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. Thomas Young, “Experimental Demonstration of the General Law of the Interference of Light,” Philosophical Transactions of the Royal society of London 94, 1–16 (1804)
    [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,“00FC;ber einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt,” Annalen der Physik 17, 132 (1905)
    [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, and G. Mourou, “Self-channeling of high-peak-power femtosecond laser pulses in air,” Optics Letters 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 wiewed 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 wiewed as Particles: Lorentz Force Derivation,” Phys. Rev. Lett. 77271–273 (1996)
[Crossref] [PubMed]

1995 (2)

A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak-power femtosecond laser pulses in air,” Optics Letters 20, 73–75 (1995)
[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]

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,“00FC;ber einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt,” Annalen der Physik 17, 132 (1905)
[Crossref]

1804 (1)

Thomas Young, “Experimental Demonstration of the General Law of the Interference of Light,” Philosophical Transactions of the Royal society of London 94, 1–16 (1804)
[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.

A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak-power femtosecond laser pulses in air,” Optics Letters 20, 73–75 (1995)
[Crossref] [PubMed]

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]

Compton, A.H.

A.H. Compton, “A Quantum Theory of the Scattering of X-rays by Light Elements,” Phys. Rev.21, 483; 22, 409 (1923)
[Crossref]

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.

A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak-power femtosecond laser pulses in air,” Optics Letters 20, 73–75 (1995)
[Crossref] [PubMed]

Einstein, A.

A. Einstein,“00FC;ber einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt,” Annalen der Physik 17, 132 (1905)
[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.

A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak-power femtosecond laser pulses in air,” Optics Letters 20, 73–75 (1995)
[Crossref] [PubMed]

Liu, X.

A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak-power femtosecond laser pulses in air,” Optics Letters 20, 73–75 (1995)
[Crossref] [PubMed]

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 wiewed 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]

Mourou, G.

A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak-power femtosecond laser pulses in air,” Optics Letters 20, 73–75 (1995)
[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 wiewed 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]

Roman, J. San

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]

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]

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 wiewed as Particles: Lorentz Force Derivation,” Phys. Rev. Lett. 77271–273 (1996)
[Crossref] [PubMed]

Squier, J.

A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak-power femtosecond laser pulses in air,” Optics Letters 20, 73–75 (1995)
[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]

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, Thomas

Thomas Young, “Experimental Demonstration of the General Law of the Interference of Light,” Philosophical Transactions of the Royal society of London 94, 1–16 (1804)
[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]

Zouw, G. van der

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]

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,“00FC;ber einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt,” Annalen der Physik 17, 132 (1905)
[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]

Optics Letters (1)

A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak-power femtosecond laser pulses in air,” Optics Letters 20, 73–75 (1995)
[Crossref] [PubMed]

Philosophical Transactions of the Royal society of London (1)

Thomas Young, “Experimental Demonstration of the General Law of the Interference of Light,” Philosophical Transactions of the Royal society of London 94, 1–16 (1804)
[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]

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 wiewed as Particles: Lorentz Force Derivation,” Phys. Rev. Lett. 77271–273 (1996)
[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]

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)

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

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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