Abstract

Parametric gain associated with discrete modulational instability due to the second order nonlinearity χ(2)(-2ω;ω,ω) was investigated experimentally in periodically poled lithium niobate arrays of weakly coupled channel waveguides for conditions of both positive and negative phase-mismatch for second harmonic generation.

© 2005 Optical Society of America

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References

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  2. E. Infeld and G. Rowlands, Nonlinear Waves, Solitons and Chaos (Cambridge University Press, Cambridge, 1990).
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    [CrossRef]
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    [CrossRef] [PubMed]
  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).
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    [CrossRef] [PubMed]
  12. A. V. Buryak, P. Di Trapani, D. Skryabin, and S. Trillo, �??Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,�?? Phys. Reports 370, 63-235 (2002).
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  13. G.I. Stegeman, D.J. Hagan, and L. Torner, �??�?(2) Cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,�?? J. Opt. Quantum Electron. 28, 1691-1740 (1996).
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J. Opt. Quantum Electron. (1)

G.I. Stegeman, D.J. Hagan, and L. Torner, �??�?(2) Cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,�?? J. Opt. Quantum Electron. 28, 1691-1740 (1996).
[CrossRef]

Nature (2)

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

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, �??Observation of two-dimensional discrete solitons in optically-induced nonlinear photonic lattices,�?? Nature 422, 147�??150 (2003).
[CrossRef] [PubMed]

Opt. Lett. (2)

Phys. Reports (1)

A. V. Buryak, P. Di Trapani, D. Skryabin, and S. Trillo, �??Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,�?? Phys. Reports 370, 63-235 (2002).
[CrossRef]

Phys. Rev. Lett. (4)

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, G. Salamo, and J.S. Aitchison, �??Experimental Observation of Discrete Modulational Instability,�?? Phys. Rev. Lett. 92, 163902, (2004).
[CrossRef] [PubMed]

R. Iwanow, R. Schiek, G. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, �??Observation of discrete quadratic solitons,�?? Phys. Rev. Lett. 93 113902 (2004).
[CrossRef] [PubMed]

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, and S. Trillo, �??Spatial modulational instability and multisoliton-like generation in a quadratically nonlinear optical medium,�?? Phys. Rev. Lett. 78, 2756-2759 (1997).
[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]

Science (1)

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, �??Modulation instability and pattern formation in spatially incoherent light beams,�?? Science 290, 495-498, (2000).
[CrossRef] [PubMed]

Other (2)

N. N. Akhmediev and A. Ankiewicz, Solitons: Nonlinear Pulses and Beams (Chapman and Hall, London, 1997).

E. Infeld and G. Rowlands, Nonlinear Waves, Solitons and Chaos (Cambridge University Press, Cambridge, 1990).

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Figures (7)

Fig. 1.
Fig. 1.

Geometry of the wide, high intensity fundamental beam interacting with a PPLN array near its phase-matching condition for second harmonic generation.

Fig. 2.
Fig. 2.

The first derivative dky/dkx of the dispersion relation obtained by plotting the centroid at the output facet of a fundamental beam injected into the PPLN arrays as a function of the relative phase between the adjacent channels.

Fig. 3
Fig. 3

Output from PPLN array as a function of increasing input fundamental energy. Left-hand-side: positive phase-mismatch of 170π. Right-hand-side: negative phase-mismatch of -40π.

Fig. 4.
Fig. 4.

Spatial Fourier transform of the output intensity patterns shown in Fig. 3.. Left-hand-side: positive phase-mismatch of 170π. Right-hand-side: negative phase-mismatch=-40π.

Fig. 5.
Fig. 5.

Low and high power output intensity distribution from the array at high (green) and low (blue) powers. Left-hand-side: positive phase-mismatch of 170π. Right-hand-side: negative phase-mismatch of -40π.

Fig. 6.
Fig. 6.

Calculated evolution of a seeded fundamental beam in the PPLN array as a function of increasing peak input fundamental power in the middle channel. Experimental parameters were assumed. Left-hand-side: positive phase-mismatch of 170π. Right-hand-side: negative phase-mismatch of -40π.

Fig. 7.
Fig. 7.

Distribution across the array of the fundamental beam output power from the PPLN array for incidence of the fundamental beam as a function of the relative input phase between adjacent channels. Positive phase mismatch = 170π on the left; negative phase-mismatch=-40π on the right. The input pulse energy was 0.27μJ corresponding to a peak power of 620W in the middle channel. Regions of high contrast filaments are identified by ellipses.

Equations (2)

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i u n z + i δ u n t + c ( u n + 1 + u n 1 ) + 2 γ u n * v n = 0
i v n z Δ βv n + γ u n 2 = 0 ,

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