Abstract

The interaction between parallel beams in one-dimensional discrete Kerr systems has been investigated using arrays of coupled channel waveguides. The experiments were performed in AlGaAs waveguides at 1550 nm which corresponds to photon energies just below one half the semiconductor’s bandgap. The input intensity and relative input phase between the input beams was varied and the output intensity patterns were recorded. Observed was behavior ranging from a linear response, to soliton interactions between moderately and then strongly localized spatial solitons. Finally the influence of multiphoton absorption and asymmetric beam inputs on these interactions was investigated at very high intensities.

© 2005 Optical Society of America

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References

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  1. G. I. Stegeman and M. Segev, "Bright Spatial Soliton Interactions" in Optical Solitons: Theoretical Challenges and Industrial Perspectives, edited by S. Wabnitz and V. E. Zakharov (Springer-Verlag, Berlin, 1999), 313-334.
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    [CrossRef] [PubMed]
  3. F. Lederer and J. S. Aitchison, "Discrete Solitons in Nonlinear Waveguide Arrays" in Optical Solitons: Theoretical Challenges and Industrial Perspectives, edited by V. E. Zakharov and S. Wabnitz (Springer, Berlin, 1998), 349-3
  4. D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817-823 (2003).
    [CrossRef] [PubMed]
  5. S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, "Channel Optical Waveguide Directional Couplers," Appl. Phys. Lett. 22, 46-47 (1973).
    [CrossRef]
  6. 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, 3383-3386 (1998).
    [CrossRef]
  7. D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett. 90, 053902/1-4 (2003).
    [CrossRef]
  8. J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Discrete vector solitons in Kerr nonlinear waveguide arrays," Phys. Rev. Lett. 91, 143907-143910 (2003).
    [CrossRef] [PubMed]
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    [CrossRef]
  10. J. Meier, G. I. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Nonlinear Optical Beam Interactions In Waveguide Arrays," Phys. Rev. Lett. 93, 93903-93906 (2004).
    [CrossRef]
  11. J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, "Beam interactions with a "blocker" soliton in 1D arrays," Opt. Lett., accepted (2004).
  12. G. I. Stegeman, A. Villeneuve, J. Kang, J. S. Aitchison, C. N. Ironside, K. Alhemyari, C. C. Yang, C. H. Lin, H. H. Lin, G. T. Kennedy, R. S. Grant, and W. Sibbett, "AlGaAs Below Half Bandgap - the Silicon of Nonlinear-Optical Materials," Int. J. Nonlinear. Opt. 3, 347-371 (1994).
    [CrossRef]
  13. J. 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, 341-348 (1997).
    [CrossRef]
  14. D. N. Christodoulides and E. D. Eugenieva, "Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays," Phys. Rev. Lett. 8723, 233901 (2001).
    [CrossRef]
  15. O. Bang and P. D. Miller, "Exploiting discreteness for switching in waveguide arrays," Opt. Lett. 21, 1105-1107 (1996).
    [CrossRef] [PubMed]
  16. L. Friedrich, R. Malendevich, G. I. Stegeman, J. M. Soto-Crespo, N. N. Akhmediev, and J. S. Aitchison, "Radiation related polarization instability of fast Kerr spatial solitons in slab waveguides," Opt. Commun. 186, 335-341 (2000).
    [CrossRef]

Appl. Phys. Lett. (1)

S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, "Channel Optical Waveguide Directional Couplers," Appl. Phys. Lett. 22, 46-47 (1973).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. 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, 341-348 (1997).
[CrossRef]

Int. J. Nonlinear. Opt. (1)

G. I. Stegeman, A. Villeneuve, J. Kang, J. S. Aitchison, C. N. Ironside, K. Alhemyari, C. C. Yang, C. H. Lin, H. H. Lin, G. T. Kennedy, R. S. Grant, and W. Sibbett, "AlGaAs Below Half Bandgap - the Silicon of Nonlinear-Optical Materials," Int. J. Nonlinear. Opt. 3, 347-371 (1994).
[CrossRef]

Nature (1)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817-823 (2003).
[CrossRef] [PubMed]

Opt. Commun. (1)

L. Friedrich, R. Malendevich, G. I. Stegeman, J. M. Soto-Crespo, N. N. Akhmediev, and J. S. Aitchison, "Radiation related polarization instability of fast Kerr spatial solitons in slab waveguides," Opt. Commun. 186, 335-341 (2000).
[CrossRef]

Opt. Lett. (3)

D. N. Christodoulides and R. I. Joseph, "Discrete Self-Focusing in Nonlinear Arrays of Coupled Waveguides," Opt. Lett. 13, 794-796 (1988).
[CrossRef] [PubMed]

O. Bang and P. D. Miller, "Exploiting discreteness for switching in waveguide arrays," Opt. Lett. 21, 1105-1107 (1996).
[CrossRef] [PubMed]

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, "Beam interactions with a "blocker" soliton in 1D arrays," Opt. Lett., accepted (2004).

Phys. Rev. E (1)

A. B. Aceves, C. DeAngelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, "Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays," Phys. Rev. E 53, 1172-1189 (1996).
[CrossRef]

Phys. Rev. Lett. (5)

J. Meier, G. I. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Nonlinear Optical Beam Interactions In Waveguide Arrays," Phys. Rev. Lett. 93, 93903-93906 (2004).
[CrossRef]

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, 3383-3386 (1998).
[CrossRef]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett. 90, 053902/1-4 (2003).
[CrossRef]

J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Discrete vector solitons in Kerr nonlinear waveguide arrays," Phys. Rev. Lett. 91, 143907-143910 (2003).
[CrossRef] [PubMed]

D. N. Christodoulides and E. D. Eugenieva, "Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays," Phys. Rev. Lett. 8723, 233901 (2001).
[CrossRef]

Other (2)

G. I. Stegeman and M. Segev, "Bright Spatial Soliton Interactions" in Optical Solitons: Theoretical Challenges and Industrial Perspectives, edited by S. Wabnitz and V. E. Zakharov (Springer-Verlag, Berlin, 1999), 313-334.

F. Lederer and J. S. Aitchison, "Discrete Solitons in Nonlinear Waveguide Arrays" in Optical Solitons: Theoretical Challenges and Industrial Perspectives, edited by V. E. Zakharov and S. Wabnitz (Springer, Berlin, 1998), 349-3

Supplementary Material (4)

» Media 1: MPG (459 KB)     
» Media 2: MPG (509 KB)     
» Media 3: MPG (639 KB)     
» Media 4: MPG (841 KB)     

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Figures (12)

Fig. 1.
Fig. 1.

CW numerical simulation of the propagation along the 8mm sample. Images on the left are for in-phase excitation where-as those on the right are for out-of-phase input beams. The input power is 500 W for simulations (a) and (b) and 1.1 kW for (c) and (d). Note that in this figure the discrete result has been convolved with a Gaussian envelope to mimic the actual waveguide modes.

Fig 2.
Fig 2.

cw simulations of the waveguide array output versus the total input power for each input beam (assumed Gaussian in shape) at the relative phase angles of (a) Δϕ=0, (b) Δϕ=π/2 and (c) Δϕ=π. The simulation parameters are for the 4 mm AlGaAs sample investigated experimentally.

Fig. 4.
Fig. 4.

(a) Sample cross-section; (b) Top-view image of an array (waveguide width w=4µm, etch depth e=0.2…1.0µm, waveguide pitch d=6…11µm)

Fig. 5.
Fig. 5.

Experimental apparatus. Inset: Input beam distributions used for the collinear interactions (thick blue line) and waveguide modes (dotted line).

Fig. 6.
Fig. 6.

Comparison of the measured discrete diffraction pattern (continuous line) with the best-fit prediction of the discrete wave equation.

Fig. 7.
Fig. 7.

(460kB, 509kB) Movies showing the measured array output intensity distribution from (a) the 4mm sample and (b) the 8 mm sample as a function of phase difference between the two input beams. Power is increased from frame to frame and can be found in the upper left-hand-corner. Shown in the strips at the left-hand sides are the outputs when the individual beams are excited separately (no interaction).

Fig. 8.
Fig. 8.

(639 kB) Movie showing the theoretical (calculated) array output intensity distribution (cw assumed) from the 4mm sample as a function of phase difference between the two input beams. Power is increased from frame to frame and can be found in the upper right-hand-corner. No absorption effects were included in the simulations

Fig. 9.
Fig. 9.

The total throughput power from the array as a function of increasing input power

Fig. 10.
Fig. 10.

Schematic of the blocker-signal interaction showing partial reflection (green) of the input signal (blue) as well as the displacement of the blocker (red) by a channel (purple).

Fig. 11.
Fig. 11.

Shape of the two input beams for orthogonally polarized blocker experiments. The grey line indicates the modes of the array.

Fig. 12.
Fig. 12.

(840kB) Movie of the experimentally observed output beams for the TE (left) and TM (right) polarizations. The narrow images on the far left show the input beams, the narrow images on the far right depict the output beams when only one beam is present. The two images in the center show the output beams for TE (left) and TM (right) polarization when their relative phase is varied.

Fig. 13.
Fig. 13.

Power Exchange due to FWM. Black: linear interference. Blue: TE and TM beam power for a signal power of 873 W. Red: TE and TM beam power for a signal power of 3.06 kW

Equations (6)

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i d a n d z + C ( a n + 1 + a n 1 ) + γ a n 2 a n = 0 .
a n ( z = 0 ) = [ I 1 f ( n n l ) + I 2 f ( n + n r ) exp ( i Δ ϕ ) ] ,
a n ( z = 0 ) = I a f ( n n l )
b n ( z = 0 ) = I b f ( n + n r ) exp ( i Δ ϕ )
i d a n d z + β a a n + C a ( a n + 1 + a n 1 ) + γ [ a n 2 + b n 2 + 1 2 b n 2 a n * exp ( 2 i Δ β ) ] a n = 0
i d a n d z + β a b n + C a ( b n + 1 + b n 1 ) + γ [ b n 2 + a n 2 + 1 2 a n 2 b n * exp ( 2 i Δ β ) ] b n = 0

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