Abstract

The Young’s double slit experiment is recreated using intense and short laser pulses. Our experiment evidences the role of the non-linear Kerr effect in the formation of interference patterns. In particular, our results evidence a mixed mechanism in which the zeroth diffraction order of each slit are mainly affected by self-focusing and self-phase modulation, while the higher orders propagate linearly. Despite of the complexity of the general problem of non-linear propagation, we demonstrate that this experiment retains its simplicity and allows for a geometrical interpretation in terms of simple optical paths. In consequence, our results may provide key ideas on experiments on the formation of interference patterns with intense laser fields in Kerr media.

© 2006 Optical Society of America

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  1. T. Young, "Experimental demonstration of the general law of the interference of light," Philos. Trans. R. Soc. London 94, 1-16 (1804).Q1
    [CrossRef]
  2. C. Jönsson, "Elektroneninterferenzen an mehreren künstlich hergestellter Feinspalten," Zeitschrift fur Physik 161454-474 (1961).
    [CrossRef]
  3. A. Tonomura, J. Endo, T. Matsuda, T. Kawasaki and H. Ezawa, "Demonstration of single-electron buildup of an interference pattern," Am. J. Phys. 57, 117-120 (1989).
    [CrossRef]
  4. A. Zelinger, R. Gähler, C. G. Shull, W. Treimer and W. Mampe, "Single- and double-slit diffraction of neutrons," Rev. Mod. Phys. 601067-1073 (1988).
    [CrossRef]
  5. O. Carnal and J. Mlynek, "Young’s double-slit experiment with atoms: A simple atom interferometer," Phys. Rev. Lett. 662689-2692 (1991).
    [CrossRef] [PubMed]
  6. M. W. Noel and C. R. Stroud, "Young’s double-slit interferometry within an Atom," Phys. Rev. Lett. 751252-1255 (1995).
    [CrossRef] [PubMed]
  7. M. Arndt, O. Nairz, J. Vos-Andreae, C. Keller, G. van der Zouw and A. Zeilinger, "Wave-particle duality of C60 molecules," Nature 401680-682, (1999).
    [CrossRef]
  8. A. Einstein, "Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt," Annalen der Physik 17, 132 (1905).Q2
    [CrossRef]
  9. R. A. Millikan, "A direct photoelectric determination of Planck’s "h"," Phys. Rev. 7, 355 (1916).
    [CrossRef]
  10. A. H. Compton, "A quantum theory of the scattering of x-rays by light elements," Phys. Rev. 21, 483; 22, 409 (1923).
    [CrossRef]
  11. G. Méchain, A. Couairon, M. Franco, B. Prade and A. Mysyrowicz, "Organizing multiple femtosecond filaments in air," Phys. Rev. Lett. 93, 035003 (2004).
    [CrossRef] [PubMed]
  12. A detailed description of the system can be obtained at the group web page http:\\optica.usal.es.
  13. A. Braun, G. Korn, X. Liu, D. Du, J. Squier ang and G. Mourou, "Self-channeling of high-peak-power femtosecond laser pulses in air," Opt. Lett. 20, 73-75 (1995).
    [CrossRef] [PubMed]
  14. C. Ruiz, J. San Roman, C. Mendez, V. Diaz, L. Plaja, I. Arias and L. Roso, "Observation of spontaneous self-channeling of light in air below the collapse threshold," Phys. Rev. Lett. 95053905 (2005).
    [CrossRef] [PubMed]
  15. D. J. Mitchell, A. W. Snyder and L. Poladian, "Interacting self-guided beams viewed as particles: Lorentz Force Derivation," Phys. Rev. Lett. 77271-273 (1996).
    [CrossRef] [PubMed]

2005 (1)

C. Ruiz, J. San Roman, C. Mendez, V. Diaz, L. Plaja, I. Arias and L. Roso, "Observation of spontaneous self-channeling of light in air below the collapse threshold," Phys. Rev. Lett. 95053905 (2005).
[CrossRef] [PubMed]

2004 (1)

G. Méchain, A. Couairon, M. Franco, B. Prade and A. Mysyrowicz, "Organizing multiple femtosecond filaments in air," Phys. Rev. Lett. 93, 035003 (2004).
[CrossRef] [PubMed]

1999 (1)

M. Arndt, O. Nairz, J. Vos-Andreae, C. Keller, G. van der Zouw and A. Zeilinger, "Wave-particle duality of C60 molecules," Nature 401680-682, (1999).
[CrossRef]

1996 (1)

D. J. Mitchell, A. W. Snyder and L. Poladian, "Interacting self-guided beams viewed as particles: Lorentz Force Derivation," Phys. Rev. Lett. 77271-273 (1996).
[CrossRef] [PubMed]

1995 (2)

1991 (1)

O. Carnal and J. Mlynek, "Young’s double-slit experiment with atoms: A simple atom interferometer," Phys. Rev. Lett. 662689-2692 (1991).
[CrossRef] [PubMed]

1989 (1)

A. Tonomura, J. Endo, T. Matsuda, T. Kawasaki and H. Ezawa, "Demonstration of single-electron buildup of an interference pattern," Am. J. Phys. 57, 117-120 (1989).
[CrossRef]

1988 (1)

A. Zelinger, R. Gähler, C. G. Shull, W. Treimer and W. Mampe, "Single- and double-slit diffraction of neutrons," Rev. Mod. Phys. 601067-1073 (1988).
[CrossRef]

1961 (1)

C. Jönsson, "Elektroneninterferenzen an mehreren künstlich hergestellter Feinspalten," Zeitschrift fur Physik 161454-474 (1961).
[CrossRef]

1916 (1)

R. A. Millikan, "A direct photoelectric determination of Planck’s "h"," Phys. Rev. 7, 355 (1916).
[CrossRef]

1905 (1)

A. Einstein, "Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt," Annalen der Physik 17, 132 (1905).Q2
[CrossRef]

1804 (1)

T. Young, "Experimental demonstration of the general law of the interference of light," Philos. Trans. R. Soc. London 94, 1-16 (1804).Q1
[CrossRef]

Arias, I.

C. Ruiz, J. San Roman, C. Mendez, V. Diaz, L. Plaja, I. Arias and L. Roso, "Observation of spontaneous self-channeling of light in air below the collapse threshold," Phys. Rev. Lett. 95053905 (2005).
[CrossRef] [PubMed]

Arndt, M.

M. Arndt, O. Nairz, J. Vos-Andreae, C. Keller, G. van der Zouw and A. Zeilinger, "Wave-particle duality of C60 molecules," Nature 401680-682, (1999).
[CrossRef]

Braun, A.

Carnal, O.

O. Carnal and J. Mlynek, "Young’s double-slit experiment with atoms: A simple atom interferometer," Phys. Rev. Lett. 662689-2692 (1991).
[CrossRef] [PubMed]

Couairon, A.

G. Méchain, A. Couairon, M. Franco, B. Prade and A. Mysyrowicz, "Organizing multiple femtosecond filaments in air," Phys. Rev. Lett. 93, 035003 (2004).
[CrossRef] [PubMed]

Diaz, V.

C. Ruiz, J. San Roman, C. Mendez, V. Diaz, L. Plaja, I. Arias and L. Roso, "Observation of spontaneous self-channeling of light in air below the collapse threshold," Phys. Rev. Lett. 95053905 (2005).
[CrossRef] [PubMed]

Du, D.

Einstein, A.

A. Einstein, "Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt," Annalen der Physik 17, 132 (1905).Q2
[CrossRef]

Endo, J.

A. Tonomura, J. Endo, T. Matsuda, T. Kawasaki and H. Ezawa, "Demonstration of single-electron buildup of an interference pattern," Am. J. Phys. 57, 117-120 (1989).
[CrossRef]

Ezawa, H.

A. Tonomura, J. Endo, T. Matsuda, T. Kawasaki and H. Ezawa, "Demonstration of single-electron buildup of an interference pattern," Am. J. Phys. 57, 117-120 (1989).
[CrossRef]

Franco, M.

G. Méchain, A. Couairon, M. Franco, B. Prade and A. Mysyrowicz, "Organizing multiple femtosecond filaments in air," Phys. Rev. Lett. 93, 035003 (2004).
[CrossRef] [PubMed]

Gähler, R.

A. Zelinger, R. Gähler, C. G. Shull, W. Treimer and W. Mampe, "Single- and double-slit diffraction of neutrons," Rev. Mod. Phys. 601067-1073 (1988).
[CrossRef]

Jönsson, C.

C. Jönsson, "Elektroneninterferenzen an mehreren künstlich hergestellter Feinspalten," Zeitschrift fur Physik 161454-474 (1961).
[CrossRef]

Kawasaki, T.

A. Tonomura, J. Endo, T. Matsuda, T. Kawasaki and H. Ezawa, "Demonstration of single-electron buildup of an interference pattern," Am. J. Phys. 57, 117-120 (1989).
[CrossRef]

Keller, C.

M. Arndt, O. Nairz, J. Vos-Andreae, C. Keller, G. van der Zouw and A. Zeilinger, "Wave-particle duality of C60 molecules," Nature 401680-682, (1999).
[CrossRef]

Korn, G.

Liu, X.

Mampe, W.

A. Zelinger, R. Gähler, C. G. Shull, W. Treimer and W. Mampe, "Single- and double-slit diffraction of neutrons," Rev. Mod. Phys. 601067-1073 (1988).
[CrossRef]

Matsuda, T.

A. Tonomura, J. Endo, T. Matsuda, T. Kawasaki and H. Ezawa, "Demonstration of single-electron buildup of an interference pattern," Am. J. Phys. 57, 117-120 (1989).
[CrossRef]

Méchain, G.

G. Méchain, A. Couairon, M. Franco, B. Prade and A. Mysyrowicz, "Organizing multiple femtosecond filaments in air," Phys. Rev. Lett. 93, 035003 (2004).
[CrossRef] [PubMed]

Mendez, C.

C. Ruiz, J. San Roman, C. Mendez, V. Diaz, L. Plaja, I. Arias and L. Roso, "Observation of spontaneous self-channeling of light in air below the collapse threshold," Phys. Rev. Lett. 95053905 (2005).
[CrossRef] [PubMed]

Millikan, R. A.

R. A. Millikan, "A direct photoelectric determination of Planck’s "h"," Phys. Rev. 7, 355 (1916).
[CrossRef]

Mitchell, D. J.

D. J. Mitchell, A. W. Snyder and L. Poladian, "Interacting self-guided beams viewed as particles: Lorentz Force Derivation," Phys. Rev. Lett. 77271-273 (1996).
[CrossRef] [PubMed]

Mlynek, J.

O. Carnal and J. Mlynek, "Young’s double-slit experiment with atoms: A simple atom interferometer," Phys. Rev. Lett. 662689-2692 (1991).
[CrossRef] [PubMed]

Mysyrowicz, A.

G. Méchain, A. Couairon, M. Franco, B. Prade and A. Mysyrowicz, "Organizing multiple femtosecond filaments in air," Phys. Rev. Lett. 93, 035003 (2004).
[CrossRef] [PubMed]

Nairz, O.

M. Arndt, O. Nairz, J. Vos-Andreae, C. Keller, G. van der Zouw and A. Zeilinger, "Wave-particle duality of C60 molecules," Nature 401680-682, (1999).
[CrossRef]

Noel, M. W.

M. W. Noel and C. R. Stroud, "Young’s double-slit interferometry within an Atom," Phys. Rev. Lett. 751252-1255 (1995).
[CrossRef] [PubMed]

Plaja, L.

C. Ruiz, J. San Roman, C. Mendez, V. Diaz, L. Plaja, I. Arias and L. Roso, "Observation of spontaneous self-channeling of light in air below the collapse threshold," Phys. Rev. Lett. 95053905 (2005).
[CrossRef] [PubMed]

Poladian, L.

D. J. Mitchell, A. W. Snyder and L. Poladian, "Interacting self-guided beams viewed as particles: Lorentz Force Derivation," Phys. Rev. Lett. 77271-273 (1996).
[CrossRef] [PubMed]

Prade, B.

G. Méchain, A. Couairon, M. Franco, B. Prade and A. Mysyrowicz, "Organizing multiple femtosecond filaments in air," Phys. Rev. Lett. 93, 035003 (2004).
[CrossRef] [PubMed]

Roso, L.

C. Ruiz, J. San Roman, C. Mendez, V. Diaz, L. Plaja, I. Arias and L. Roso, "Observation of spontaneous self-channeling of light in air below the collapse threshold," Phys. Rev. Lett. 95053905 (2005).
[CrossRef] [PubMed]

Ruiz, C.

C. Ruiz, J. San Roman, C. Mendez, V. Diaz, L. Plaja, I. Arias and L. Roso, "Observation of spontaneous self-channeling of light in air below the collapse threshold," Phys. Rev. Lett. 95053905 (2005).
[CrossRef] [PubMed]

San Roman, J.

C. Ruiz, J. San Roman, C. Mendez, V. Diaz, L. Plaja, I. Arias and L. Roso, "Observation of spontaneous self-channeling of light in air below the collapse threshold," Phys. Rev. Lett. 95053905 (2005).
[CrossRef] [PubMed]

Shull, C. G.

A. Zelinger, R. Gähler, C. G. Shull, W. Treimer and W. Mampe, "Single- and double-slit diffraction of neutrons," Rev. Mod. Phys. 601067-1073 (1988).
[CrossRef]

Snyder, A. W.

D. J. Mitchell, A. W. Snyder and L. Poladian, "Interacting self-guided beams viewed as particles: Lorentz Force Derivation," Phys. Rev. Lett. 77271-273 (1996).
[CrossRef] [PubMed]

Stroud, C. R.

M. W. Noel and C. R. Stroud, "Young’s double-slit interferometry within an Atom," Phys. Rev. Lett. 751252-1255 (1995).
[CrossRef] [PubMed]

Tonomura, A.

A. Tonomura, J. Endo, T. Matsuda, T. Kawasaki and H. Ezawa, "Demonstration of single-electron buildup of an interference pattern," Am. J. Phys. 57, 117-120 (1989).
[CrossRef]

Treimer, W.

A. Zelinger, R. Gähler, C. G. Shull, W. Treimer and W. Mampe, "Single- and double-slit diffraction of neutrons," Rev. Mod. Phys. 601067-1073 (1988).
[CrossRef]

van der Zouw, G.

M. Arndt, O. Nairz, J. Vos-Andreae, C. Keller, G. van der Zouw and A. Zeilinger, "Wave-particle duality of C60 molecules," Nature 401680-682, (1999).
[CrossRef]

Vos-Andreae, J.

M. Arndt, O. Nairz, J. Vos-Andreae, C. Keller, G. van der Zouw and A. Zeilinger, "Wave-particle duality of C60 molecules," Nature 401680-682, (1999).
[CrossRef]

Young, T.

T. Young, "Experimental demonstration of the general law of the interference of light," Philos. Trans. R. Soc. London 94, 1-16 (1804).Q1
[CrossRef]

Zeilinger, A.

M. Arndt, O. Nairz, J. Vos-Andreae, C. Keller, G. van der Zouw and A. Zeilinger, "Wave-particle duality of C60 molecules," Nature 401680-682, (1999).
[CrossRef]

Zelinger, A.

A. Zelinger, R. Gähler, C. G. Shull, W. Treimer and W. Mampe, "Single- and double-slit diffraction of neutrons," Rev. Mod. Phys. 601067-1073 (1988).
[CrossRef]

Am. J. Phys. (1)

A. Tonomura, J. Endo, T. Matsuda, T. Kawasaki and H. Ezawa, "Demonstration of single-electron buildup of an interference pattern," Am. J. Phys. 57, 117-120 (1989).
[CrossRef]

Annalen der Physik (1)

A. Einstein, "Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt," Annalen der Physik 17, 132 (1905).Q2
[CrossRef]

Nature (1)

M. Arndt, O. Nairz, J. Vos-Andreae, C. Keller, G. van der Zouw and A. Zeilinger, "Wave-particle duality of C60 molecules," Nature 401680-682, (1999).
[CrossRef]

Opt. Lett. (1)

Philos. Trans. R. Soc. London (1)

T. Young, "Experimental demonstration of the general law of the interference of light," Philos. Trans. R. Soc. London 94, 1-16 (1804).Q1
[CrossRef]

Phys. Rev. (1)

R. A. Millikan, "A direct photoelectric determination of Planck’s "h"," Phys. Rev. 7, 355 (1916).
[CrossRef]

Phys. Rev. Lett. (5)

O. Carnal and J. Mlynek, "Young’s double-slit experiment with atoms: A simple atom interferometer," Phys. Rev. Lett. 662689-2692 (1991).
[CrossRef] [PubMed]

M. W. Noel and C. R. Stroud, "Young’s double-slit interferometry within an Atom," Phys. Rev. Lett. 751252-1255 (1995).
[CrossRef] [PubMed]

G. Méchain, A. Couairon, M. Franco, B. Prade and A. Mysyrowicz, "Organizing multiple femtosecond filaments in air," Phys. Rev. Lett. 93, 035003 (2004).
[CrossRef] [PubMed]

C. Ruiz, J. San Roman, C. Mendez, V. Diaz, L. Plaja, I. Arias and L. Roso, "Observation of spontaneous self-channeling of light in air below the collapse threshold," Phys. Rev. Lett. 95053905 (2005).
[CrossRef] [PubMed]

D. J. Mitchell, A. W. Snyder and L. Poladian, "Interacting self-guided beams viewed as particles: Lorentz Force Derivation," Phys. Rev. Lett. 77271-273 (1996).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

A. Zelinger, R. Gähler, C. G. Shull, W. Treimer and W. Mampe, "Single- and double-slit diffraction of neutrons," Rev. Mod. Phys. 601067-1073 (1988).
[CrossRef]

Zeitschrift fur Physik (1)

C. Jönsson, "Elektroneninterferenzen an mehreren künstlich hergestellter Feinspalten," Zeitschrift fur Physik 161454-474 (1961).
[CrossRef]

Other (2)

A. H. Compton, "A quantum theory of the scattering of x-rays by light elements," Phys. Rev. 21, 483; 22, 409 (1923).
[CrossRef]

A detailed description of the system can be obtained at the group web page http:\\optica.usal.es.

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Figures (5)

Fig. 1.
Fig. 1.

Experimental setup.

Fig. 2.
Fig. 2.

Detected interference patterns vs. distance from the slits for (a) lineal (250 μJ), (b) non-lineal (14 mJ) cases. The patterns shown correspond to the intensities integrated over the vertical direction.

Fig. 3.
Fig. 3.

Positions of the intensity maximum of the right fringe for the linear (black color) and non-linear case (red color). The points correspond to the experimental maxima position for both cases while the lines have been obtained from the computed Fresnel propagator presented in eq. (1) (linear case) and with its extension according with the model described in the text (non-linear case).

Fig. 4.
Fig. 4.

Linear interference pattern (black line) at distances (a) 3.5 m and (b) 5 m from the slit, as resulting from the superposition of the field components propagated from the left slit (red line) and the right slit (blue line).

Fig. 5.
Fig. 5.

Model scheme of the interference build up in the non-linear case. The (effectively self-trapped in the experimental distance range) zeroth diffraction orders are represented by shadowed areas and the first order coming from the left fringe by its optical path (the symmetric process has been omitted for simplicity).

Equations (2)

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U ± ( x , y , z ) = ik ± 2 πz e ik ± z ± c a 2 ± c + a 2 b 2 b 2 e i k ± 2 z [ ( x ζ ) 2 + ( y η ) 2 ] U 0 e ( ζ 2 + η 2 ) σ 2 e i k ± 2 f [ ζ 2 + η 2 ]
ΔΓ ( z ) = z 1 z n 2 I ( z′ ) dz′ n 2 I ( z 1 ) ( z z 1 )

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