Abstract

We study resonant light scattering in arrays of channel optical waveguides in which tunable quadratic nonlinearity is introduced as nonlinear defects by periodic poling of single (or several) waveguides in the array. We describe novel features of wave scattering that can be observed in this structure and show that it is a good candidate for observation of Fano resonance in nonlinear optics.

© 2005 Optical Society of America

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References

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  1. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, San Diego, Calif., 2003).
  2. A. A. Sukhorukov, Yu. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, IEEE J. Quantum Electron. 39, 31 (2003).
    [Crossref]
  3. D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
    [Crossref] [PubMed]
  4. For a review, see A. V. Buryak, P. Di Trapani, D. V. Skryabin, and S. Trillo, Phys. Rep. 370, 63 (2002).
    [Crossref]
  5. R. Iwanov, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Phys. Rev. Lett. 93, 113902 (2004).
    [Crossref]
  6. R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, Opt. Lett. 28, 834 (2003).
    [Crossref] [PubMed]
  7. C. B. Clausen and L. Torner, Phys. Rev. Lett. 81, 790 (1998).
    [Crossref]
  8. A. A. Sukhorukov, Yu. S. Kivshar, and O. Bang, Phys. Rev. E 60, R41 (1999).
    [Crossref]
  9. U. Fano, Phys. Rev. 124, 1866 (1961).
    [Crossref]
  10. G. D. Mahan, Many-Particle Physics (Plenum, New York, 1993).
  11. S. Flach, A. E. Miroshnichenko, V. Fleurov, and M. V. Fistul, Phys. Rev. Lett. 90, 084101 (2003).
    [Crossref]
  12. A. E. Miroshnichenko, S. Flach, and B. Malomed, Chaos 13, 874 (2003).
    [Crossref] [PubMed]
  13. D. W. L. Sprung, H. Wu, and J. Martorell, Am. J. Phys. 61, 1118 (1993).
    [Crossref]

2004 (1)

R. Iwanov, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Phys. Rev. Lett. 93, 113902 (2004).
[Crossref]

2003 (5)

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, Opt. Lett. 28, 834 (2003).
[Crossref] [PubMed]

A. A. Sukhorukov, Yu. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, IEEE J. Quantum Electron. 39, 31 (2003).
[Crossref]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[Crossref] [PubMed]

S. Flach, A. E. Miroshnichenko, V. Fleurov, and M. V. Fistul, Phys. Rev. Lett. 90, 084101 (2003).
[Crossref]

A. E. Miroshnichenko, S. Flach, and B. Malomed, Chaos 13, 874 (2003).
[Crossref] [PubMed]

2002 (1)

For a review, see A. V. Buryak, P. Di Trapani, D. V. Skryabin, and S. Trillo, Phys. Rep. 370, 63 (2002).
[Crossref]

1999 (1)

A. A. Sukhorukov, Yu. S. Kivshar, and O. Bang, Phys. Rev. E 60, R41 (1999).
[Crossref]

1998 (1)

C. B. Clausen and L. Torner, Phys. Rev. Lett. 81, 790 (1998).
[Crossref]

1993 (1)

D. W. L. Sprung, H. Wu, and J. Martorell, Am. J. Phys. 61, 1118 (1993).
[Crossref]

1961 (1)

U. Fano, Phys. Rev. 124, 1866 (1961).
[Crossref]

Agrawal, G. P.

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, San Diego, Calif., 2003).

Aitchison, J. S.

Bang, O.

A. A. Sukhorukov, Yu. S. Kivshar, and O. Bang, Phys. Rev. E 60, R41 (1999).
[Crossref]

Buryak, A. V.

For a review, see A. V. Buryak, P. Di Trapani, D. V. Skryabin, and S. Trillo, Phys. Rep. 370, 63 (2002).
[Crossref]

Christodoulides, D. N.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[Crossref] [PubMed]

Clausen, C. B.

C. B. Clausen and L. Torner, Phys. Rev. Lett. 81, 790 (1998).
[Crossref]

Di Trapani, P.

For a review, see A. V. Buryak, P. Di Trapani, D. V. Skryabin, and S. Trillo, Phys. Rep. 370, 63 (2002).
[Crossref]

Eisenberg, H. S.

Fano, U.

U. Fano, Phys. Rev. 124, 1866 (1961).
[Crossref]

Fistul, M. V.

S. Flach, A. E. Miroshnichenko, V. Fleurov, and M. V. Fistul, Phys. Rev. Lett. 90, 084101 (2003).
[Crossref]

Flach, S.

S. Flach, A. E. Miroshnichenko, V. Fleurov, and M. V. Fistul, Phys. Rev. Lett. 90, 084101 (2003).
[Crossref]

A. E. Miroshnichenko, S. Flach, and B. Malomed, Chaos 13, 874 (2003).
[Crossref] [PubMed]

Fleurov, V.

S. Flach, A. E. Miroshnichenko, V. Fleurov, and M. V. Fistul, Phys. Rev. Lett. 90, 084101 (2003).
[Crossref]

Iwanov, R.

R. Iwanov, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Phys. Rev. Lett. 93, 113902 (2004).
[Crossref]

Kivshar, Yu. S.

A. A. Sukhorukov, Yu. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, IEEE J. Quantum Electron. 39, 31 (2003).
[Crossref]

A. A. Sukhorukov, Yu. S. Kivshar, and O. Bang, Phys. Rev. E 60, R41 (1999).
[Crossref]

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, San Diego, Calif., 2003).

Lederer, F.

R. Iwanov, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Phys. Rev. Lett. 93, 113902 (2004).
[Crossref]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[Crossref] [PubMed]

Mahan, G. D.

G. D. Mahan, Many-Particle Physics (Plenum, New York, 1993).

Malomed, B.

A. E. Miroshnichenko, S. Flach, and B. Malomed, Chaos 13, 874 (2003).
[Crossref] [PubMed]

Mandelik, D.

Martorell, J.

D. W. L. Sprung, H. Wu, and J. Martorell, Am. J. Phys. 61, 1118 (1993).
[Crossref]

Min, Y.

R. Iwanov, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Phys. Rev. Lett. 93, 113902 (2004).
[Crossref]

Miroshnichenko, A. E.

S. Flach, A. E. Miroshnichenko, V. Fleurov, and M. V. Fistul, Phys. Rev. Lett. 90, 084101 (2003).
[Crossref]

A. E. Miroshnichenko, S. Flach, and B. Malomed, Chaos 13, 874 (2003).
[Crossref] [PubMed]

Modotto, D.

Morandotti, R.

Pertsch, T.

R. Iwanov, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Phys. Rev. Lett. 93, 113902 (2004).
[Crossref]

Schiek, R.

R. Iwanov, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Phys. Rev. Lett. 93, 113902 (2004).
[Crossref]

Silberberg, Y.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[Crossref] [PubMed]

A. A. Sukhorukov, Yu. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, IEEE J. Quantum Electron. 39, 31 (2003).
[Crossref]

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, Opt. Lett. 28, 834 (2003).
[Crossref] [PubMed]

Skryabin, D. V.

For a review, see A. V. Buryak, P. Di Trapani, D. V. Skryabin, and S. Trillo, Phys. Rep. 370, 63 (2002).
[Crossref]

Sohler, W.

R. Iwanov, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Phys. Rev. Lett. 93, 113902 (2004).
[Crossref]

Sorel, M.

Sprung, D. W. L.

D. W. L. Sprung, H. Wu, and J. Martorell, Am. J. Phys. 61, 1118 (1993).
[Crossref]

Stanley, C. R.

Stegeman, G. I.

R. Iwanov, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Phys. Rev. Lett. 93, 113902 (2004).
[Crossref]

Sukhorukov, A. A.

A. A. Sukhorukov, Yu. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, IEEE J. Quantum Electron. 39, 31 (2003).
[Crossref]

A. A. Sukhorukov, Yu. S. Kivshar, and O. Bang, Phys. Rev. E 60, R41 (1999).
[Crossref]

Torner, L.

C. B. Clausen and L. Torner, Phys. Rev. Lett. 81, 790 (1998).
[Crossref]

Trillo, S.

For a review, see A. V. Buryak, P. Di Trapani, D. V. Skryabin, and S. Trillo, Phys. Rep. 370, 63 (2002).
[Crossref]

Wu, H.

D. W. L. Sprung, H. Wu, and J. Martorell, Am. J. Phys. 61, 1118 (1993).
[Crossref]

Am. J. Phys. (1)

D. W. L. Sprung, H. Wu, and J. Martorell, Am. J. Phys. 61, 1118 (1993).
[Crossref]

Chaos (1)

A. E. Miroshnichenko, S. Flach, and B. Malomed, Chaos 13, 874 (2003).
[Crossref] [PubMed]

IEEE J. Quantum Electron. (1)

A. A. Sukhorukov, Yu. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, IEEE J. Quantum Electron. 39, 31 (2003).
[Crossref]

Nature (1)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[Crossref] [PubMed]

Opt. Lett. (1)

Phys. Rep. (1)

For a review, see A. V. Buryak, P. Di Trapani, D. V. Skryabin, and S. Trillo, Phys. Rep. 370, 63 (2002).
[Crossref]

Phys. Rev. (1)

U. Fano, Phys. Rev. 124, 1866 (1961).
[Crossref]

Phys. Rev. E (1)

A. A. Sukhorukov, Yu. S. Kivshar, and O. Bang, Phys. Rev. E 60, R41 (1999).
[Crossref]

Phys. Rev. Lett. (3)

C. B. Clausen and L. Torner, Phys. Rev. Lett. 81, 790 (1998).
[Crossref]

R. Iwanov, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Phys. Rev. Lett. 93, 113902 (2004).
[Crossref]

S. Flach, A. E. Miroshnichenko, V. Fleurov, and M. V. Fistul, Phys. Rev. Lett. 90, 084101 (2003).
[Crossref]

Other (2)

G. D. Mahan, Many-Particle Physics (Plenum, New York, 1993).

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, San Diego, Calif., 2003).

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Figures (3)

Fig. 1
Fig. 1

Schematic of an array of channel waveguides with quadratic nonlinearity in which nonlinear defects are created by periodic poling. The arrows show the scattering process.

Fig. 2
Fig. 2

Examples of the FF transmission coefficient of scattering by the quadratic impurity waveguide for c u = 1 and (a) c v = 0 , Δ = 0 ; (b) c v = 0 , Δ = 2 ; (c) c v = 0.5 , Δ = 0 ; (d) c v = 0.5 , Δ = 2 for I = 1 (solid curves) and I = 2 (dashed curves).

Fig. 3
Fig. 3

Top, resonant generation of the trapped SH field by a Gaussian beam of the (a) FF and (b) SH fields for parameters c u = 1 , c v = 0 , Δ = 0 , and k = π 2 . Bottom, comparison of the transmission coefficients of the plane waves (solid curves) and Gaussian beam (crosses) for c u = 1 , c v = 0 and (c) Δ = 0 and (d) k = π 2 . Because of its finite spectral width, the transmission coefficient of the Gaussian beam does not vanish.

Equations (10)

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i d u n d z + c u ( u n + 1 + u n 1 ) + 2 m = 0 N u m * v m δ n m = 0 ,
i d v n d z + c v ( v n + 1 + v n 1 ) Δ v n + m = 0 N u m 2 δ n m = 0 ,
u n ( z ) = exp ( i β 1 z ) { I exp ( i k n ) + R exp ( i k n ) n < 0 T exp ( i k n ) n 0 } ,
v n ( z ) = exp ( i β 2 z ) { R ̃ exp ( i q n ) n < 0 T ̃ exp ( i q n ) n 0 } ,
β 1 u n = c u ( u n + 1 + u n 1 ) + 2 u 0 * v δ n 0 ,
2 β 1 v = Δ v + u 0 2 ,
β 1 u n = c u ( u n + 1 + u n 1 ) + 2 u 0 2 u 0 2 β 1 + Δ δ n 0 ,
2 β 1 ( k F ) = Δ ,
t 3 + γ ( k ) ( t 1 ) = 0 ,
2 β 1 ( k F 1 , 2 ) = Δ ± 2 c v ,

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