulse quality factor,” Opt. Lett.27(18), 1649–1651 (2002).
[CrossRef] [PubMed]

Saari, P.

P. Saari, “How small a packet of photons can be made?” Laser Phys.16(4), 556–561 (2006).
[CrossRef]

P. Saari, M. Menert, and H. Valtna, “Photon localization barrier can be overcome,” Opt. Commun.246(4-6), 445–450 (2005).
[CrossRef]

K. Reivelt and P. Saari, “Bessel-Gauss pulse as an appropriate mathematical model for optically realizable localized waves,” Opt. Lett.29(11), 1176–1178 (2004).
[CrossRef] [PubMed]

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] [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(5), 310–312 (1997).
[CrossRef] [PubMed]

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

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

Sadiq, D.

Salik, B.

Santarsiero, M.

Schmidt, S.

Scott, G.

G. Scott, “Efficient generation of nearly diffraction-free beams using an axicon,” Opt. Eng.31(12), 2640–2646 (1992).
[CrossRef]

Siegman, A.

A. Siegman, “New developments in laser resonators,” Proc. SPIE1224, 2–14 (1990).
[CrossRef]

Silies, M.

Soljacic, M.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater.5(2), 93–96 (2006).
[CrossRef] [PubMed]

Sõnajalg, H.

Sprangle, P.

P. Sprangle and B. Hafizi, “Comment on nondiffracting beams,” Phys. Rev. Lett.66(6), 837 (1991).
[CrossRef] [PubMed]

Staudt, P.

M. Bock, S. K. Das, R. Grunwald, S. Osten, P. Staudt, and G. Stibenz, “Spectral and temporal response of liquid-crystal-on-silicon spatial light modulators,” Appl. Phys. Lett.92(15), 151105 (2008).
[CrossRef]

Steinmeyer, G.

Stibenz, G.

M. Bock, S. K. Das, R. Grunwald, S. Osten, P. Staudt, and G. Stibenz, “Spectral and temporal response of liquid-crystal-on-silicon spatial light modulators,” Appl. Phys. Lett.92(15), 151105 (2008).
[CrossRef]

R. Grunwald, M. Bock, V. Kebbel, S. Huferath, U. Neumann, G. Steinmeyer, G. Stibenz, J.-L. Néron, and M. Piché, “Ultrashort-pulsed truncated polychromatic Bessel-Gauss beams,” Opt. Express16(2), 1077–1089 (2008).
[CrossRef] [PubMed]

Suntsov, S.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett.105(25), 253901 (2010).
[CrossRef] [PubMed]

Tacca, M.

Tandon, S.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater.5(2), 93–96 (2006).
[CrossRef] [PubMed]

Trillo, S.

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(9), 093904 (2003).
[CrossRef] [PubMed]

Trull, J.

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(9), 093904 (2003).
[CrossRef] [PubMed]

Turunen, J.

Tzortzakis, S.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett.105(25), 253901 (2010).
[CrossRef] [PubMed]

Valiulis, G.

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(9), 093904 (2003).
[CrossRef] [PubMed]

Valtna, H.

P. Saari, M. Menert, and H. Valtna, “Photon localization barrier can be overcome,” Opt. Commun.246(4-6), 445–450 (2005).
[CrossRef]

Vasa, P.

Vasara, A.

Wagner, J.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun.151(4-6), 207–211 (1998).
[CrossRef]

Weber, H.

M. Bouafia, A. Bencheikh, L. Bouamama, and H. Weber, “M2 quality factor as a key for mastering laser beam propagation,” Proc. SPIE5456, 130–140 (2004).
[CrossRef]

Wiggins, T. A.

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. Photonics4(2), 103–106 (2010).
[CrossRef]

Yariv, A.

Zamboni-Rached, M.

M. Zamboni-Rached, “Unidirectional decomposition method for obtaining exact localized wave solutions totally free of backward components,” Phys. Rev. A79(1), 013816 (2009).
[CrossRef]

M. Zamboni-Rached, E. Recami, and H. E. Hernández-Figueroa, “Theory of 'frozen waves': modeling the shape of stationary wave fields,” J. Opt. Soc. Am. A22, 2465–2475 (2005).

M. Zamboni-Rached, E. Recami, and H. E. Hernández-Figueroa, “New localized Superluminal solutions to the wave equations with finite total energies and arbitrary frequencies,” Eur. Phys. J. D21(2), 217–228 (2002).
[CrossRef]

Zhao, D.

Appl. Opt.

Appl. Phys. Lett.

M. Bock, S. K. Das, R. Grunwald, S. Osten, P. Staudt, and G. Stibenz, “Spectral and temporal response of liquid-crystal-on-silicon spatial light modulators,” Appl. Phys. Lett.92(15), 151105 (2008).
[CrossRef]

Eur. Phys. J. D

M. Zamboni-Rached, E. Recami, and H. E. Hernández-Figueroa, “New localized Superluminal solutions to the wave equations with finite total energies and arbitrary frequencies,” Eur. Phys. J. D21(2), 217–228 (2002).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control

J. Y. Lu and J. F. Greenleaf, “Nondiffracting X waves. Exact solutions to free space scalar wave equation and their finite aperture realizations,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control39(1), 19–31 (1992).
[CrossRef] [PubMed]

J. Y. Lu and J. F. Greenleaf, “Experimental verification of nondiffracting X waves,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control39(3), 441–446 (1992).
[CrossRef] [PubMed]

J. Mod. Opt.

S. Chávez-Cerda, “A new approach to Bessel beams,” J. Mod. Opt.46, 923–930 (1999).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

JEOS:RP

R. Grunwald and M. Bock, “Spatially encoded localized wavepackets for ultrafast optical data transfer,” JEOS:RP (submitted to).

Laser Phys.

P. Saari, “How small a packet of photons can be made?” Laser Phys.16(4), 556–561 (2006).
[CrossRef]

Nat. Mater.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater.5(2), 93–96 (2006).
[CrossRef] [PubMed]

Nat. Photonics

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics4(2), 103–106 (2010).
[CrossRef]

Opt. & Photon. News

M. Mansuripur, “The uncertainty principle in classical optics,” Opt. & Photon. News, Jan. 2002, 44–48 (2002).

Opt. Commun.

S.-A. Amarande, “Beam propagation factor and the kurtosis parameter of flattened Gaussian beams,” Opt. Commun.129, 311–317 (1996).

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun.64(6), 491–495 (1987).
[CrossRef]

P. Saari, M. Menert, and H. Valtna, “Photon localization barrier can be overcome,” Opt. Commun.246(4-6), 445–450 (2005).
[CrossRef]

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun.151(4-6), 207–211 (1998).
[CrossRef]

Opt. Eng.

G. Scott, “Efficient generation of nearly diffraction-free beams using an axicon,” Opt. Eng.31(12), 2640–2646 (1992).
[CrossRef]

Opt. Express

Opt. Lett.

M. Bock, S. K. Das, C. Fischer, M. Diehl, P. Börner, and R. Grunwald, “Reconfigurable wavefront sensor for ultrashort pulses,” Opt. Lett.37(7), 1154–1156 (2012).
[CrossRef] [PubMed]

J. Arlt and M. J. Padgett, “Generation of a beam with a dark focus surrounded by regions of higher intensity: the optical bottle beam,” Opt. Lett.25(4), 191–193 (2000).
[CrossRef] [PubMed]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Comparison of Bessel and Gaussian beams,” Opt. Lett.13(2), 79–80 (1988).
[CrossRef] [PubMed]

B. Salik, J. Rosen, and A. Yariv, “Nondiffracting images under coherent illumination,” Opt. Lett.20(17), 1743–1745 (1995).
[CrossRef] [PubMed]

R. Borghi and M. Santarsiero, “M2 factor of Bessel-Gauss beams,” Opt. Lett.22(5), 262–264 (1997).
[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(5), 310–312 (1997).
[CrossRef] [PubMed]

I. Golub, “Fresnel axicon,” Opt. Lett.31(12), 1890–1892 (2006).
[CrossRef] [PubMed]

R. Grunwald, S. Huferath, M. Bock, U. Neumann, and S. Langer, “Angular tolerance of Shack-Hartmann wavefront sensors with microaxicons,” Opt. Lett.32(11), 1533–1535 (2007).
[CrossRef] [PubMed]

G. Rousseau, N. McCarthy, and M. Pichãé, “Description of pulse propagation in a dispersive medium by use of a pulse quality factor,” Opt. Lett.27(18), 1649–1651 (2002).
[CrossRef] [PubMed]

R. Grunwald, U. Neumann, U. Griebner, K. Reimann, G. Steinmeyer, and V. Kebbel, “Ultrashort-pulse wave-front autocorrelation,” Opt. Lett.28(23), 2399–2401 (2003).
[CrossRef] [PubMed]

K. Reivelt and P. Saari, “Bessel-Gauss pulse as an appropriate mathematical model for optically realizable localized waves,” Opt. Lett.29(11), 1176–1178 (2004).
[CrossRef] [PubMed]

Phys. Rev. A

M. Z. Rached and E. Recami, “Subluminal wave bullets: Exact localized subluminal solutions to the wave equations,” Phys. Rev. A77(3), 033824 (2008).
[CrossRef]

M. Zamboni-Rached, “Unidirectional decomposition method for obtaining exact localized wave solutions totally free of backward components,” Phys. Rev. A79(1), 013816 (2009).
[CrossRef]

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. A67(6), 063820 (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] [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]

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(9), 093904 (2003).
[CrossRef] [PubMed]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

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

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett.105(25), 253901 (2010).
[CrossRef] [PubMed]

P. Sprangle and B. Hafizi, “Comment on nondiffracting beams,” Phys. Rev. Lett.66(6), 837 (1991).
[CrossRef] [PubMed]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Durnin, Miceli, and Eberly Reply,” Phys. Rev. Lett.66(6), 838 (1991).
[CrossRef] [PubMed]

Proc. SPIE

A. Siegman, “New developments in laser resonators,” Proc. SPIE1224, 2–14 (1990).
[CrossRef]

M. Bock, S. K. Das, and R. Grunwald, “Adaptive shaping of complex pulsed nondiffracting light fields,” Proc. SPIE7716, 7950–7958 (2011).

R. Grunwald and M. Bock, “Programmable microoptics for ultrashort pulses,” Proc. SPIE7716, 77160P, 77160P-8 (2010).
[CrossRef]

M. Bouafia, A. Bencheikh, L. Bouamama, and H. Weber, “M2 quality factor as a key for mastering laser beam propagation,” Proc. SPIE5456, 130–140 (2004).
[CrossRef]

Other

R. Grunwald and M. Bock, “Programmable micro-optics for ultrashort pulses,” SPIE Newsroom (2010). http://spie.org/x39625.xml?highlight=x2422&ArticleID=x39625 .

M. Piché and R. Grunwald, private communication. In the discussion, the product of M2 and P2 was considered to be used to describe the spatio-temporal beam properties of pulsed Bessel beams.

R. Grunwald and M. Bock, “Spatio-spectral analysis and encoding of ultrashort pulses with higher-order statistical moments,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper CThM2.

R. Grunwald, Thin-film microoptics - new frontiers of spatio-temporal beam shaping (Elsevier, Amsterdam, 2007).

H. E. Hernández-Figueroa, M. Zamboni-Rached, and E. Recami, eds., Localized Waves, Theory and Experiments (Wiley & Sons, New York, 2008).

J. A. Stratton, Electromagnetic Theory (McGraw Hill, New York, 1941), 356.

P. Saari, “Photon Localization Revisited,” in: Quantum Optics and Laser Experiments Sergiy Lyagushin Ed. (InTech - Open Access Publisher, Croatia, 2012), 49–66.

R. Grunwald, U. Griebner, U. Neumann, A. Kummrow, E. T. J. Nibbering, M. Piché, G. Rousseau, M. Fortin, and V. Kebbel, “Generation of ultrashort-pulse nondiffracting beams and X-waves with thin-film axicons,” in: M. Murnane, N. F. Scherer, and A. M. Weiner (Eds.), Ultrafast Phenomena XIII (Springer-Verlag, New York, 2002) 247–249.

S. Trillo and W. Torruellas Eds, Spatial Dolitons (Springer, Berlin, 2001), pp. 73–74.

Y. S, Kivshar and G. P. Agrawal, Optical solitons - From fibers to photonic crystals (Academic Press, Elsevier Science, Amsterdam, 2003), pp. 226–228.

Supplementary Material (3)

» Media 1: AVI (28150 KB)     
» Media 2: AVI (25777 KB)     
» Media 3: AVI (14697 KB)     

Cited By

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

Alert me when this article is cited.


Figures (15)

Fig. 1
Fig. 1

Principle of generating highly localized wavepackets (HLWs). Self-apodized (diffraction-free) spatial filtering of a pulsed Bessel beam (BB) is used to generate a radially symmetric needle beam (NB). By linear and circular transform algorithms (circular and double arrow), non-radially symmetric profiles of stretched (linear beam, LB) and tubular structure (tubular beam, TB) can be obtained. The propagation remains quasi-nondiffracting in the spatial and temporal domain.

Fig. 2
Fig. 2

Setup for the generation and characterization of programmable HLWs (schematically). The pulses emitted by a Ti:sapphire oscillator (Venteon, minimum pulse duration 6 fs, center wavelength 800 nm, FWHM spectral bandwidth 300 nm, pulse energy 7 nJ, repetition frequency 80 MHz) are shaped with an LCoS-SLM. The time-integrated intensity distribution is detected with a CCD or EMCCD camera (EMCCD). For a 2D spatially resolved analysis of the temporal pulse properties, second order autocorrelation is performed with a balanced interferometer (M1-M4 = mirrors, BS = beam splitter, BBO = beta barium borate crystal for SHG) by tuning the length one interferometer arm. The resulting time delay Δτ is doubled in a round trip and leads to a final delay of 2Δτ between the pulse replicas. Spectral maps are detected with a position-controlled fiber spectrometer (Ocean optics).

Fig. 3
Fig. 3

Selected basic types of axicons for the generation of highly localized wavepackets: (a) conus axicon shaping needle beams, (b) torus axicon shaping tubular beams, and (c) stretched conus axicon with central bi-prismatic zone shaping linear beams (effective height profiles, schematically). Possible apodization (e.g. by flattened contact angles) is not shown here.

Fig. 4
Fig. 4

Comparison of the propagation characteristics of pulsed diffractive and nondiffractive twin beams, left: phase distributions of pairs of (a) hard circular apertures and (d) flat axicons programmed into the SLM as gray value maps. The maximum brightness in (a) indicates the largest phase value for this device (π). Pictures (b),(e) and (c),(f) show intensity profiles measured at distances of z1 = 18.5 mm and z2 = 138.5 mm, respectively. Double beams were chosen to study cross-talk and interference effects of neighboring beams (radii: 380 µm; average conical angle of axicon: 0.13°, incident angle about 20°). The field of view was 2.3 x 2.3 mm2 in all cases.

Fig. 5
Fig. 5

Comparison of the propagation of Gaussian and needle beams (data corresponding to Figs. 4(e,f)): (a) increase of the radii (radial intensity decay to 1/e2) as a function of distance; circles: simulation for monochromatic (800 nm) Gaussian beam; squares: experimental data for a polychromatic needle beam (Ti:sapphire oscillator, pulse duration 6 fs), (b) measured and theoretical center intensity as a function of distance for a needle and Gaussian beam, respectively (green dashed line: input intensity without phase profile at zero voltage). The lines represent fit curves. To enable a better comparison, the Gaussian beam was transferred to the waist position of the needle beam. The deviations in the beginning of the propagation of the needle beam result from a non-perfect shape of the axicons in the central region.

Fig. 6
Fig. 6

Nonlinear characterization of multiple few-cycle wavepackets at a distance of 100 mm generated by an array of conical profiles (axicons) programmed in the phase map of an LCoS-SLM: (a) intensity distribution at zero time delay, (b) autocorrelation trace for a selected position in comparison to a theoretical bandwidth-limited pulse (flat spectral phase), (c) Visualization of the spatio-temporal structure by post-processed data of spatio-temporal 2nd order autocorrelation (fixed DC value added, size and brightness encoded according to the absolute value, perspective drawing with vanishing point). Conditions: axicon period 720 µm, effective height 400 nm, conical angle 0.13°, incident angle 43°; source: Ti:sapphire oscillator, nonlinear converter: 10 µm thick BBO crystal, pulse duration 6.5 fs, detector: EMCCD).

Fig. 7
Fig. 7

Programmable torus axicons: comparison of two discretized structures of different symmetry. (a) and (b): 2D gray value maps (1 pixel), (c) linear cuts with effective height profiles. The corresponding symmetry factors were SF = 0.50 in the picture (a) and the curve with red dots in (c), and SF = 1.00 in (b) and the curve with blue squares in (c).

Fig. 8
Fig. 8

Geometry of hollow beams as a function of the axicon symmetry: (a) intensity profile at a distance of z = 8 mm for SF = 0.5 (blue squares), 0.7 (green circles) and 0.9 (red triangles). At this distance, the best overall contrast was obtained. Inner and outer contrast Ci = 84% and Ca = 55% keep nearly constant over the considered range of SF; (b) dependence of the hollow beam diameter (peak-to-peak distance for central cut) on SF. One recognizes that the diameter scales linearly with this parameter in fairly good approximation.

Fig. 9
Fig. 9

Propagation of a hollow beam array (a) 3D-reconstruction from measured x-, y- and z- intensity data (b) Intensity map of a hexagonal array of hollow beams generated with an LCoS-SLM (period about 430 µm, distance z = 8 mm, ellipticity corrected by a linear transform factor SF = 0.9 in one direction, field of view: 1.2 x 0.8 mm2).

Fig. 10
Fig. 10

Stable propagation zone of a pulsed hollow beam generated with an asymmetric toroidal axicon (SF = 0.8): (a) intensity profiles measured at distances between 0 and 15 mm; (b) peak intensity (red dots) and normalized diameter (related to a reference diameter of 394 µm) as a function of distance (please notice the different scales for CCD-signal and diameter).

Fig. 11
Fig. 11

Temporal properties of a solitary few-cycle ring-shaped HLW generated by programming a toroidal axicon (outer diameter 3.2 mm, conical beam angle 0.029°) into an LCoS-SLM: (a) 2nd order autocorrelation function (ACF) measured at a distance of 400 mm (FWHM 9.8 fs, green line: derived intensity autocorrelation), (b) propagation-dependent FWHM of the ACF (black squares) and peak-to-peak ring diameter (blue circles). The averaged pulse duration along the zone was 6.7 ± 0.2 fs.

Fig. 12
Fig. 12

Reconstructed time-dependent E-field of the HLW. To indicate the structure of a ring-shaped light bullet, the iso-electric-field surface of 6.8-fs pulses was retrieved from spatially resolved second-order autocorrelation. For visualization purposes, a DC-field (corresponding to the maximum field amplitude) was added [64] (red circles: field maxima, d = maximum-to-maximum ring diameter, Δτcycle = field oscillation period in time).

Fig. 13
Fig. 13

Stack of pulsed nondiffracting linear HLWs (light blades) generated from the Ti:sapphire oscillator beam: (a) 3D plot with a nonlinear dependence of the color coded structure on the intensity (initial pulse duration 6.5 fs, perspective drawing with vanishing point, see Media 1); (b) axially dependent thickness of the light blades. Within the first 15 mm of propagation it was found to be about 60 µm.

Fig. 14
Fig. 14

Quasi-undistorted propagation of a small-scale ultrashort-pulsed pattern (MBI logo) composed of linear HLWs as elementary beams [52,65]. The “flying images” were generated by programming bi-prismatic microaxicon profiles in the phase map of an LCoS-SLM (red square, left). These experiments were performed with a Ti:sapphire laser oscillator at pulse duration of 13 fs and a center wavelength of 800 nm (image detection with CCD camera, image contrast slightly enhanced). A movie of the propagation is found in Media 2 for 13 fs (between z = 2.5 and 8.5 mm) and in Media 3 for 6.5 fs pulses (between z = 0.0 and 5.0 mm).

Fig. 15
Fig. 15

Propagation dependent contrast of a selected feature (a) of the pattern corresponding to the experimental data used for Fig. 14 (red bar: cut, inset in red square: enlarged cut area). For distances < 10 mm, high contrast was observed (b). The increase of the FWHM diameter of the image feature as a function of the propagation distance is indicated in (c).

Equations (8)

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

U(r,t)=exp[i(kxωt)] J 0 (kr),
M 2 =4π σ 0 σ f
D(z)=f(z) λ 2nsinθ
I NB (r)f( z 0 ) J 0 2 for r < r 1
I NB (r)=0 for r> r 1
P 2 =4π σ υ σ t
L 2 = M 2 P 2 =4π σ 0 σ f σ υ σ t
SF= 2 r i R

Metrics