Abstract

We observe clamping of the output spatial light distribution of a waveguide array. Using a chirped pulse amplifier we reach peak intensities in the waveguides of ~24 GW/cm2. At this level, three photon absorption in the AlGaAs material clamps the discrete spatial soliton to a set distribution. Further increase in intensity does not change the distribution.

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  1. D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 13(9), 794–796 (1988).
    [CrossRef] [PubMed]
  2. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
    [CrossRef]
  3. R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86(15), 3296–3299 (2001).
    [CrossRef] [PubMed]
  4. H. S. Eisenberg, R. Morandotti, Y. Silberberg, J. M. Arnold, G. Pennelli, and J. S. Aitchison, “Optical discrete solitons in waveguide arrays. I. Soliton formation,” J. Opt. Soc. Am. B 19(12), 2938 (2002).
    [CrossRef]
  5. F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
    [CrossRef]
  6. J. L. Proctor and J. N. Kutz, “Passive mode-locking by use of waveguide arrays,” Opt. Lett. 30(15), 2013–2015 (2005).
    [CrossRef] [PubMed]
  7. D. Marcuse, Theory of dielectric optical waveguides, (Academic Press, 1974).
  8. J. S. Aitchison, Y. Silberberg, A. M. Weiner, D. E. Leaird, M. K. Oliver, J. L. Jackel, E. M. Vogel, and P. W. E. Smith, “Spatial optical solitons in planar glass waveguides,” J. Opt. Soc. Am. B 8(6), 1290–1297 (1991).
    [CrossRef]
  9. V. V. Afanasjev, J. S. Aitchison, and Y. S. Kivshar, “Splitting of high-order spatial solitons under the action of two-photon absorption,” Opt. Commun. 116(4-6), 331–338 (1995).
    [CrossRef]
  10. J. Kang, G. Stegeman, and J. Aitchison, “All-optical multiplexing of femtosecond signals using an AlGaAs nonlinear directional coupler,” Electron. Lett. 31(2), 118 (1995).
    [CrossRef]
  11. A. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The Nonlinear Optical Properties of AlGaAs at the Half Band Gap,” IEEE J. Quantum Electron. 33(3), 341–348 (1997).
    [CrossRef]
  12. D. D. Hudson, K. Shish, T. R. Schibli, J. N. Kutz, D. N. Christodoulides, R. Morandotti, and S. T. Cundiff, “Nonlinear femtosecond pulse reshaping in waveguide arrays,” Opt. Lett. 33(13), 1440–1442 (2008).
    [CrossRef] [PubMed]

2008 (2)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[CrossRef]

D. D. Hudson, K. Shish, T. R. Schibli, J. N. Kutz, D. N. Christodoulides, R. Morandotti, and S. T. Cundiff, “Nonlinear femtosecond pulse reshaping in waveguide arrays,” Opt. Lett. 33(13), 1440–1442 (2008).
[CrossRef] [PubMed]

2005 (1)

2002 (1)

2001 (1)

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86(15), 3296–3299 (2001).
[CrossRef] [PubMed]

1998 (1)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[CrossRef]

1997 (1)

A. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The Nonlinear Optical Properties of AlGaAs at the Half Band Gap,” IEEE J. Quantum Electron. 33(3), 341–348 (1997).
[CrossRef]

1995 (2)

V. V. Afanasjev, J. S. Aitchison, and Y. S. Kivshar, “Splitting of high-order spatial solitons under the action of two-photon absorption,” Opt. Commun. 116(4-6), 331–338 (1995).
[CrossRef]

J. Kang, G. Stegeman, and J. Aitchison, “All-optical multiplexing of femtosecond signals using an AlGaAs nonlinear directional coupler,” Electron. Lett. 31(2), 118 (1995).
[CrossRef]

1991 (1)

1988 (1)

Afanasjev, V. V.

V. V. Afanasjev, J. S. Aitchison, and Y. S. Kivshar, “Splitting of high-order spatial solitons under the action of two-photon absorption,” Opt. Commun. 116(4-6), 331–338 (1995).
[CrossRef]

Aitchison, A. S.

A. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The Nonlinear Optical Properties of AlGaAs at the Half Band Gap,” IEEE J. Quantum Electron. 33(3), 341–348 (1997).
[CrossRef]

Aitchison, J.

J. Kang, G. Stegeman, and J. Aitchison, “All-optical multiplexing of femtosecond signals using an AlGaAs nonlinear directional coupler,” Electron. Lett. 31(2), 118 (1995).
[CrossRef]

Aitchison, J. S.

H. S. Eisenberg, R. Morandotti, Y. Silberberg, J. M. Arnold, G. Pennelli, and J. S. Aitchison, “Optical discrete solitons in waveguide arrays. I. Soliton formation,” J. Opt. Soc. Am. B 19(12), 2938 (2002).
[CrossRef]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86(15), 3296–3299 (2001).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[CrossRef]

V. V. Afanasjev, J. S. Aitchison, and Y. S. Kivshar, “Splitting of high-order spatial solitons under the action of two-photon absorption,” Opt. Commun. 116(4-6), 331–338 (1995).
[CrossRef]

J. S. Aitchison, Y. Silberberg, A. M. Weiner, D. E. Leaird, M. K. Oliver, J. L. Jackel, E. M. Vogel, and P. W. E. Smith, “Spatial optical solitons in planar glass waveguides,” J. Opt. Soc. Am. B 8(6), 1290–1297 (1991).
[CrossRef]

Arnold, J. M.

Assanto, G.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[CrossRef]

Boyd, A. R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[CrossRef]

Christodoulides, D. N.

Cundiff, S. T.

Eisenberg, H. S.

H. S. Eisenberg, R. Morandotti, Y. Silberberg, J. M. Arnold, G. Pennelli, and J. S. Aitchison, “Optical discrete solitons in waveguide arrays. I. Soliton formation,” J. Opt. Soc. Am. B 19(12), 2938 (2002).
[CrossRef]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86(15), 3296–3299 (2001).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[CrossRef]

Hudson, D. D.

Hutchings, D. C.

A. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The Nonlinear Optical Properties of AlGaAs at the Half Band Gap,” IEEE J. Quantum Electron. 33(3), 341–348 (1997).
[CrossRef]

Jackel, J. L.

Joseph, R. I.

Kang, J.

J. Kang, G. Stegeman, and J. Aitchison, “All-optical multiplexing of femtosecond signals using an AlGaAs nonlinear directional coupler,” Electron. Lett. 31(2), 118 (1995).
[CrossRef]

Kang, J. U.

A. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The Nonlinear Optical Properties of AlGaAs at the Half Band Gap,” IEEE J. Quantum Electron. 33(3), 341–348 (1997).
[CrossRef]

Kivshar, Y. S.

V. V. Afanasjev, J. S. Aitchison, and Y. S. Kivshar, “Splitting of high-order spatial solitons under the action of two-photon absorption,” Opt. Commun. 116(4-6), 331–338 (1995).
[CrossRef]

Kutz, J. N.

Leaird, D. E.

Lederer, F.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[CrossRef]

Morandotti, R.

D. D. Hudson, K. Shish, T. R. Schibli, J. N. Kutz, D. N. Christodoulides, R. Morandotti, and S. T. Cundiff, “Nonlinear femtosecond pulse reshaping in waveguide arrays,” Opt. Lett. 33(13), 1440–1442 (2008).
[CrossRef] [PubMed]

H. S. Eisenberg, R. Morandotti, Y. Silberberg, J. M. Arnold, G. Pennelli, and J. S. Aitchison, “Optical discrete solitons in waveguide arrays. I. Soliton formation,” J. Opt. Soc. Am. B 19(12), 2938 (2002).
[CrossRef]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86(15), 3296–3299 (2001).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[CrossRef]

Oliver, M. K.

Pennelli, G.

Proctor, J. L.

Schibli, T. R.

Segev, M.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[CrossRef]

Shish, K.

Silberberg, Y.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[CrossRef]

H. S. Eisenberg, R. Morandotti, Y. Silberberg, J. M. Arnold, G. Pennelli, and J. S. Aitchison, “Optical discrete solitons in waveguide arrays. I. Soliton formation,” J. Opt. Soc. Am. B 19(12), 2938 (2002).
[CrossRef]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86(15), 3296–3299 (2001).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[CrossRef]

J. S. Aitchison, Y. Silberberg, A. M. Weiner, D. E. Leaird, M. K. Oliver, J. L. Jackel, E. M. Vogel, and P. W. E. Smith, “Spatial optical solitons in planar glass waveguides,” J. Opt. Soc. Am. B 8(6), 1290–1297 (1991).
[CrossRef]

Smith, P. W. E.

Sorel, M.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86(15), 3296–3299 (2001).
[CrossRef] [PubMed]

Stegeman, G.

J. Kang, G. Stegeman, and J. Aitchison, “All-optical multiplexing of femtosecond signals using an AlGaAs nonlinear directional coupler,” Electron. Lett. 31(2), 118 (1995).
[CrossRef]

Stegeman, G. I.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[CrossRef]

A. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The Nonlinear Optical Properties of AlGaAs at the Half Band Gap,” IEEE J. Quantum Electron. 33(3), 341–348 (1997).
[CrossRef]

Villeneuve, A.

A. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The Nonlinear Optical Properties of AlGaAs at the Half Band Gap,” IEEE J. Quantum Electron. 33(3), 341–348 (1997).
[CrossRef]

Vogel, E. M.

Weiner, A. M.

Electron. Lett. (1)

J. Kang, G. Stegeman, and J. Aitchison, “All-optical multiplexing of femtosecond signals using an AlGaAs nonlinear directional coupler,” Electron. Lett. 31(2), 118 (1995).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, “The Nonlinear Optical Properties of AlGaAs at the Half Band Gap,” IEEE J. Quantum Electron. 33(3), 341–348 (1997).
[CrossRef]

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

Opt. Commun. (1)

V. V. Afanasjev, J. S. Aitchison, and Y. S. Kivshar, “Splitting of high-order spatial solitons under the action of two-photon absorption,” Opt. Commun. 116(4-6), 331–338 (1995).
[CrossRef]

Opt. Lett. (3)

Phys. Rep. (1)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1-3), 1–126 (2008).
[CrossRef]

Phys. Rev. Lett. (2)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[CrossRef]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86(15), 3296–3299 (2001).
[CrossRef] [PubMed]

Other (1)

D. Marcuse, Theory of dielectric optical waveguides, (Academic Press, 1974).

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Figures (6)

Fig. 1
Fig. 1

Experimental Setup. An Erbium-doped mode-locked fiber laser is amplified. A grating compressor re-compresses the pulses. A microscope objective lens couples the pulses into the central waveguide. The output facet is imaged and a slit is scanned through the magnified image to measure the spatial distribution.

Fig. 2
Fig. 2

(a) Autocorrelation and (b) power distribution for a normally chirped pulse after the waveguide array. At low input power, the power distribution is spread out and the outer waveguides actually contain more power than the central waveguide. As the input power is increased, discrete diffraction gives way to self-focusing and the central waveguide eventually dominates the power distribution.

Fig. 4
Fig. 4

(a) Autocorrelation and (b) 3D power distribution for an anomalous chirp input pulse.

Fig. 3
Fig. 3

(a) Autocorrelation and (b) 3D power distribution for an input pulse with zero chirp.

Fig. 5
Fig. 5

Power in neighboring waveguides relative to the central waveguide. The shortest input pulse (red) reaches the distribution clamping threshold at around 13 GW/cm2. The anomalous input pulse (blue) and normal input pulse (green) achieve lower peak powers than the shortest pulse due to the limited average power in the setup.

Fig. 6
Fig. 6

Numerical simulation of the effect of 3PA on the spatial distribution of the discrete spatial solitons for an input pulse with no chirp. The blue line (3PA term included) converges to a higher relative power than the red line (no 3PA term), and levels off to a steady value. In contrast, the black line monotonically decreases, indicating that the discrete spatial soliton is changing its spatial light distribution by putting more and more energy into the central waveguide.

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i A n z β 2 2 A n t 2 +γ | A n | 2 A n +iσ | A n | 4 A n +c( A n+1 + A n1 )=0

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