Abstract

We numerically investigate the spatiotemporal structure of Bessel beams generated with spatial light modulators (SLMs). Grating-like phase masks enable the spatial filtering of undesired diffraction orders produced by SLMs. Pulse front tilt and temporal broadening effects are investigated. In addition, we explore the influence of phase wrapping and show that the spatiotemporal structure of SLM-generated femtosecond Bessel beams is similar to Bessel X-pulses at short propagation distance and to subluminal pulsed Bessel beams at long propagation distance.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
    [CrossRef]
  2. D. Mcgloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
    [CrossRef]
  3. T. Cižmár, V. Kollárová, X. Tsampoula, F. Gunn-Moore, W. Sibbett, Z. Bouchal, and K. Dholakia, “Generation of multiple Bessel beams for a biophotonics workstation,” Opt. Express 16, 14024–14035 (2008).
    [CrossRef]
  4. F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010).
    [CrossRef]
  5. P. Saari and K. Reivelt, “Evidence of x-shaped propagation-invariant localized light waves,” Phys. Rev. Lett. 79, 4135 (1997).
    [CrossRef]
  6. P. Polynkin, M. Kolesik, A. Roberts, D. Faccio, P. Di Trapani, and J. Moloney, “Generation of extended plasma channels in air using femtosecond Bessel beams,” Opt. Express 16, 15733–15740 (2008).
    [CrossRef]
  7. M. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear unbalanced Bessel beams: stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93, 153902 (2004).
    [CrossRef]
  8. Y. Matsuoka, Y. Kizuka, and T. Inoue, “The characteristics of laser micro drilling using Bessel beam,” Appl. Phys. A 84, 423–430 (2006).
    [CrossRef]
  9. M. K. Bhuyan, F. Courvoisier, P.-A. Lacourt, M. Jacquot, L. Furfaro, M. J. Withford, and J. M. Dudley, “High aspect ratio taper-free microchannel fabrication using femtosecond Bessel beams,” Opt. Express 18, 566–574 (2010).
    [CrossRef]
  10. M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett. 97, 081102 (2010).
    [CrossRef]
  11. M. A. Porras, P. Di Trapani, and W. Hu, “Optical wave modes: localized and propagation-invariant wave packets in optically transparent dispersive media,” in Localized Waves, H. E. Hernandez-Figueroa, M. Zamboni-Rached, and E. Recami, eds. (Wiley, 2008), pp. 217–241.
  12. M. Clerici, D. Faccio, A. Lotti, E. Rubino, O. Jedrkiewicz, J. Biegert, and P. Di Trapani, “Finite-energy, accelerating Bessel pulses,” Opt. Express 16, 19807–19811 (2008).
    [CrossRef]
  13. C. Sheppard, “Bessel pulse beams and focus wave modes,” J. Opt. Soc. Am. A 18, 2594–2600 (2001).
    [CrossRef]
  14. A. Vasara, J. Turunen, and A. T. Friberg, “Realization of general nondiffracting beams with computer-generated holograms,” J. Opt. Soc. Am. A 6, 1748–1754 (1989).
    [CrossRef]
  15. M. Bock, S. K. Das, and R. Grunwald, “Programmable ultrashort-pulsed flying images,” Opt. Express 17, 7465–7478 (2009).
    [CrossRef]
  16. N. Chattrapiban, E. A. Rogers, D. Cofield, W. T. Hill, and R. Roy, “Generation of nondiffracting Bessel beams by use of a spatial light modulator,” Opt. Lett. 28, 2183–2185 (2003).
    [CrossRef]
  17. M. Bock, S. K. Das, and R. Grunwald, “Ultrashort highly localized wavepackets,” Opt. Express 20, 12563–12578 (2012).
    [CrossRef]
  18. M. Bock, S. K. Das, C. Fischer, M. Diehl, P. Börner, and R. Grunwald, “Reconfigurable wavefront sensor for ultrashort pulses,” Opt. Lett. 37, 1154–1156 (2012).
    [CrossRef]
  19. T. Hara, “A liquid crystal spatial light phase modulator and its applications,” Proc. SPIE 5642, 78–89 (2005).
    [CrossRef]
  20. J. Leach, G. M. Gibson, M. J. Padgett, E. Esposito, G. McConnell, A. J. Wright, and J. M. Girkin, “Generation of achromatic Bessel beams using a compensated spatial light modulator,” Opt. Express 14, 5581–5587 (2006).
    [CrossRef]
  21. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  22. A. M. Weiner, Ultrafast Optics (Wiley, 2009).

2012 (2)

2010 (3)

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010).
[CrossRef]

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett. 97, 081102 (2010).
[CrossRef]

M. K. Bhuyan, F. Courvoisier, P.-A. Lacourt, M. Jacquot, L. Furfaro, M. J. Withford, and J. M. Dudley, “High aspect ratio taper-free microchannel fabrication using femtosecond Bessel beams,” Opt. Express 18, 566–574 (2010).
[CrossRef]

2009 (1)

2008 (3)

2006 (2)

2005 (2)

T. Hara, “A liquid crystal spatial light phase modulator and its applications,” Proc. SPIE 5642, 78–89 (2005).
[CrossRef]

D. Mcgloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[CrossRef]

2004 (1)

M. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear unbalanced Bessel beams: stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93, 153902 (2004).
[CrossRef]

2003 (1)

2001 (1)

1997 (1)

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

1989 (1)

1987 (1)

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

Bhuyan, M. K.

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett. 97, 081102 (2010).
[CrossRef]

M. K. Bhuyan, F. Courvoisier, P.-A. Lacourt, M. Jacquot, L. Furfaro, M. J. Withford, and J. M. Dudley, “High aspect ratio taper-free microchannel fabrication using femtosecond Bessel beams,” Opt. Express 18, 566–574 (2010).
[CrossRef]

Biegert, J.

Bock, M.

Börner, P.

Bouchal, Z.

Chattrapiban, N.

Cižmár, T.

Clerici, M.

Cofield, D.

Courvoisier, F.

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett. 97, 081102 (2010).
[CrossRef]

M. K. Bhuyan, F. Courvoisier, P.-A. Lacourt, M. Jacquot, L. Furfaro, M. J. Withford, and J. M. Dudley, “High aspect ratio taper-free microchannel fabrication using femtosecond Bessel beams,” Opt. Express 18, 566–574 (2010).
[CrossRef]

Das, S. K.

Dholakia, K.

Di Trapani, P.

P. Polynkin, M. Kolesik, A. Roberts, D. Faccio, P. Di Trapani, and J. Moloney, “Generation of extended plasma channels in air using femtosecond Bessel beams,” Opt. Express 16, 15733–15740 (2008).
[CrossRef]

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

M. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear unbalanced Bessel beams: stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93, 153902 (2004).
[CrossRef]

M. A. Porras, P. Di Trapani, and W. Hu, “Optical wave modes: localized and propagation-invariant wave packets in optically transparent dispersive media,” in Localized Waves, H. E. Hernandez-Figueroa, M. Zamboni-Rached, and E. Recami, eds. (Wiley, 2008), pp. 217–241.

Diehl, M.

Dubietis, A.

M. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear unbalanced Bessel beams: stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93, 153902 (2004).
[CrossRef]

Dudley, J. M.

M. K. Bhuyan, F. Courvoisier, P.-A. Lacourt, M. Jacquot, L. Furfaro, M. J. Withford, and J. M. Dudley, “High aspect ratio taper-free microchannel fabrication using femtosecond Bessel beams,” Opt. Express 18, 566–574 (2010).
[CrossRef]

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett. 97, 081102 (2010).
[CrossRef]

Durnin, J.

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

Eberly, J. H.

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

Esposito, E.

Faccio, D.

Fahrbach, F. O.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010).
[CrossRef]

Fischer, C.

Friberg, A. T.

Furfaro, L.

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett. 97, 081102 (2010).
[CrossRef]

M. K. Bhuyan, F. Courvoisier, P.-A. Lacourt, M. Jacquot, L. Furfaro, M. J. Withford, and J. M. Dudley, “High aspect ratio taper-free microchannel fabrication using femtosecond Bessel beams,” Opt. Express 18, 566–574 (2010).
[CrossRef]

Gibson, G. M.

Girkin, J. M.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Grunwald, R.

Gunn-Moore, F.

Hara, T.

T. Hara, “A liquid crystal spatial light phase modulator and its applications,” Proc. SPIE 5642, 78–89 (2005).
[CrossRef]

Hill, W. T.

Hu, W.

M. A. Porras, P. Di Trapani, and W. Hu, “Optical wave modes: localized and propagation-invariant wave packets in optically transparent dispersive media,” in Localized Waves, H. E. Hernandez-Figueroa, M. Zamboni-Rached, and E. Recami, eds. (Wiley, 2008), pp. 217–241.

Inoue, T.

Y. Matsuoka, Y. Kizuka, and T. Inoue, “The characteristics of laser micro drilling using Bessel beam,” Appl. Phys. A 84, 423–430 (2006).
[CrossRef]

Jacquot, M.

M. K. Bhuyan, F. Courvoisier, P.-A. Lacourt, M. Jacquot, L. Furfaro, M. J. Withford, and J. M. Dudley, “High aspect ratio taper-free microchannel fabrication using femtosecond Bessel beams,” Opt. Express 18, 566–574 (2010).
[CrossRef]

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett. 97, 081102 (2010).
[CrossRef]

Jedrkiewicz, O.

Kizuka, Y.

Y. Matsuoka, Y. Kizuka, and T. Inoue, “The characteristics of laser micro drilling using Bessel beam,” Appl. Phys. A 84, 423–430 (2006).
[CrossRef]

Kolesik, M.

Kollárová, V.

Lacourt, P. A.

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett. 97, 081102 (2010).
[CrossRef]

Lacourt, P.-A.

Leach, J.

Lotti, A.

Matsuoka, Y.

Y. Matsuoka, Y. Kizuka, and T. Inoue, “The characteristics of laser micro drilling using Bessel beam,” Appl. Phys. A 84, 423–430 (2006).
[CrossRef]

McConnell, G.

Mcgloin, D.

D. Mcgloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[CrossRef]

Miceli, J. J.

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

Moloney, J.

Padgett, M. J.

Parola, A.

M. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear unbalanced Bessel beams: stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93, 153902 (2004).
[CrossRef]

Polynkin, P.

Porras, M.

M. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear unbalanced Bessel beams: stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93, 153902 (2004).
[CrossRef]

Porras, M. A.

M. A. Porras, P. Di Trapani, and W. Hu, “Optical wave modes: localized and propagation-invariant wave packets in optically transparent dispersive media,” in Localized Waves, H. E. Hernandez-Figueroa, M. Zamboni-Rached, and E. Recami, eds. (Wiley, 2008), pp. 217–241.

Reivelt, K.

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

Roberts, A.

Rogers, E. A.

Rohrbach, A.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010).
[CrossRef]

Roy, R.

Rubino, E.

Saari, P.

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

Salut, R.

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett. 97, 081102 (2010).
[CrossRef]

Sheppard, C.

Sibbett, W.

Simon, P.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010).
[CrossRef]

Tsampoula, X.

Turunen, J.

Vasara, A.

Weiner, A. M.

A. M. Weiner, Ultrafast Optics (Wiley, 2009).

Withford, M. J.

Wright, A. J.

Appl. Phys. A (1)

Y. Matsuoka, Y. Kizuka, and T. Inoue, “The characteristics of laser micro drilling using Bessel beam,” Appl. Phys. A 84, 423–430 (2006).
[CrossRef]

Appl. Phys. Lett. (1)

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett. 97, 081102 (2010).
[CrossRef]

Contemp. Phys. (1)

D. Mcgloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[CrossRef]

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

Nat. Photonics (1)

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010).
[CrossRef]

Opt. Express (7)

Opt. Lett. (2)

Phys. Rev. Lett. (3)

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

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

M. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear unbalanced Bessel beams: stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93, 153902 (2004).
[CrossRef]

Proc. SPIE (1)

T. Hara, “A liquid crystal spatial light phase modulator and its applications,” Proc. SPIE 5642, 78–89 (2005).
[CrossRef]

Other (3)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

A. M. Weiner, Ultrafast Optics (Wiley, 2009).

M. A. Porras, P. Di Trapani, and W. Hu, “Optical wave modes: localized and propagation-invariant wave packets in optically transparent dispersive media,” in Localized Waves, H. E. Hernandez-Figueroa, M. Zamboni-Rached, and E. Recami, eds. (Wiley, 2008), pp. 217–241.

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 (6)

Fig. 1.
Fig. 1.

Experimental setup for femtosecond Bessel beam generation. A 100 fs laser beam is incident onto an SLM on which is encoded a phase mask. Spatial filtering is performed in the Fourier plane of the first lens of the demagnification system. Lens and microscope objective form a 4-f demagnification system to increase the range of achievable conical angles.

Fig. 2.
Fig. 2.

Intensity map I(z,r) for three different wavelengths covering the spectral FWHM of a 100 fs laser beam encoded on three color channels. The white regions show clearly where the spectral content of the beam is homogeneous. This shows the effect of the small angular dispersion (γ1°).

Fig. 3.
Fig. 3.

(a) Comparison of the experimental and numerical intensity maps in the (r,z) plane for a 100 fs Bessel beam with conical angle of 26°. (b) Corresponding experimental beam cross section.

Fig. 4.
Fig. 4.

Normalized intensity map of the pulse I(r,t) at different propagation distances z. (a) is the intensity profile for a radius equal to zero of the different temporal snapshots showing the small temporal broadening at z=200μm. For z=200μm the reference pulse (red) has been superposed to the one that has propagated 200 μm (green). (b) highlights the presence of a pulse front tilt Δτ visible for z=0. The pulse front tilt is also observed for the different z positions.

Fig. 5.
Fig. 5.

Schematic pulse propagation after the SLM in the (r,z) space. The insets in the upper part of the figure are the different simulated intensity snapshots at different times t0=0t1=Lcosθ/c, t2=t2+δ/c, t3=2t1.

Fig. 6.
Fig. 6.

Intensity distribution of a 10 fs pulse in the (r,t) space at different propagation distances z after the SLM. The Bessel beam has a conical angle θ=5°. Time is expressed in the reference frame of the pulse, moving at speed of light c. In the left column (a)–(c), the phase wrapping is performed over 2π, and in the right column (d)–(f) it is over 16π. The propagation distances are (a) z=0, (b) z=100μm (<L), (c) z=1000μm (L), (d) z=0, (e) z=500μm (<L), and (f) z=3000μm (L). Note that the value of L depends on the wrapping (N=2 or 16). In the insets of each subfigure, we compare with PBB and BXP with the same conical angle and identical propagation distances.

Equations (1)

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

Φ(r⃗,ω)=ωω0Φ(r⃗,ω0)=ωω0[ω0crsinθ+k⃗1·r⃗[2π]],

Metrics