Abstract

A finite difference method in real space is presented for calculating nonlinear optical processes in two-dimensional optical superlattices. The focused second-harmonic generation under the local quasi-phase-matched condition is calculated as an example. The field distribution of both the fundamental and the harmonic wave can be simulated well using this method, and the result agrees well with previous theoretical predictions and experimental studies. It is shown that this method is a simple and rapid technique to analysis nonlinear processes in optical superlattices.

© 2012 OSA

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  1. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
    [CrossRef]
  2. A. Arie, G. Rosenman, V. Mahal, A. Skliar, M. Oron, M. Katz, and D. Eger, “Green and ultraviolet quasi-phase-matched second harmonic generation in bulk periodically-poled KTiOPO4,” Opt. Commun. 142(4-6), 265–268 (1997).
    [CrossRef]
  3. S. Wang, V. Pasiskevicius, F. Laurell, and H. Karlsson, “Ultraviolet generation by first-order frequency doubling in periodically poled KTiOPO4.,” Opt. Lett. 23(24), 1883–1885 (1998).
    [CrossRef] [PubMed]
  4. I. Yokohama, M. Asobe, A. Yokoo, H. Itoh, and T. Kaino, “All-optical switching by use of cascading of phase-matched sum-frequency generation and difference-frequency generation processes,” J. Opt. Soc. Am. B 14(12), 3368 (1997).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  12. T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3, 395–398 (2009).
    [CrossRef]
  13. I. Dolev, T. Ellenbogen, and A. Arie, “Switching the acceleration direction of Airy beams by a nonlinear optical process,” Opt. Lett. 35(10), 1581–1583 (2010).
    [CrossRef] [PubMed]
  14. M. S. Kushwaha, P. Halevi, G. Martínez, L. Dobrzynski, and B. Djafari-Rouhani, “Theory of acoustic band structure of periodic elastic composites,” Phys. Rev. B Condens. Matter 49(4), 2313–2322 (1994).
    [CrossRef] [PubMed]
  15. F. R. Montero de Espinosa, E. Jimenez, and M. Torres, “Ultrasonic band gap in a periodic two-dimensional composite,” Phys. Rev. Lett. 80(6), 1208–1211 (1998).
    [CrossRef]
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    [CrossRef] [PubMed]
  17. Y. Tanaka, Y. Tomoyasu, and S. I. Tamura, “Band structure of acoustic waves in phononic lattices: Two-dimensional composites with large acoustic mismatch,” Phys. Rev. B 62(11), 7387–7392 (2000).
    [CrossRef]
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2010 (1)

2009 (3)

A. Massaro, V. Tasco, M. T. Todaro, T. Stomeo, R. Cingolani, M. De Vittorio, and A. Passaseo, “FEM design and modeling ofχ(2),” J. Lightwave Technol. 27, 4262–4268 (2009).
[CrossRef]

J. J. Chen and X. F. Chen, “Phase matching in three-dimensional nonlinear photonic crystals,” Phys. Rev. A 80(1), 013801 (2009).
[CrossRef]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3, 395–398 (2009).
[CrossRef]

2008 (2)

Y. Q. Qin, C. Zhang, Y. Y. Zhu, X. P. Hu, and G. Zhao, “Wave-front engineering by Huygens-Fresnel principle for nonlinear optical interactions in domain engineered structures,” Phys. Rev. Lett. 100(6), 063902 (2008).
[CrossRef] [PubMed]

C. Zhang, Y. Q. Qin, and Y. Y. Zhu, “Perfect quasi-phase matching for the third-harmonic generation using focused Gaussian beams,” Opt. Lett. 33(7), 720–722 (2008).
[CrossRef] [PubMed]

2006 (1)

2004 (1)

P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, “Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal,” Phys. Rev. Lett. 93(13), 133904 (2004).
[CrossRef] [PubMed]

2000 (3)

R. Drezek, A. Dunn, and R. Richards-Kortum, “A pulsed finite-difference time-domain (FDTD) method for calculating light scattering from biological cells over broad wavelength ranges,” Opt. Express 6(7), 147–157 (2000).
[CrossRef] [PubMed]

Y. Tanaka, Y. Tomoyasu, and S. I. Tamura, “Band structure of acoustic waves in phononic lattices: Two-dimensional composites with large acoustic mismatch,” Phys. Rev. B 62(11), 7387–7392 (2000).
[CrossRef]

M. M. Sigalas and N. Garcia, “Importance of coupling between longitudinal and transverse components for the creation of acoustic band gaps: The aluminum in mercury case,” Appl. Phys. Lett. 76(16), 2307 (2000).
[CrossRef]

1998 (3)

F. R. Montero de Espinosa, E. Jimenez, and M. Torres, “Ultrasonic band gap in a periodic two-dimensional composite,” Phys. Rev. Lett. 80(6), 1208–1211 (1998).
[CrossRef]

S. Wang, V. Pasiskevicius, F. Laurell, and H. Karlsson, “Ultraviolet generation by first-order frequency doubling in periodically poled KTiOPO4.,” Opt. Lett. 23(24), 1883–1885 (1998).
[CrossRef] [PubMed]

V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81(19), 4136–4139 (1998).
[CrossRef]

1997 (3)

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278(5339), 843–846 (1997).
[CrossRef]

A. Arie, G. Rosenman, V. Mahal, A. Skliar, M. Oron, M. Katz, and D. Eger, “Green and ultraviolet quasi-phase-matched second harmonic generation in bulk periodically-poled KTiOPO4,” Opt. Commun. 142(4-6), 265–268 (1997).
[CrossRef]

I. Yokohama, M. Asobe, A. Yokoo, H. Itoh, and T. Kaino, “All-optical switching by use of cascading of phase-matched sum-frequency generation and difference-frequency generation processes,” J. Opt. Soc. Am. B 14(12), 3368 (1997).
[CrossRef]

1995 (1)

C. T. Chan, Q. L. Yu, and K. M. Ho, “Order-N spectral method for electromagnetic waves,” Phys. Rev. B Condens. Matter 51(23), 16635–16642 (1995).
[CrossRef] [PubMed]

1994 (1)

M. S. Kushwaha, P. Halevi, G. Martínez, L. Dobrzynski, and B. Djafari-Rouhani, “Theory of acoustic band structure of periodic elastic composites,” Phys. Rev. B Condens. Matter 49(4), 2313–2322 (1994).
[CrossRef] [PubMed]

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Adibi, A.

Arie, A.

I. Dolev, T. Ellenbogen, and A. Arie, “Switching the acceleration direction of Airy beams by a nonlinear optical process,” Opt. Lett. 35(10), 1581–1583 (2010).
[CrossRef] [PubMed]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3, 395–398 (2009).
[CrossRef]

A. Arie, G. Rosenman, V. Mahal, A. Skliar, M. Oron, M. Katz, and D. Eger, “Green and ultraviolet quasi-phase-matched second harmonic generation in bulk periodically-poled KTiOPO4,” Opt. Commun. 142(4-6), 265–268 (1997).
[CrossRef]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Asobe, M.

Berger, V.

V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81(19), 4136–4139 (1998).
[CrossRef]

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Chan, C. T.

C. T. Chan, Q. L. Yu, and K. M. Ho, “Order-N spectral method for electromagnetic waves,” Phys. Rev. B Condens. Matter 51(23), 16635–16642 (1995).
[CrossRef] [PubMed]

Chen, J. J.

J. J. Chen and X. F. Chen, “Phase matching in three-dimensional nonlinear photonic crystals,” Phys. Rev. A 80(1), 013801 (2009).
[CrossRef]

Chen, X. F.

J. J. Chen and X. F. Chen, “Phase matching in three-dimensional nonlinear photonic crystals,” Phys. Rev. A 80(1), 013801 (2009).
[CrossRef]

Cingolani, R.

De Vittorio, M.

Djafari-Rouhani, B.

M. S. Kushwaha, P. Halevi, G. Martínez, L. Dobrzynski, and B. Djafari-Rouhani, “Theory of acoustic band structure of periodic elastic composites,” Phys. Rev. B Condens. Matter 49(4), 2313–2322 (1994).
[CrossRef] [PubMed]

Dobrzynski, L.

M. S. Kushwaha, P. Halevi, G. Martínez, L. Dobrzynski, and B. Djafari-Rouhani, “Theory of acoustic band structure of periodic elastic composites,” Phys. Rev. B Condens. Matter 49(4), 2313–2322 (1994).
[CrossRef] [PubMed]

Dolev, I.

Drezek, R.

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Dunn, A.

Eger, D.

A. Arie, G. Rosenman, V. Mahal, A. Skliar, M. Oron, M. Katz, and D. Eger, “Green and ultraviolet quasi-phase-matched second harmonic generation in bulk periodically-poled KTiOPO4,” Opt. Commun. 142(4-6), 265–268 (1997).
[CrossRef]

Ellenbogen, T.

I. Dolev, T. Ellenbogen, and A. Arie, “Switching the acceleration direction of Airy beams by a nonlinear optical process,” Opt. Lett. 35(10), 1581–1583 (2010).
[CrossRef] [PubMed]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3, 395–398 (2009).
[CrossRef]

Ganany-Padowicz, A.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3, 395–398 (2009).
[CrossRef]

Garcia, N.

M. M. Sigalas and N. Garcia, “Importance of coupling between longitudinal and transverse components for the creation of acoustic band gaps: The aluminum in mercury case,” Appl. Phys. Lett. 76(16), 2307 (2000).
[CrossRef]

Halevi, P.

M. S. Kushwaha, P. Halevi, G. Martínez, L. Dobrzynski, and B. Djafari-Rouhani, “Theory of acoustic band structure of periodic elastic composites,” Phys. Rev. B Condens. Matter 49(4), 2313–2322 (1994).
[CrossRef] [PubMed]

He, J. L.

P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, “Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal,” Phys. Rev. Lett. 93(13), 133904 (2004).
[CrossRef] [PubMed]

Ho, K. M.

C. T. Chan, Q. L. Yu, and K. M. Ho, “Order-N spectral method for electromagnetic waves,” Phys. Rev. B Condens. Matter 51(23), 16635–16642 (1995).
[CrossRef] [PubMed]

Hu, X. P.

Y. Q. Qin, C. Zhang, Y. Y. Zhu, X. P. Hu, and G. Zhao, “Wave-front engineering by Huygens-Fresnel principle for nonlinear optical interactions in domain engineered structures,” Phys. Rev. Lett. 100(6), 063902 (2008).
[CrossRef] [PubMed]

Itoh, H.

Jafarpour, A.

Ji, S. H.

P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, “Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal,” Phys. Rev. Lett. 93(13), 133904 (2004).
[CrossRef] [PubMed]

Jimenez, E.

F. R. Montero de Espinosa, E. Jimenez, and M. Torres, “Ultrasonic band gap in a periodic two-dimensional composite,” Phys. Rev. Lett. 80(6), 1208–1211 (1998).
[CrossRef]

Kaino, T.

Karlsson, H.

Katz, M.

A. Arie, G. Rosenman, V. Mahal, A. Skliar, M. Oron, M. Katz, and D. Eger, “Green and ultraviolet quasi-phase-matched second harmonic generation in bulk periodically-poled KTiOPO4,” Opt. Commun. 142(4-6), 265–268 (1997).
[CrossRef]

Khorasani, S.

Kushwaha, M. S.

M. S. Kushwaha, P. Halevi, G. Martínez, L. Dobrzynski, and B. Djafari-Rouhani, “Theory of acoustic band structure of periodic elastic composites,” Phys. Rev. B Condens. Matter 49(4), 2313–2322 (1994).
[CrossRef] [PubMed]

Laurell, F.

Lee, R. K.

Mahal, V.

A. Arie, G. Rosenman, V. Mahal, A. Skliar, M. Oron, M. Katz, and D. Eger, “Green and ultraviolet quasi-phase-matched second harmonic generation in bulk periodically-poled KTiOPO4,” Opt. Commun. 142(4-6), 265–268 (1997).
[CrossRef]

Martínez, G.

M. S. Kushwaha, P. Halevi, G. Martínez, L. Dobrzynski, and B. Djafari-Rouhani, “Theory of acoustic band structure of periodic elastic composites,” Phys. Rev. B Condens. Matter 49(4), 2313–2322 (1994).
[CrossRef] [PubMed]

Massaro, A.

Ming, N. B.

P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, “Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal,” Phys. Rev. Lett. 93(13), 133904 (2004).
[CrossRef] [PubMed]

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278(5339), 843–846 (1997).
[CrossRef]

Momeni, B.

Montero de Espinosa, F. R.

F. R. Montero de Espinosa, E. Jimenez, and M. Torres, “Ultrasonic band gap in a periodic two-dimensional composite,” Phys. Rev. Lett. 80(6), 1208–1211 (1998).
[CrossRef]

Oron, M.

A. Arie, G. Rosenman, V. Mahal, A. Skliar, M. Oron, M. Katz, and D. Eger, “Green and ultraviolet quasi-phase-matched second harmonic generation in bulk periodically-poled KTiOPO4,” Opt. Commun. 142(4-6), 265–268 (1997).
[CrossRef]

Pasiskevicius, V.

Passaseo, A.

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Qin, Y. Q.

Y. Q. Qin, C. Zhang, Y. Y. Zhu, X. P. Hu, and G. Zhao, “Wave-front engineering by Huygens-Fresnel principle for nonlinear optical interactions in domain engineered structures,” Phys. Rev. Lett. 100(6), 063902 (2008).
[CrossRef] [PubMed]

C. Zhang, Y. Q. Qin, and Y. Y. Zhu, “Perfect quasi-phase matching for the third-harmonic generation using focused Gaussian beams,” Opt. Lett. 33(7), 720–722 (2008).
[CrossRef] [PubMed]

Reinke, C. M.

Richards-Kortum, R.

Rosenman, G.

A. Arie, G. Rosenman, V. Mahal, A. Skliar, M. Oron, M. Katz, and D. Eger, “Green and ultraviolet quasi-phase-matched second harmonic generation in bulk periodically-poled KTiOPO4,” Opt. Commun. 142(4-6), 265–268 (1997).
[CrossRef]

Sigalas, M. M.

M. M. Sigalas and N. Garcia, “Importance of coupling between longitudinal and transverse components for the creation of acoustic band gaps: The aluminum in mercury case,” Appl. Phys. Lett. 76(16), 2307 (2000).
[CrossRef]

Skliar, A.

A. Arie, G. Rosenman, V. Mahal, A. Skliar, M. Oron, M. Katz, and D. Eger, “Green and ultraviolet quasi-phase-matched second harmonic generation in bulk periodically-poled KTiOPO4,” Opt. Commun. 142(4-6), 265–268 (1997).
[CrossRef]

Soltani, M.

Stomeo, T.

Sun, J.

P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, “Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal,” Phys. Rev. Lett. 93(13), 133904 (2004).
[CrossRef] [PubMed]

Tamura, S. I.

Y. Tanaka, Y. Tomoyasu, and S. I. Tamura, “Band structure of acoustic waves in phononic lattices: Two-dimensional composites with large acoustic mismatch,” Phys. Rev. B 62(11), 7387–7392 (2000).
[CrossRef]

Tanaka, Y.

Y. Tanaka, Y. Tomoyasu, and S. I. Tamura, “Band structure of acoustic waves in phononic lattices: Two-dimensional composites with large acoustic mismatch,” Phys. Rev. B 62(11), 7387–7392 (2000).
[CrossRef]

Tasco, V.

Todaro, M. T.

Tomoyasu, Y.

Y. Tanaka, Y. Tomoyasu, and S. I. Tamura, “Band structure of acoustic waves in phononic lattices: Two-dimensional composites with large acoustic mismatch,” Phys. Rev. B 62(11), 7387–7392 (2000).
[CrossRef]

Torres, M.

F. R. Montero de Espinosa, E. Jimenez, and M. Torres, “Ultrasonic band gap in a periodic two-dimensional composite,” Phys. Rev. Lett. 80(6), 1208–1211 (1998).
[CrossRef]

Voloch-Bloch, N.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3, 395–398 (2009).
[CrossRef]

Wang, H. T.

P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, “Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal,” Phys. Rev. Lett. 93(13), 133904 (2004).
[CrossRef] [PubMed]

Wang, S.

Xu, P.

P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, “Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal,” Phys. Rev. Lett. 93(13), 133904 (2004).
[CrossRef] [PubMed]

Xu, Y.

Yokohama, I.

Yokoo, A.

Yu, Q. L.

C. T. Chan, Q. L. Yu, and K. M. Ho, “Order-N spectral method for electromagnetic waves,” Phys. Rev. B Condens. Matter 51(23), 16635–16642 (1995).
[CrossRef] [PubMed]

Yu, X. Q.

P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, “Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal,” Phys. Rev. Lett. 93(13), 133904 (2004).
[CrossRef] [PubMed]

Zhang, C.

Y. Q. Qin, C. Zhang, Y. Y. Zhu, X. P. Hu, and G. Zhao, “Wave-front engineering by Huygens-Fresnel principle for nonlinear optical interactions in domain engineered structures,” Phys. Rev. Lett. 100(6), 063902 (2008).
[CrossRef] [PubMed]

C. Zhang, Y. Q. Qin, and Y. Y. Zhu, “Perfect quasi-phase matching for the third-harmonic generation using focused Gaussian beams,” Opt. Lett. 33(7), 720–722 (2008).
[CrossRef] [PubMed]

Zhao, G.

Y. Q. Qin, C. Zhang, Y. Y. Zhu, X. P. Hu, and G. Zhao, “Wave-front engineering by Huygens-Fresnel principle for nonlinear optical interactions in domain engineered structures,” Phys. Rev. Lett. 100(6), 063902 (2008).
[CrossRef] [PubMed]

Zhu, S. N.

P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, “Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal,” Phys. Rev. Lett. 93(13), 133904 (2004).
[CrossRef] [PubMed]

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278(5339), 843–846 (1997).
[CrossRef]

Zhu, Y. Y.

Y. Q. Qin, C. Zhang, Y. Y. Zhu, X. P. Hu, and G. Zhao, “Wave-front engineering by Huygens-Fresnel principle for nonlinear optical interactions in domain engineered structures,” Phys. Rev. Lett. 100(6), 063902 (2008).
[CrossRef] [PubMed]

C. Zhang, Y. Q. Qin, and Y. Y. Zhu, “Perfect quasi-phase matching for the third-harmonic generation using focused Gaussian beams,” Opt. Lett. 33(7), 720–722 (2008).
[CrossRef] [PubMed]

P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, “Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal,” Phys. Rev. Lett. 93(13), 133904 (2004).
[CrossRef] [PubMed]

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278(5339), 843–846 (1997).
[CrossRef]

Appl. Phys. Lett. (1)

M. M. Sigalas and N. Garcia, “Importance of coupling between longitudinal and transverse components for the creation of acoustic band gaps: The aluminum in mercury case,” Appl. Phys. Lett. 76(16), 2307 (2000).
[CrossRef]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. B (1)

Nat. Photonics (1)

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3, 395–398 (2009).
[CrossRef]

Opt. Commun. (1)

A. Arie, G. Rosenman, V. Mahal, A. Skliar, M. Oron, M. Katz, and D. Eger, “Green and ultraviolet quasi-phase-matched second harmonic generation in bulk periodically-poled KTiOPO4,” Opt. Commun. 142(4-6), 265–268 (1997).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Phys. Rev. A (1)

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Figures (4)

Fig. 1
Fig. 1

Dispersion relations of the present method, the red curve is the calculated result of Eq. (6) after normalization; the black curve is the numerical dispersion relations of free space.

Fig. 2
Fig. 2

Numerical results with this differential method: (a) Domain structure of the LiTaO3 OSL; (b) Field distribution of the fundamental wave; (c) Field distribution of the second-harmonics.

Fig. 3
Fig. 3

Intensity distribution of the harmonics at the focusing plane: (a) The fundamental wave; (b) Second-harmonic wave, respectively.

Fig. 4
Fig. 4

The field distributions of second-harmonic wave inside 23μm*23μm LiTaO3 domain-inverted structure using FD method (a) and FDTD method (b), respectively. The wavelength was set to be 1064nm, and the working temperature was 100°C.The period of the structure was 7.7µm, the radius of cylinder was 1.93µm.

Equations (8)

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{ A 1 x = i 2 k 1 2 A 1 y 2 iKf(x,y) A 2 A 1 * exp(iΔkx) A 2 x = i 2 k 2 2 A 2 y 2 1 2 iKf(x,y) A 1 2 exp(iΔkx)
A 1 (x+Δx,y)= A 1 (xΔx,y) iΔx k 1 Δ y 2 [ A 1 (x,y+Δy)+ A 1 (x,yΔy)2 A 1 (x,y)] 2iΔxKf(x,y) A 2 A 1 * exp(iΔkx)
A 2 (x+Δx,y)= A 2 (xΔx,y) iΔx k 2 Δ y 2 [ A 2 (x,y+Δy)+ A 2 (x,yΔy)2 A 2 (x,y)] iΔxKf(x,y) A 1 2 exp(iΔkx)
{ A 1 | x=0 =A e ( y y 0 r 0 ) 2 A 2 | x=0 =0
{ A 1 | y=0 =0 A 1 | y=L =0 A 2 | y=0 =0 A 2 | y=L =0
k ix = k iy 2 2 k i (i=1,2)
k ix = 1 Δx arcsin{ Δx k i Δ y 2 [ 1cos( k iy Δy ) ] }(i=1,2)
f(x,y)={ 1 cos(2 k 1 x+ k 2 r)0 1 cos(2 k 1 x+ k 2 r)0

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