Abstract

We present a technique for mapping the complete 3D spatial intensity profile of a laser beam from its fluorescence in an atomic vapour. We propagate shaped light through a rubidium vapour cell and record the resonant scattering from the side. From a single measurement we obtain a camera limited resolution of 200 × 200 transverse points and 659 longitudinal points. In constrast to invasive methods in which the camera is placed in the beam path, our method is capable of measuring patterns formed by counterpropagating laser beams. It has high resolution in all 3 dimensions, is fast and can be completely automated. The technique has applications in areas which require complex beam shapes, such as optical tweezers, atom trapping and pattern formation.

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References

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  1. D. G. Grier, “A revolution in optical manipulation,” Nature424, 810–816 (2003).
    [CrossRef] [PubMed]
  2. R. Grimm, M. Weidemüller, and Y. B. Ovchinnikov, “Optical dipole traps for neutral atoms,” Adv. Atom. Mol. Opt. Phys.42, 95 (2000).
    [CrossRef]
  3. R. W. Bowman and M. J. Padgett, “Optical trapping and binding,” Rep. Prog. Phys.76, 026401 (2013).
    [CrossRef] [PubMed]
  4. S. Franke-Arnold, J. Leach, M. J. Padgett, V. E. Lembessis, D. Ellinas, A. J. Wright, J. M. Girkin, P. Ohberg, and A. S. Arnold, “Optical ferris wheel for ultracold atoms,” Opt. Express15, 8619–8625 (2007).
    [CrossRef] [PubMed]
  5. Y. Zhang, “Generation of three-dimensional dark spots with a perfect light shell with a radially polarized laguerre–gaussian beam,” Appl. Opt.49, 6217–6223 (2010).
    [CrossRef] [PubMed]
  6. A. S. Arnold, “Extending dark optical trapping geometries,” Opt. Lett.37, 2505–2507 (2012).
    [CrossRef] [PubMed]
  7. R. Ozeri, L. Khaykovich, and N. Davidson, “Long spin relaxation times in a single-beam blue-detuned optical trap,” Phys. Rev. A59, R1750 (1999).
    [CrossRef]
  8. P. Xu, X. He, J. Wang, and M. Zhan, “Trapping a single atom in a blue detuned optical bottle beam trap,” Opt. Lett.35, 2164–2166 (2010).
    [CrossRef] [PubMed]
  9. M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics5, 343–348 (2011).
    [CrossRef]
  10. M. Lee, A. Curran, G. Gibson, M. Tassieri, N. Heckenberg, and M. Padgett, “Optical shield: measuring viscosity of turbid fluids using optical tweezers,” Opt. Express20, 12127–12132 (2012).
    [CrossRef] [PubMed]
  11. R. Bowman, G. Gibson, and M. Padgett, “Particle tracking stereomicroscopy in optical tweezers: control of trap shape,” Opt. Express18, 11785–11790 (2010).
    [CrossRef] [PubMed]
  12. G. Whyte and J. Courtial, “Experimental demonstration of holographic three-dimensional light shaping using a gerchberg–saxton algorithm,” New J. Phys.7, 117 (2005).
    [CrossRef]
  13. J. Romero, J. Leach, B. Jack, M. Dennis, S. Franke-Arnold, S. Barnett, and M. Padgett, “Entangled optical vortex links,” Phys. Rev Lett.106, 100407 (2011).
    [CrossRef] [PubMed]
  14. D. Walker, “A fluorescence technique for measurement of concentration in mixing liquids,” J. Phys. E20, 217 (1987).
    [CrossRef]
  15. A. J. Smits and T. T. Lim, Flow Visualisation: Techniques and Examples (Imperial College Press, London, 2000).
  16. A. Hoffmann, F. Zimmermann, H. Scharr, S. Krömker, and C. Schulz, “Instantaneous three-dimensional visualization of concentration distributions in turbulent flows with crossed-plane laser-induced fluorescence imaging,” Appl. Phys. B80, 125–131 (2005).
    [CrossRef]
  17. C. J. Foot, Atomic Physics (Oxford University Press, Oxford, 2004).
  18. J. Radon, “Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten,” Ber. Ver. Sächs. Akad. Wiss. Leipzig, Math-Phys. Kl.69, 262–277 (1917). In German. An English translation can be found in S. R. Deans: The Radon Transform and Some of Its Applications.
  19. R. Bowman, V. DAmbrosio, E. Rubino, O. Jedrkiewicz, P. Di Trapani, and M. Padgett, “Optimisation of a low cost slm for diffraction efficiency and ghost order suppression,” E. Phys. J. Spec. Top.199, 149–158 (2011).
    [CrossRef]
  20. J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett.88, 257901–257901 (2002).
    [CrossRef] [PubMed]

2013 (1)

R. W. Bowman and M. J. Padgett, “Optical trapping and binding,” Rep. Prog. Phys.76, 026401 (2013).
[CrossRef] [PubMed]

2012 (2)

2011 (3)

R. Bowman, V. DAmbrosio, E. Rubino, O. Jedrkiewicz, P. Di Trapani, and M. Padgett, “Optimisation of a low cost slm for diffraction efficiency and ghost order suppression,” E. Phys. J. Spec. Top.199, 149–158 (2011).
[CrossRef]

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics5, 343–348 (2011).
[CrossRef]

J. Romero, J. Leach, B. Jack, M. Dennis, S. Franke-Arnold, S. Barnett, and M. Padgett, “Entangled optical vortex links,” Phys. Rev Lett.106, 100407 (2011).
[CrossRef] [PubMed]

2010 (3)

2007 (1)

2005 (2)

A. Hoffmann, F. Zimmermann, H. Scharr, S. Krömker, and C. Schulz, “Instantaneous three-dimensional visualization of concentration distributions in turbulent flows with crossed-plane laser-induced fluorescence imaging,” Appl. Phys. B80, 125–131 (2005).
[CrossRef]

G. Whyte and J. Courtial, “Experimental demonstration of holographic three-dimensional light shaping using a gerchberg–saxton algorithm,” New J. Phys.7, 117 (2005).
[CrossRef]

2003 (1)

D. G. Grier, “A revolution in optical manipulation,” Nature424, 810–816 (2003).
[CrossRef] [PubMed]

2002 (1)

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett.88, 257901–257901 (2002).
[CrossRef] [PubMed]

2000 (1)

R. Grimm, M. Weidemüller, and Y. B. Ovchinnikov, “Optical dipole traps for neutral atoms,” Adv. Atom. Mol. Opt. Phys.42, 95 (2000).
[CrossRef]

1999 (1)

R. Ozeri, L. Khaykovich, and N. Davidson, “Long spin relaxation times in a single-beam blue-detuned optical trap,” Phys. Rev. A59, R1750 (1999).
[CrossRef]

1987 (1)

D. Walker, “A fluorescence technique for measurement of concentration in mixing liquids,” J. Phys. E20, 217 (1987).
[CrossRef]

1917 (1)

J. Radon, “Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten,” Ber. Ver. Sächs. Akad. Wiss. Leipzig, Math-Phys. Kl.69, 262–277 (1917). In German. An English translation can be found in S. R. Deans: The Radon Transform and Some of Its Applications.

Arnold, A. S.

Barnett, S.

J. Romero, J. Leach, B. Jack, M. Dennis, S. Franke-Arnold, S. Barnett, and M. Padgett, “Entangled optical vortex links,” Phys. Rev Lett.106, 100407 (2011).
[CrossRef] [PubMed]

Barnett, S. M.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett.88, 257901–257901 (2002).
[CrossRef] [PubMed]

Bowman, R.

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics5, 343–348 (2011).
[CrossRef]

R. Bowman, V. DAmbrosio, E. Rubino, O. Jedrkiewicz, P. Di Trapani, and M. Padgett, “Optimisation of a low cost slm for diffraction efficiency and ghost order suppression,” E. Phys. J. Spec. Top.199, 149–158 (2011).
[CrossRef]

R. Bowman, G. Gibson, and M. Padgett, “Particle tracking stereomicroscopy in optical tweezers: control of trap shape,” Opt. Express18, 11785–11790 (2010).
[CrossRef] [PubMed]

Bowman, R. W.

R. W. Bowman and M. J. Padgett, “Optical trapping and binding,” Rep. Prog. Phys.76, 026401 (2013).
[CrossRef] [PubMed]

Courtial, J.

G. Whyte and J. Courtial, “Experimental demonstration of holographic three-dimensional light shaping using a gerchberg–saxton algorithm,” New J. Phys.7, 117 (2005).
[CrossRef]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett.88, 257901–257901 (2002).
[CrossRef] [PubMed]

Curran, A.

DAmbrosio, V.

R. Bowman, V. DAmbrosio, E. Rubino, O. Jedrkiewicz, P. Di Trapani, and M. Padgett, “Optimisation of a low cost slm for diffraction efficiency and ghost order suppression,” E. Phys. J. Spec. Top.199, 149–158 (2011).
[CrossRef]

Davidson, N.

R. Ozeri, L. Khaykovich, and N. Davidson, “Long spin relaxation times in a single-beam blue-detuned optical trap,” Phys. Rev. A59, R1750 (1999).
[CrossRef]

Dennis, M.

J. Romero, J. Leach, B. Jack, M. Dennis, S. Franke-Arnold, S. Barnett, and M. Padgett, “Entangled optical vortex links,” Phys. Rev Lett.106, 100407 (2011).
[CrossRef] [PubMed]

Di Trapani, P.

R. Bowman, V. DAmbrosio, E. Rubino, O. Jedrkiewicz, P. Di Trapani, and M. Padgett, “Optimisation of a low cost slm for diffraction efficiency and ghost order suppression,” E. Phys. J. Spec. Top.199, 149–158 (2011).
[CrossRef]

Ellinas, D.

Foot, C. J.

C. J. Foot, Atomic Physics (Oxford University Press, Oxford, 2004).

Franke-Arnold, S.

J. Romero, J. Leach, B. Jack, M. Dennis, S. Franke-Arnold, S. Barnett, and M. Padgett, “Entangled optical vortex links,” Phys. Rev Lett.106, 100407 (2011).
[CrossRef] [PubMed]

S. Franke-Arnold, J. Leach, M. J. Padgett, V. E. Lembessis, D. Ellinas, A. J. Wright, J. M. Girkin, P. Ohberg, and A. S. Arnold, “Optical ferris wheel for ultracold atoms,” Opt. Express15, 8619–8625 (2007).
[CrossRef] [PubMed]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett.88, 257901–257901 (2002).
[CrossRef] [PubMed]

Gibson, G.

Girkin, J. M.

Grier, D. G.

D. G. Grier, “A revolution in optical manipulation,” Nature424, 810–816 (2003).
[CrossRef] [PubMed]

Grimm, R.

R. Grimm, M. Weidemüller, and Y. B. Ovchinnikov, “Optical dipole traps for neutral atoms,” Adv. Atom. Mol. Opt. Phys.42, 95 (2000).
[CrossRef]

He, X.

Heckenberg, N.

Hoffmann, A.

A. Hoffmann, F. Zimmermann, H. Scharr, S. Krömker, and C. Schulz, “Instantaneous three-dimensional visualization of concentration distributions in turbulent flows with crossed-plane laser-induced fluorescence imaging,” Appl. Phys. B80, 125–131 (2005).
[CrossRef]

Jack, B.

J. Romero, J. Leach, B. Jack, M. Dennis, S. Franke-Arnold, S. Barnett, and M. Padgett, “Entangled optical vortex links,” Phys. Rev Lett.106, 100407 (2011).
[CrossRef] [PubMed]

Jedrkiewicz, O.

R. Bowman, V. DAmbrosio, E. Rubino, O. Jedrkiewicz, P. Di Trapani, and M. Padgett, “Optimisation of a low cost slm for diffraction efficiency and ghost order suppression,” E. Phys. J. Spec. Top.199, 149–158 (2011).
[CrossRef]

Khaykovich, L.

R. Ozeri, L. Khaykovich, and N. Davidson, “Long spin relaxation times in a single-beam blue-detuned optical trap,” Phys. Rev. A59, R1750 (1999).
[CrossRef]

Krömker, S.

A. Hoffmann, F. Zimmermann, H. Scharr, S. Krömker, and C. Schulz, “Instantaneous three-dimensional visualization of concentration distributions in turbulent flows with crossed-plane laser-induced fluorescence imaging,” Appl. Phys. B80, 125–131 (2005).
[CrossRef]

Leach, J.

J. Romero, J. Leach, B. Jack, M. Dennis, S. Franke-Arnold, S. Barnett, and M. Padgett, “Entangled optical vortex links,” Phys. Rev Lett.106, 100407 (2011).
[CrossRef] [PubMed]

S. Franke-Arnold, J. Leach, M. J. Padgett, V. E. Lembessis, D. Ellinas, A. J. Wright, J. M. Girkin, P. Ohberg, and A. S. Arnold, “Optical ferris wheel for ultracold atoms,” Opt. Express15, 8619–8625 (2007).
[CrossRef] [PubMed]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett.88, 257901–257901 (2002).
[CrossRef] [PubMed]

Lee, M.

Lembessis, V. E.

Lim, T. T.

A. J. Smits and T. T. Lim, Flow Visualisation: Techniques and Examples (Imperial College Press, London, 2000).

Ohberg, P.

Ovchinnikov, Y. B.

R. Grimm, M. Weidemüller, and Y. B. Ovchinnikov, “Optical dipole traps for neutral atoms,” Adv. Atom. Mol. Opt. Phys.42, 95 (2000).
[CrossRef]

Ozeri, R.

R. Ozeri, L. Khaykovich, and N. Davidson, “Long spin relaxation times in a single-beam blue-detuned optical trap,” Phys. Rev. A59, R1750 (1999).
[CrossRef]

Padgett, M.

M. Lee, A. Curran, G. Gibson, M. Tassieri, N. Heckenberg, and M. Padgett, “Optical shield: measuring viscosity of turbid fluids using optical tweezers,” Opt. Express20, 12127–12132 (2012).
[CrossRef] [PubMed]

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics5, 343–348 (2011).
[CrossRef]

J. Romero, J. Leach, B. Jack, M. Dennis, S. Franke-Arnold, S. Barnett, and M. Padgett, “Entangled optical vortex links,” Phys. Rev Lett.106, 100407 (2011).
[CrossRef] [PubMed]

R. Bowman, V. DAmbrosio, E. Rubino, O. Jedrkiewicz, P. Di Trapani, and M. Padgett, “Optimisation of a low cost slm for diffraction efficiency and ghost order suppression,” E. Phys. J. Spec. Top.199, 149–158 (2011).
[CrossRef]

R. Bowman, G. Gibson, and M. Padgett, “Particle tracking stereomicroscopy in optical tweezers: control of trap shape,” Opt. Express18, 11785–11790 (2010).
[CrossRef] [PubMed]

Padgett, M. J.

R. W. Bowman and M. J. Padgett, “Optical trapping and binding,” Rep. Prog. Phys.76, 026401 (2013).
[CrossRef] [PubMed]

S. Franke-Arnold, J. Leach, M. J. Padgett, V. E. Lembessis, D. Ellinas, A. J. Wright, J. M. Girkin, P. Ohberg, and A. S. Arnold, “Optical ferris wheel for ultracold atoms,” Opt. Express15, 8619–8625 (2007).
[CrossRef] [PubMed]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett.88, 257901–257901 (2002).
[CrossRef] [PubMed]

Radon, J.

J. Radon, “Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten,” Ber. Ver. Sächs. Akad. Wiss. Leipzig, Math-Phys. Kl.69, 262–277 (1917). In German. An English translation can be found in S. R. Deans: The Radon Transform and Some of Its Applications.

Romero, J.

J. Romero, J. Leach, B. Jack, M. Dennis, S. Franke-Arnold, S. Barnett, and M. Padgett, “Entangled optical vortex links,” Phys. Rev Lett.106, 100407 (2011).
[CrossRef] [PubMed]

Rubino, E.

R. Bowman, V. DAmbrosio, E. Rubino, O. Jedrkiewicz, P. Di Trapani, and M. Padgett, “Optimisation of a low cost slm for diffraction efficiency and ghost order suppression,” E. Phys. J. Spec. Top.199, 149–158 (2011).
[CrossRef]

Scharr, H.

A. Hoffmann, F. Zimmermann, H. Scharr, S. Krömker, and C. Schulz, “Instantaneous three-dimensional visualization of concentration distributions in turbulent flows with crossed-plane laser-induced fluorescence imaging,” Appl. Phys. B80, 125–131 (2005).
[CrossRef]

Schulz, C.

A. Hoffmann, F. Zimmermann, H. Scharr, S. Krömker, and C. Schulz, “Instantaneous three-dimensional visualization of concentration distributions in turbulent flows with crossed-plane laser-induced fluorescence imaging,” Appl. Phys. B80, 125–131 (2005).
[CrossRef]

Smits, A. J.

A. J. Smits and T. T. Lim, Flow Visualisation: Techniques and Examples (Imperial College Press, London, 2000).

Tassieri, M.

Walker, D.

D. Walker, “A fluorescence technique for measurement of concentration in mixing liquids,” J. Phys. E20, 217 (1987).
[CrossRef]

Wang, J.

Weidemüller, M.

R. Grimm, M. Weidemüller, and Y. B. Ovchinnikov, “Optical dipole traps for neutral atoms,” Adv. Atom. Mol. Opt. Phys.42, 95 (2000).
[CrossRef]

Whyte, G.

G. Whyte and J. Courtial, “Experimental demonstration of holographic three-dimensional light shaping using a gerchberg–saxton algorithm,” New J. Phys.7, 117 (2005).
[CrossRef]

Wright, A. J.

Xu, P.

Zhan, M.

Zhang, Y.

Zimmermann, F.

A. Hoffmann, F. Zimmermann, H. Scharr, S. Krömker, and C. Schulz, “Instantaneous three-dimensional visualization of concentration distributions in turbulent flows with crossed-plane laser-induced fluorescence imaging,” Appl. Phys. B80, 125–131 (2005).
[CrossRef]

Adv. Atom. Mol. Opt. Phys. (1)

R. Grimm, M. Weidemüller, and Y. B. Ovchinnikov, “Optical dipole traps for neutral atoms,” Adv. Atom. Mol. Opt. Phys.42, 95 (2000).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

A. Hoffmann, F. Zimmermann, H. Scharr, S. Krömker, and C. Schulz, “Instantaneous three-dimensional visualization of concentration distributions in turbulent flows with crossed-plane laser-induced fluorescence imaging,” Appl. Phys. B80, 125–131 (2005).
[CrossRef]

Ber. Ver. Sächs. Akad. Wiss. Leipzig, Math-Phys. Kl. (1)

J. Radon, “Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten,” Ber. Ver. Sächs. Akad. Wiss. Leipzig, Math-Phys. Kl.69, 262–277 (1917). In German. An English translation can be found in S. R. Deans: The Radon Transform and Some of Its Applications.

E. Phys. J. Spec. Top. (1)

R. Bowman, V. DAmbrosio, E. Rubino, O. Jedrkiewicz, P. Di Trapani, and M. Padgett, “Optimisation of a low cost slm for diffraction efficiency and ghost order suppression,” E. Phys. J. Spec. Top.199, 149–158 (2011).
[CrossRef]

J. Phys. E (1)

D. Walker, “A fluorescence technique for measurement of concentration in mixing liquids,” J. Phys. E20, 217 (1987).
[CrossRef]

Nat. Photonics (1)

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics5, 343–348 (2011).
[CrossRef]

Nature (1)

D. G. Grier, “A revolution in optical manipulation,” Nature424, 810–816 (2003).
[CrossRef] [PubMed]

New J. Phys. (1)

G. Whyte and J. Courtial, “Experimental demonstration of holographic three-dimensional light shaping using a gerchberg–saxton algorithm,” New J. Phys.7, 117 (2005).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev Lett. (1)

J. Romero, J. Leach, B. Jack, M. Dennis, S. Franke-Arnold, S. Barnett, and M. Padgett, “Entangled optical vortex links,” Phys. Rev Lett.106, 100407 (2011).
[CrossRef] [PubMed]

Phys. Rev. A (1)

R. Ozeri, L. Khaykovich, and N. Davidson, “Long spin relaxation times in a single-beam blue-detuned optical trap,” Phys. Rev. A59, R1750 (1999).
[CrossRef]

Phys. Rev. Lett. (1)

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett.88, 257901–257901 (2002).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

R. W. Bowman and M. J. Padgett, “Optical trapping and binding,” Rep. Prog. Phys.76, 026401 (2013).
[CrossRef] [PubMed]

Other (2)

A. J. Smits and T. T. Lim, Flow Visualisation: Techniques and Examples (Imperial College Press, London, 2000).

C. J. Foot, Atomic Physics (Oxford University Press, Oxford, 2004).

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Figures (4)

Fig. 1
Fig. 1

a) Illustration of a laser beam and its projections on the xy, xz and yz planes. The beam shown is a superposition of two Laguerre Gaussian beams with l numbers 3 and −3. b) Cut of the same beam at z = 0 illustrating the Radon transform: the two profiles are the projections of the 2D pattern in the x and y planes.

Fig. 2
Fig. 2

Sample Reconstruction. a) Calculated transverse profile of the beam shown in Fig. 1. b) Reconstruction of the same profile from 30 1D projections, performed in 0.15 s. c) Analysis of the reconstruction accuracy with the number of projections. The residuals are the absolute difference between the original profile and the reconstruction, summed over all pixels and divided by the total of all pixels in the original image.

Fig. 3
Fig. 3

a) Experimental setup with beam shaping and detection sections as detailled in the main text. Right: Fluorescence image of the LG superposition of l=3,−3. at 0° (b) and 90° (c). d) Sample reconstruction from 116 projections taken from the same dataset.

Fig. 4
Fig. 4

Full 3D beam reconstruction

Equations (1)

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R sc = Γ 2 ( I / I sat ) 1 + ( I / I sat ) + 4 ( Δ / Γ ) 2 ,

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