Abstract

Self-imaging of ultrashort-pulsed nondiffracting needle beams, i.e., fringe-free Bessel beams, is analyzed. In contrast to the classical diffractive Talbot effect, pulse revivals with minimum spectral and temporal distortion are obtained. Robustness is further enhanced by self-reconstruction. The high-fidelity pulse transfer enables spatial and temporal multiplexing in free space without the need for a nonlinear medium, even at pulse durations down to the few-cycle range.

© 2017 Optical Society of America

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References

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2017 (1)

A. Treffer, M. Bock, U. Wallrabe, and R. Grunwald, Proc. SPIE 10120, 101200S (2017).
[Crossref]

2016 (1)

Y. Zhang, H. Zhong, M. R. Belić, N. Ahmed, Y. Zhang, and M. Xiao, Sci. Rep. 6, 23645 (2016).
[Crossref]

2015 (1)

2014 (1)

R. Grunwald, T. Elsaesser, and M. Bock, Sci. Rep. 4, 07148 (2014).
[Crossref]

2013 (5)

G. S. Sokolowskii, V. V. Dudelev, S. N. Losev, M. Butkus, K. K. Soboleva, A. I. Sobolev, A. G. Deryagin, V. I. Kuchinskii, W. Sibbett, and E. U. Rafailov, Quantum Electron. 43, 423 (2013).
[Crossref]

K. Yoshii, J. K. Anthony, and M. Katsuragawa, Light: Sci. Appl. 2, e58 (2013).
[Crossref]

M. Bock and R. Grunwald, Appl. Sci. 3, 139 (2013).
[Crossref]

J. Wen, Y. Zhang, and M. Xiao, Adv. Opt. Photon. 5, 83 (2013).
[Crossref]

J. Brunne and U. Wallrabe, Opt. Lett. 38, 1939 (2013).
[Crossref]

2012 (2)

2010 (1)

F. O. Fahrbach, P. Simon, and A. Rohrbach, Nat. Photonics 4, 780 (2010).
[Crossref]

2009 (1)

2008 (2)

2007 (1)

2003 (1)

Z. Bouchal, Czech. J. Phys. 53, 537 (2003).
[Crossref]

2002 (1)

2001 (1)

M. V. Berry, I. Marzoli, and W. P. Schleich, Phys. World 14, 39 (2001).
[Crossref]

2000 (1)

1999 (1)

1998 (2)

1992 (1)

1988 (1)

A. W. Lohmann, Optik 79, 41 (1988).

1981 (1)

T. Jannson and J. Jannson, J. Opt. Soc. Am. B 71, 1373 (1981).
[Crossref]

1967 (1)

1965 (1)

1927 (1)

H. T. Davis and W. J. Kirkham, Bull. Amer. Math. Soc. 33, 760 (1927).
[Crossref]

1836 (1)

W. H. F. Talbot, Philos. Mag. 9(56), 401 (1836).
[Crossref]

Ahmed, N.

Y. Zhang, H. Zhong, M. R. Belić, N. Ahmed, Y. Zhang, and M. Xiao, Sci. Rep. 6, 23645 (2016).
[Crossref]

Anthony, J. K.

K. Yoshii, J. K. Anthony, and M. Katsuragawa, Light: Sci. Appl. 2, e58 (2013).
[Crossref]

Azaña, J.

Belic, M. R.

Y. Zhang, H. Zhong, M. R. Belić, N. Ahmed, Y. Zhang, and M. Xiao, Sci. Rep. 6, 23645 (2016).
[Crossref]

Y. Zhang, H. Zhong, M. R. Belić, X. Liu, W. Zhong, Y. Zhang, and M. Xiao, Opt. Lett. 40, 5742 (2015).
[Crossref]

Berry, M. V.

M. V. Berry, I. Marzoli, and W. P. Schleich, Phys. World 14, 39 (2001).
[Crossref]

Bock, M.

A. Treffer, M. Bock, U. Wallrabe, and R. Grunwald, Proc. SPIE 10120, 101200S (2017).
[Crossref]

R. Grunwald, T. Elsaesser, and M. Bock, Sci. Rep. 4, 07148 (2014).
[Crossref]

M. Bock and R. Grunwald, Appl. Sci. 3, 139 (2013).
[Crossref]

M. Bock, S. K. Das, and R. Grunwald, Opt. Express 20, 12563 (2012).
[Crossref]

M. Bock, S. K. Das, C. Fischer, M. Diehl, P. Börner, and R. Grunwald, Opt. Lett. 37, 1154 (2012).
[Crossref]

M. Bock, S. K. Das, and R. Grunwald, Opt. Express 17, 7465 (2009).
[Crossref]

M. Bock, S. K. Das, R. Grunwald, S. Osten, P. Staudt, and G. Stibenz, Appl. Phys. Lett. 92, 151105 (2008).
[Crossref]

R. Grunwald, M. Bock, V. Kebbel, S. Huferath, U. Neumann, G. Steinmeyer, G. Stibenz, J.-L. Néron, and M. Piché, Opt. Express 16, 1077 (2008).
[Crossref]

R. Grunwald, S. Huferath, M. Bock, U. Neumann, and S. Langer, Opt. Lett. 32, 1533 (2007).
[Crossref]

R. Grunwald, U. Neumann, U. Griebner, G. Steinmeyer, G. Stibenz, M. Bock, and V. Kebbel, Localized Waves, Theory and Experiments, M. Zamboni-Rached, E. Recami, and H. E. Hernández-Figueroa, eds. (Wiley, 2008), pp. 299–313.

Börner, P.

Bouchal, Z.

Z. Bouchal, Czech. J. Phys. 53, 537 (2003).
[Crossref]

Z. Bouchal, J. Wagner, and M. Chlup, Opt. Commun. 151, 207 (1998).
[Crossref]

Brunne, J.

Butkus, M.

G. S. Sokolowskii, V. V. Dudelev, S. N. Losev, M. Butkus, K. K. Soboleva, A. I. Sobolev, A. G. Deryagin, V. I. Kuchinskii, W. Sibbett, and E. U. Rafailov, Quantum Electron. 43, 423 (2013).
[Crossref]

Chávez-Cerda, S.

Chlup, M.

Z. Bouchal, J. Wagner, and M. Chlup, Opt. Commun. 151, 207 (1998).
[Crossref]

Course, R. F.

Das, S. K.

Davis, H. T.

H. T. Davis and W. J. Kirkham, Bull. Amer. Math. Soc. 33, 760 (1927).
[Crossref]

Deryagin, A. G.

G. S. Sokolowskii, V. V. Dudelev, S. N. Losev, M. Butkus, K. K. Soboleva, A. I. Sobolev, A. G. Deryagin, V. I. Kuchinskii, W. Sibbett, and E. U. Rafailov, Quantum Electron. 43, 423 (2013).
[Crossref]

Diehl, M.

Dudelev, V. V.

G. S. Sokolowskii, V. V. Dudelev, S. N. Losev, M. Butkus, K. K. Soboleva, A. I. Sobolev, A. G. Deryagin, V. I. Kuchinskii, W. Sibbett, and E. U. Rafailov, Quantum Electron. 43, 423 (2013).
[Crossref]

Elsaesser, T.

R. Grunwald, T. Elsaesser, and M. Bock, Sci. Rep. 4, 07148 (2014).
[Crossref]

Fahrbach, F. O.

F. O. Fahrbach, P. Simon, and A. Rohrbach, Nat. Photonics 4, 780 (2010).
[Crossref]

Fischer, C.

Griebner, U.

R. Grunwald, U. Neumann, U. Griebner, G. Steinmeyer, G. Stibenz, M. Bock, and V. Kebbel, Localized Waves, Theory and Experiments, M. Zamboni-Rached, E. Recami, and H. E. Hernández-Figueroa, eds. (Wiley, 2008), pp. 299–313.

Grunwald, R.

A. Treffer, M. Bock, U. Wallrabe, and R. Grunwald, Proc. SPIE 10120, 101200S (2017).
[Crossref]

R. Grunwald, T. Elsaesser, and M. Bock, Sci. Rep. 4, 07148 (2014).
[Crossref]

M. Bock and R. Grunwald, Appl. Sci. 3, 139 (2013).
[Crossref]

M. Bock, S. K. Das, and R. Grunwald, Opt. Express 20, 12563 (2012).
[Crossref]

M. Bock, S. K. Das, C. Fischer, M. Diehl, P. Börner, and R. Grunwald, Opt. Lett. 37, 1154 (2012).
[Crossref]

M. Bock, S. K. Das, and R. Grunwald, Opt. Express 17, 7465 (2009).
[Crossref]

M. Bock, S. K. Das, R. Grunwald, S. Osten, P. Staudt, and G. Stibenz, Appl. Phys. Lett. 92, 151105 (2008).
[Crossref]

R. Grunwald, M. Bock, V. Kebbel, S. Huferath, U. Neumann, G. Steinmeyer, G. Stibenz, J.-L. Néron, and M. Piché, Opt. Express 16, 1077 (2008).
[Crossref]

R. Grunwald, S. Huferath, M. Bock, U. Neumann, and S. Langer, Opt. Lett. 32, 1533 (2007).
[Crossref]

R. Grunwald, U. Neumann, U. Griebner, G. Steinmeyer, G. Stibenz, M. Bock, and V. Kebbel, Localized Waves, Theory and Experiments, M. Zamboni-Rached, E. Recami, and H. E. Hernández-Figueroa, eds. (Wiley, 2008), pp. 299–313.

R. Grunwald, Thin-Film Microoptics—New Frontiers of Spatio-Temporal Beam Shaping (Elsevier, 2007), pp. 147–154.

Herman, R. M.

Hickmann, J. M.

Huferath, S.

Jannson, J.

T. Jannson and J. Jannson, J. Opt. Soc. Am. B 71, 1373 (1981).
[Crossref]

Jannson, T.

T. Jannson and J. Jannson, J. Opt. Soc. Am. B 71, 1373 (1981).
[Crossref]

Katsuragawa, M.

K. Yoshii, J. K. Anthony, and M. Katsuragawa, Light: Sci. Appl. 2, e58 (2013).
[Crossref]

Kebbel, V.

R. Grunwald, M. Bock, V. Kebbel, S. Huferath, U. Neumann, G. Steinmeyer, G. Stibenz, J.-L. Néron, and M. Piché, Opt. Express 16, 1077 (2008).
[Crossref]

R. Grunwald, U. Neumann, U. Griebner, G. Steinmeyer, G. Stibenz, M. Bock, and V. Kebbel, Localized Waves, Theory and Experiments, M. Zamboni-Rached, E. Recami, and H. E. Hernández-Figueroa, eds. (Wiley, 2008), pp. 299–313.

Kirkham, W. J.

H. T. Davis and W. J. Kirkham, Bull. Amer. Math. Soc. 33, 760 (1927).
[Crossref]

Kuchinskii, V. I.

G. S. Sokolowskii, V. V. Dudelev, S. N. Losev, M. Butkus, K. K. Soboleva, A. I. Sobolev, A. G. Deryagin, V. I. Kuchinskii, W. Sibbett, and E. U. Rafailov, Quantum Electron. 43, 423 (2013).
[Crossref]

Langer, S.

Latimer, P.

Liu, X.

Lohmann, A. W.

A. W. Lohmann, Optik 79, 41 (1988).

Losev, S. N.

G. S. Sokolowskii, V. V. Dudelev, S. N. Losev, M. Butkus, K. K. Soboleva, A. I. Sobolev, A. G. Deryagin, V. I. Kuchinskii, W. Sibbett, and E. U. Rafailov, Quantum Electron. 43, 423 (2013).
[Crossref]

Marzoli, I.

M. V. Berry, I. Marzoli, and W. P. Schleich, Phys. World 14, 39 (2001).
[Crossref]

Meneses-Nava, M. A.

Montgomery, W. D.

Muriel, M. A.

Néron, J.-L.

Neumann, U.

R. Grunwald, M. Bock, V. Kebbel, S. Huferath, U. Neumann, G. Steinmeyer, G. Stibenz, J.-L. Néron, and M. Piché, Opt. Express 16, 1077 (2008).
[Crossref]

R. Grunwald, S. Huferath, M. Bock, U. Neumann, and S. Langer, Opt. Lett. 32, 1533 (2007).
[Crossref]

R. Grunwald, U. Neumann, U. Griebner, G. Steinmeyer, G. Stibenz, M. Bock, and V. Kebbel, Localized Waves, Theory and Experiments, M. Zamboni-Rached, E. Recami, and H. E. Hernández-Figueroa, eds. (Wiley, 2008), pp. 299–313.

Osten, S.

M. Bock, S. K. Das, R. Grunwald, S. Osten, P. Staudt, and G. Stibenz, Appl. Phys. Lett. 92, 151105 (2008).
[Crossref]

Patorski, K.

K. Patorski, Progress in Optics, E. Wolf, ed. (North-Holland, 1989), Vol. 27, pp. 1–108.

Piché, M.

Rafailov, E. U.

G. S. Sokolowskii, V. V. Dudelev, S. N. Losev, M. Butkus, K. K. Soboleva, A. I. Sobolev, A. G. Deryagin, V. I. Kuchinskii, W. Sibbett, and E. U. Rafailov, Quantum Electron. 43, 423 (2013).
[Crossref]

Reivelt, K.

Rohrbach, A.

F. O. Fahrbach, P. Simon, and A. Rohrbach, Nat. Photonics 4, 780 (2010).
[Crossref]

Schleich, W. P.

M. V. Berry, I. Marzoli, and W. P. Schleich, Phys. World 14, 39 (2001).
[Crossref]

Sibbett, W.

G. S. Sokolowskii, V. V. Dudelev, S. N. Losev, M. Butkus, K. K. Soboleva, A. I. Sobolev, A. G. Deryagin, V. I. Kuchinskii, W. Sibbett, and E. U. Rafailov, Quantum Electron. 43, 423 (2013).
[Crossref]

Simon, P.

F. O. Fahrbach, P. Simon, and A. Rohrbach, Nat. Photonics 4, 780 (2010).
[Crossref]

Sobolev, A. I.

G. S. Sokolowskii, V. V. Dudelev, S. N. Losev, M. Butkus, K. K. Soboleva, A. I. Sobolev, A. G. Deryagin, V. I. Kuchinskii, W. Sibbett, and E. U. Rafailov, Quantum Electron. 43, 423 (2013).
[Crossref]

Soboleva, K. K.

G. S. Sokolowskii, V. V. Dudelev, S. N. Losev, M. Butkus, K. K. Soboleva, A. I. Sobolev, A. G. Deryagin, V. I. Kuchinskii, W. Sibbett, and E. U. Rafailov, Quantum Electron. 43, 423 (2013).
[Crossref]

Sokolowskii, G. S.

G. S. Sokolowskii, V. V. Dudelev, S. N. Losev, M. Butkus, K. K. Soboleva, A. I. Sobolev, A. G. Deryagin, V. I. Kuchinskii, W. Sibbett, and E. U. Rafailov, Quantum Electron. 43, 423 (2013).
[Crossref]

Staudt, P.

M. Bock, S. K. Das, R. Grunwald, S. Osten, P. Staudt, and G. Stibenz, Appl. Phys. Lett. 92, 151105 (2008).
[Crossref]

Steinmeyer, G.

R. Grunwald, M. Bock, V. Kebbel, S. Huferath, U. Neumann, G. Steinmeyer, G. Stibenz, J.-L. Néron, and M. Piché, Opt. Express 16, 1077 (2008).
[Crossref]

R. Grunwald, U. Neumann, U. Griebner, G. Steinmeyer, G. Stibenz, M. Bock, and V. Kebbel, Localized Waves, Theory and Experiments, M. Zamboni-Rached, E. Recami, and H. E. Hernández-Figueroa, eds. (Wiley, 2008), pp. 299–313.

Stibenz, G.

R. Grunwald, M. Bock, V. Kebbel, S. Huferath, U. Neumann, G. Steinmeyer, G. Stibenz, J.-L. Néron, and M. Piché, Opt. Express 16, 1077 (2008).
[Crossref]

M. Bock, S. K. Das, R. Grunwald, S. Osten, P. Staudt, and G. Stibenz, Appl. Phys. Lett. 92, 151105 (2008).
[Crossref]

R. Grunwald, U. Neumann, U. Griebner, G. Steinmeyer, G. Stibenz, M. Bock, and V. Kebbel, Localized Waves, Theory and Experiments, M. Zamboni-Rached, E. Recami, and H. E. Hernández-Figueroa, eds. (Wiley, 2008), pp. 299–313.

Talbot, W. H. F.

W. H. F. Talbot, Philos. Mag. 9(56), 401 (1836).
[Crossref]

Treffer, A.

A. Treffer, M. Bock, U. Wallrabe, and R. Grunwald, Proc. SPIE 10120, 101200S (2017).
[Crossref]

Wagner, J.

Z. Bouchal, J. Wagner, and M. Chlup, Opt. Commun. 151, 207 (1998).
[Crossref]

Wallrabe, U.

A. Treffer, M. Bock, U. Wallrabe, and R. Grunwald, Proc. SPIE 10120, 101200S (2017).
[Crossref]

J. Brunne and U. Wallrabe, Opt. Lett. 38, 1939 (2013).
[Crossref]

Wen, J.

Wiggins, T. A.

Winthrop, J. T.

Worthington, C. R.

Xiao, M.

Yoshii, K.

K. Yoshii, J. K. Anthony, and M. Katsuragawa, Light: Sci. Appl. 2, e58 (2013).
[Crossref]

Zhang, Y.

Zhong, H.

Y. Zhang, H. Zhong, M. R. Belić, N. Ahmed, Y. Zhang, and M. Xiao, Sci. Rep. 6, 23645 (2016).
[Crossref]

Y. Zhang, H. Zhong, M. R. Belić, X. Liu, W. Zhong, Y. Zhang, and M. Xiao, Opt. Lett. 40, 5742 (2015).
[Crossref]

Zhong, W.

Adv. Opt. Photon. (1)

Appl. Opt. (1)

Appl. Phys. Lett. (1)

M. Bock, S. K. Das, R. Grunwald, S. Osten, P. Staudt, and G. Stibenz, Appl. Phys. Lett. 92, 151105 (2008).
[Crossref]

Appl. Sci. (1)

M. Bock and R. Grunwald, Appl. Sci. 3, 139 (2013).
[Crossref]

Bull. Amer. Math. Soc. (1)

H. T. Davis and W. J. Kirkham, Bull. Amer. Math. Soc. 33, 760 (1927).
[Crossref]

Czech. J. Phys. (1)

Z. Bouchal, Czech. J. Phys. 53, 537 (2003).
[Crossref]

J. Opt. Soc. Am. (2)

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

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

T. Jannson and J. Jannson, J. Opt. Soc. Am. B 71, 1373 (1981).
[Crossref]

Light: Sci. Appl. (1)

K. Yoshii, J. K. Anthony, and M. Katsuragawa, Light: Sci. Appl. 2, e58 (2013).
[Crossref]

Nat. Photonics (1)

F. O. Fahrbach, P. Simon, and A. Rohrbach, Nat. Photonics 4, 780 (2010).
[Crossref]

Opt. Commun. (1)

Z. Bouchal, J. Wagner, and M. Chlup, Opt. Commun. 151, 207 (1998).
[Crossref]

Opt. Express (4)

Opt. Lett. (6)

Optik (1)

A. W. Lohmann, Optik 79, 41 (1988).

Philos. Mag. (1)

W. H. F. Talbot, Philos. Mag. 9(56), 401 (1836).
[Crossref]

Phys. World (1)

M. V. Berry, I. Marzoli, and W. P. Schleich, Phys. World 14, 39 (2001).
[Crossref]

Proc. SPIE (1)

A. Treffer, M. Bock, U. Wallrabe, and R. Grunwald, Proc. SPIE 10120, 101200S (2017).
[Crossref]

Quantum Electron. (1)

G. S. Sokolowskii, V. V. Dudelev, S. N. Losev, M. Butkus, K. K. Soboleva, A. I. Sobolev, A. G. Deryagin, V. I. Kuchinskii, W. Sibbett, and E. U. Rafailov, Quantum Electron. 43, 423 (2013).
[Crossref]

Sci. Rep. (2)

R. Grunwald, T. Elsaesser, and M. Bock, Sci. Rep. 4, 07148 (2014).
[Crossref]

Y. Zhang, H. Zhong, M. R. Belić, N. Ahmed, Y. Zhang, and M. Xiao, Sci. Rep. 6, 23645 (2016).
[Crossref]

Other (3)

R. Grunwald, Thin-Film Microoptics—New Frontiers of Spatio-Temporal Beam Shaping (Elsevier, 2007), pp. 147–154.

K. Patorski, Progress in Optics, E. Wolf, ed. (North-Holland, 1989), Vol. 27, pp. 1–108.

R. Grunwald, U. Neumann, U. Griebner, G. Steinmeyer, G. Stibenz, M. Bock, and V. Kebbel, Localized Waves, Theory and Experiments, M. Zamboni-Rached, E. Recami, and H. E. Hernández-Figueroa, eds. (Wiley, 2008), pp. 299–313.

Supplementary Material (1)

NameDescription
» Visualization 1: AVI (1374 KB)      Intensity propagation of a nondiffracting needle beam array consisting of 840 sub-beams generated from sub-3-cylce pulses of a Ti:sapphire laser oscillator.

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Figures (5)

Fig. 1.
Fig. 1.

Nondiffractive Talbot effect as a periodical constructive interference behind a finite uniform array of axicons of period a and element diameter d (schematically). θ is the half-conical beam angle. Spindle-shaped areas, needle beams (i.e., fringe-free Bessel beams); ring-shaped areas, hollow beams; L 0 , intensity maxima of first focal zones (centers of needle beams); L 1 , first nondiffractive Talbot distance; ( L 0 + L 1 ) / 2 , hollow beams with dark central regions.

Fig. 2.
Fig. 2.

Comparison of diffractive (D, black solid line) and nondiffractive Talbot distances (ND, open symbols) for a 2D array with a period of a = 100 μm and different integer Talbot orders N (parameter: half-conical beam angle θ ).

Fig. 3.
Fig. 3.

Time delay (color code) in needle beams as a function of the radius and half-conical beam angle. Inset: normalized radial intensity profiles at axial distances of maximum radius r for three angles. The needle beams are restricted to the central lobe of the squared Bessel function J 0 2 (dashed lines: suppressed outer rings). The maximum delay at the rim corresponds to a half-cycle.

Fig. 4.
Fig. 4.

Spatial and temporal propagation properties of a few-cycle needle beam array of a hexagonal structure (period: d = 230 μm , a = 445 μm , SHG). Transversal intensity profiles ( x y plane, left) and second-order autocorrelation (right) are shown for (a), (b) the axial distances of dark rings ( L 0 + L 1 ) / 2 = 60 mm ; (c), (d) the first nondiffractive Talbot distance L 1 = 105 mm ; and (e), (f) the second nondiffractive Talbot plane L 2 = 195 mm (e) and (f).

Fig. 5.
Fig. 5.

Intensity propagation of sub-three-cycle needle beams (part of an array of 840 beams) at the fundamental wavelengths (a) without and (b) with a local phase distortion as a radial-axial cut (box at the left: area of distortion). Nondiffracting self-reconstruction is indicated in transversal cuts at distances between 11.5 and 15 mm in steps of 0.5 mm (c)–(j) (axicon parameters: d = 120 μm , θ = 0.57 ° , exposure time 8 ms). The propagation of the complete beam array is presented in the supplementary material (Visualization 1).

Equations (7)

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L d = N 2 a 2 λ ,
L 0 = d 4 tan θ ,
L nd = N a tan θ + d 4 tan θ = N a tan θ + L 0 ,
L nd * = ( 4 N + 1 ) d 4 tan θ = ( 4 N + 1 ) L 0 ,
r 0 BB Z 0 2 π · λ sin θ
r 0 NB λ 2 sin θ .
Δ t = r sin θ c ,

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