Discrete modulational instability in periodically poled lithium niobate waveguide arrays

Robert Iwanow; George I. Stegeman; Roland Schiek; Yoohong Min; Wolfgang Sohler

doi:10.1364/OPEX.13.007794

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.

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References

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Year
Author
Publication

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).
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]
R. Malendevich, L. Jankovic, G. I. Stegeman, and J. S. Aitchison, “Spatial modulation instability in a Kerr slab waveguide,” Opt. Lett. 26, 1879–1881 (2001).
[Crossref]
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]
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]
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]
R. Iwanow, R. Schiek, G. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, “Observation of discrete quadratic solitons,” Phys. Rev. Lett. 93113902 (2004).
[Crossref] [PubMed]
D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
[Crossref] [PubMed]
D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 13, 794–796 (1988); Y. S. Kivshar and M. Peyrard, “Modulational instabilities in discrete lattices,” Phys. Rev. A 46, 3198–3205 (1992).
[Crossref] [PubMed]
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]
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]
G.I. Stegeman, D.J. Hagan, and L. Torner, “χ(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]

2004 (2)

R. Iwanow, R. Schiek, G. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, “Observation of discrete quadratic solitons,” Phys. Rev. Lett. 93113902 (2004).
[Crossref] [PubMed]

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]

2003 (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]

2002 (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]

2001 (1)

R. Malendevich, L. Jankovic, G. I. Stegeman, and J. S. Aitchison, “Spatial modulation instability in a Kerr slab waveguide,” Opt. Lett. 26, 1879–1881 (2001).
[Crossref]

2000 (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]

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, 3383–3386 (1998).
[Crossref]

1997 (1)

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]

1996 (1)

G.I. Stegeman, D.J. Hagan, and L. Torner, “χ(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]

1988 (1)

D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 13, 794–796 (1988); Y. S. Kivshar and M. Peyrard, “Modulational instabilities in discrete lattices,” Phys. Rev. A 46, 3198–3205 (1992).
[Crossref] [PubMed]

Aitchison, J. S.

R. Malendevich, L. Jankovic, G. I. Stegeman, and J. S. Aitchison, “Spatial modulation instability in a Kerr slab waveguide,” Opt. Lett. 26, 1879–1881 (2001).
[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]

Aitchison, J.S.

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]

Akhmediev, N. N.

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

Ankiewicz, A.

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

Baboiu, D. M.

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]

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, 3383–3386 (1998).
[Crossref]

Buryak, A. V.

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]

Christodoulides, D. N.

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]

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]

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

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]

D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 13, 794–796 (1988); Y. S. Kivshar and M. Peyrard, “Modulational instabilities in discrete lattices,” Phys. Rev. A 46, 3198–3205 (1992).
[Crossref] [PubMed]

Di Trapani, P.

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]

Efremidis, N. K.

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]

Eisenberg, H. S.

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]

Eugenieva, E.

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]

Fleischer, J. W.

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]

Fuerst, R. A.

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]

Hagan, D.J.

G.I. Stegeman, D.J. Hagan, and L. Torner, “χ(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]

Infeld, E.

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

Iwanow, R.

R. Iwanow, R. Schiek, G. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, “Observation of discrete quadratic solitons,” Phys. Rev. Lett. 93113902 (2004).
[Crossref] [PubMed]

Jankovic, L.

R. Malendevich, L. Jankovic, G. I. Stegeman, and J. S. Aitchison, “Spatial modulation instability in a Kerr slab waveguide,” Opt. Lett. 26, 1879–1881 (2001).
[Crossref]

Joseph, R. I.

D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 13, 794–796 (1988); Y. S. Kivshar and M. Peyrard, “Modulational instabilities in discrete lattices,” Phys. Rev. A 46, 3198–3205 (1992).
[Crossref] [PubMed]

Kip, D.

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]

Lawrence, B.

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]

Lederer, F.

R. Iwanow, R. Schiek, G. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, “Observation of discrete quadratic solitons,” Phys. Rev. Lett. 93113902 (2004).
[Crossref] [PubMed]

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

Malendevich, R.

R. Malendevich, L. Jankovic, G. I. Stegeman, and J. S. Aitchison, “Spatial modulation instability in a Kerr slab waveguide,” Opt. Lett. 26, 1879–1881 (2001).
[Crossref]

Meier, J.

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]

Min, Y.

R. Iwanow, R. Schiek, G. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, “Observation of discrete quadratic solitons,” Phys. Rev. Lett. 93113902 (2004).
[Crossref] [PubMed]

Morandotti, R.

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]

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]

Pertsch, T.

R. Iwanow, R. Schiek, G. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, “Observation of discrete quadratic solitons,” Phys. Rev. Lett. 93113902 (2004).
[Crossref] [PubMed]

Rowlands, G.

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

Salamo, G.

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]

Schiek, R.

R. Iwanow, R. Schiek, G. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, “Observation of discrete quadratic solitons,” Phys. Rev. Lett. 93113902 (2004).
[Crossref] [PubMed]

Segev, M.

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]

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]

Silberberg, Y.

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]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
[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, 3383–3386 (1998).
[Crossref]

Skryabin, D.

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]

Sohler, W.

R. Iwanow, R. Schiek, G. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, “Observation of discrete quadratic solitons,” Phys. Rev. Lett. 93113902 (2004).
[Crossref] [PubMed]

Soljacic, M.

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]

Stegeman, G.

R. Iwanow, R. Schiek, G. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, “Observation of discrete quadratic solitons,” Phys. Rev. Lett. 93113902 (2004).
[Crossref] [PubMed]

Stegeman, G. I.

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. Malendevich, L. Jankovic, G. I. Stegeman, and J. S. Aitchison, “Spatial modulation instability in a Kerr slab waveguide,” Opt. Lett. 26, 1879–1881 (2001).
[Crossref]

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]

Stegeman, G.I.

G.I. Stegeman, D.J. Hagan, and L. Torner, “χ(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]

Torner, L.

G.I. Stegeman, D.J. Hagan, and L. Torner, “χ(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]

Torruellas, W. E.

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]

Trillo, S.

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]

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]

J. Opt. Quantum Electron. (1)

G.I. Stegeman, D.J. Hagan, and L. Torner, “χ(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)

R. Malendevich, L. Jankovic, G. I. Stegeman, and J. S. Aitchison, “Spatial modulation instability in a Kerr slab waveguide,” Opt. Lett. 26, 1879–1881 (2001).
[Crossref]

D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 13, 794–796 (1988); Y. S. Kivshar and M. Peyrard, “Modulational instabilities in discrete lattices,” Phys. Rev. A 46, 3198–3205 (1992).
[Crossref] [PubMed]

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. 93113902 (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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Fig. 1. Geometry of the wide, high intensity fundamental beam interacting with a PPLN array near its phase-matching condition for second harmonic generation.

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Fig. 2. The first derivative dk_y/dk_x 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.

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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.

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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.

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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.

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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.

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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.

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Equations (2)

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i \frac{\partial u_{n}}{\partial z} + i δ \frac{\partial u_{n}}{\partial t} + c (u_{n + 1} + u_{n - 1}) + 2 γ u_{n}^{*} v_{n} = 0

i \frac{\partial v_{n}}{\partial z} - Δ {βv}_{n} + γ u_{n}^{2} = 0,

Abstract

References

2004 (2)

2003 (2)

2002 (1)

2001 (1)

2000 (1)

1998 (1)

1997 (1)

1996 (1)

1988 (1)

Aitchison, J. S.

Aitchison, J.S.

Akhmediev, N. N.

Ankiewicz, A.

Baboiu, D. M.

Boyd, A. R.

Buryak, A. V.

Christodoulides, D. N.

Di Trapani, P.

Efremidis, N. K.

Eisenberg, H. S.

Eugenieva, E.

Fleischer, J. W.

Fuerst, R. A.

Hagan, D.J.

Infeld, E.

Iwanow, R.

Jankovic, L.

Joseph, R. I.

Kip, D.

Lawrence, B.

Lederer, F.

Malendevich, R.

Meier, J.

Min, Y.

Morandotti, R.

Pertsch, T.

Rowlands, G.

Salamo, G.

Schiek, R.

Segev, M.

Silberberg, Y.

Skryabin, D.

Sohler, W.

Soljacic, M.

Stegeman, G.

Stegeman, G. I.

Stegeman, G.I.

Torner, L.

Torruellas, W. E.

Trillo, S.

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