Abstract

We study a scattering-assisted second harmonic generation process of a structured fundamental wave, whose phase front is periodically modulated, in a homogenous nonlinear medium. Scattering-assisted multiple-conical second harmonic in a one-dimensional structured fundamental wave and second harmonic belts in two-dimensional cases were observed. The experimental results are consistent with our analysis. This method not only allows dynamic control of the scattering-assisted second harmonic signal, but also has potential applications in various nonlinear frequency conversion processes.

© 2016 Optical Society of America

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  1. P. Xu, S. Ji, S. Zhu, X. Yu, J. Sun, H. Wang, J. He, Y. Zhu, and N. Ming, “Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: A hexagonally poled LiTaO3 crystal,” Phys. Rev. Lett. 93, 133904 (2004).
    [Crossref]
  2. N. An, Y. Zheng, H. Ren, X. Deng, and X. Chen, “Conical second harmonic generation in one-dimension nonlinear photonic crystal,” Appl. Phys. Lett. 102, 201112 (2013).
    [Crossref]
  3. H. Huang, C. Huang, C. Zhang, D. Zhu, X. Hong, J. Lu, J. Jiang, Q. Wang, and Y. Zhu, “Second-harmonic generation in a periodically poled congruent LiTaO3 sample with phase-tuned nonlinear cherenkov radiation,” Appl. Phys. Lett. 100, 022905 (2012).
    [Crossref]
  4. Z. Xie, G. Zhao, P. Xu, Z. Gao, and S. Zhu, “Study of optical elastic scattering in a quasiperiodically poled LiTaO3 crystal,” J. Appl. Phys. 101, 056104 (2007).
    [Crossref]
  5. T. Li, X. Zhao, Y. Zheng, and X. Chen, “Conical second harmonic generation in KDP crystal assisted by optical elastic scattering,” Opt. Express 23, 23827–23833 (2015).
    [Crossref] [PubMed]
  6. P. Xu, S. Zhu, X. Yu, S. Ji, Z. Gao, G. Zhao, Y. Zhu, and N. Ming, “Experimental studies of enhanced raman scattering from a hexagonally poled LiTaO3 crystal,” Phys. Rev. B 72, 064307 (2005).
    [Crossref]
  7. J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918 (1962).
    [Crossref]
  8. S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic bessel beams by transverse phase-matching in annular periodically poled structures,” Jpn. J. Appl. Phys. 47, 6777 (2008).
    [Crossref]
  9. W. Wang, Y. Sheng, Y. Kong, A. Arie, and W. Krolikowski, “Multiple čerenkov second-harmonic waves in a two-dimensional nonlinear photonic structure,” Opt. Lett. 35, 3790–3792 (2010).
    [Crossref] [PubMed]
  10. P. Molina, M. Ramírez, B. García, and L. Bausa, “Directional dependence of the second harmonic response in two-dimensional nonlinear photonic crystals,” Appl. Phys. Lett. 96, 261111 (2010).
    [Crossref]
  11. Y. Sheng, D. Ma, and W. Krolikowski, “Randomized nonlinear photonic crystal for broadband optical frequency conversion,” J. Phys. At. Mol. Opt. Phys. 46, 215401 (2013).
    [Crossref]
  12. Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, “Cerenkov third-harmonic generation in χ(2) nonlinear photonic crystal,” Appl. Phys. Lett. 98, 241114 (2011).
    [Crossref]
  13. X. Hong, B. Yang, C. Zhang, Y. Qin, and Y. Zhu, “Nonlinear volume holography for wave-front engineering,” Phys. Rev. Lett. 113, 163902 (2014).
    [Crossref] [PubMed]
  14. N. V. Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting light by nonlinear photonic crystals,” Phys. Rev. Lett. 108, 233902 (2012).
    [Crossref] [PubMed]
  15. A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Two-dimensional nonlinear beam shaping,” Opt. Lett. 37, 2136–2138 (2012).
    [Crossref] [PubMed]
  16. 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]
  17. S. Trajtenberg-Mills, I. Juwiler, and A. Arie, “On-axis shaping of second-harmonic beams,” Laser Photon. Rev. 9, L40–L44 (2015).
    [Crossref]
  18. A. Shapira, L. Naor, and A. Arie, “Nonlinear optical holograms for spatial and spectral shaping of light waves,” Sci. Bull. 60, 1403–1415 (2015).
    [Crossref]
  19. A. Shapira, I. Juwiler, and A. Arie, “Nonlinear computer-generated holograms,” Opt. Lett. 36, 3015–3017 (2011).
    [Crossref] [PubMed]
  20. Y. Zhang, J. Wen, S. Zhu, and M. Xiao, “Nonlinear talbot effect,” Phys. Rev. Lett. 104, 183901 (2010).
    [Crossref] [PubMed]
  21. Y. Sheng, A. Best, H.-J. Butt, W. Krolikowski, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualization by čerenkov-type second harmonic generation,” Opt. Express 18, 16539–16545 (2010).
    [Crossref] [PubMed]
  22. Y. Lin, K. Su, K. Huang, and Y. Chen, “Pattern formation of second harmonic conical waves in a nonlinear medium with extended defect structure,” Opt. Express 22, 27859–27868 (2014).
    [Crossref] [PubMed]
  23. A. Libster-Hershko, S. Trajtenberg-Mills, and A. Arie, “Dynamic control of light beams in second harmonic generation,” Opt. Lett. 40, 1944–1947 (2015).
    [Crossref] [PubMed]
  24. H. Liu, J. Li, X. Zhao, Y. Zheng, and X. Chen, “Nonlinear raman-nath second harmonic generation with structured fundamental wave,” Opt. Express 24, 15666–15671 (2016).
    [Crossref] [PubMed]
  25. V. Roppo, K. Kalinowski, Y. Sheng, W. Krolikowski, C. Cojocaru, and J. Trull, “Unified approach to Cerenkov second harmonic generation,” Opt. Express 21, 25715–25726 (2013).
    [Crossref] [PubMed]

2016 (1)

2015 (4)

A. Libster-Hershko, S. Trajtenberg-Mills, and A. Arie, “Dynamic control of light beams in second harmonic generation,” Opt. Lett. 40, 1944–1947 (2015).
[Crossref] [PubMed]

T. Li, X. Zhao, Y. Zheng, and X. Chen, “Conical second harmonic generation in KDP crystal assisted by optical elastic scattering,” Opt. Express 23, 23827–23833 (2015).
[Crossref] [PubMed]

S. Trajtenberg-Mills, I. Juwiler, and A. Arie, “On-axis shaping of second-harmonic beams,” Laser Photon. Rev. 9, L40–L44 (2015).
[Crossref]

A. Shapira, L. Naor, and A. Arie, “Nonlinear optical holograms for spatial and spectral shaping of light waves,” Sci. Bull. 60, 1403–1415 (2015).
[Crossref]

2014 (2)

2013 (3)

Y. Sheng, D. Ma, and W. Krolikowski, “Randomized nonlinear photonic crystal for broadband optical frequency conversion,” J. Phys. At. Mol. Opt. Phys. 46, 215401 (2013).
[Crossref]

V. Roppo, K. Kalinowski, Y. Sheng, W. Krolikowski, C. Cojocaru, and J. Trull, “Unified approach to Cerenkov second harmonic generation,” Opt. Express 21, 25715–25726 (2013).
[Crossref] [PubMed]

N. An, Y. Zheng, H. Ren, X. Deng, and X. Chen, “Conical second harmonic generation in one-dimension nonlinear photonic crystal,” Appl. Phys. Lett. 102, 201112 (2013).
[Crossref]

2012 (3)

H. Huang, C. Huang, C. Zhang, D. Zhu, X. Hong, J. Lu, J. Jiang, Q. Wang, and Y. Zhu, “Second-harmonic generation in a periodically poled congruent LiTaO3 sample with phase-tuned nonlinear cherenkov radiation,” Appl. Phys. Lett. 100, 022905 (2012).
[Crossref]

N. V. Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting light by nonlinear photonic crystals,” Phys. Rev. Lett. 108, 233902 (2012).
[Crossref] [PubMed]

A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Two-dimensional nonlinear beam shaping,” Opt. Lett. 37, 2136–2138 (2012).
[Crossref] [PubMed]

2011 (2)

A. Shapira, I. Juwiler, and A. Arie, “Nonlinear computer-generated holograms,” Opt. Lett. 36, 3015–3017 (2011).
[Crossref] [PubMed]

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, “Cerenkov third-harmonic generation in χ(2) nonlinear photonic crystal,” Appl. Phys. Lett. 98, 241114 (2011).
[Crossref]

2010 (4)

2009 (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]

2008 (1)

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic bessel beams by transverse phase-matching in annular periodically poled structures,” Jpn. J. Appl. Phys. 47, 6777 (2008).
[Crossref]

2007 (1)

Z. Xie, G. Zhao, P. Xu, Z. Gao, and S. Zhu, “Study of optical elastic scattering in a quasiperiodically poled LiTaO3 crystal,” J. Appl. Phys. 101, 056104 (2007).
[Crossref]

2005 (1)

P. Xu, S. Zhu, X. Yu, S. Ji, Z. Gao, G. Zhao, Y. Zhu, and N. Ming, “Experimental studies of enhanced raman scattering from a hexagonally poled LiTaO3 crystal,” Phys. Rev. B 72, 064307 (2005).
[Crossref]

2004 (1)

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

1962 (1)

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

An, N.

N. An, Y. Zheng, H. Ren, X. Deng, and X. Chen, “Conical second harmonic generation in one-dimension nonlinear photonic crystal,” Appl. Phys. Lett. 102, 201112 (2013).
[Crossref]

Arie, A.

S. Trajtenberg-Mills, I. Juwiler, and A. Arie, “On-axis shaping of second-harmonic beams,” Laser Photon. Rev. 9, L40–L44 (2015).
[Crossref]

A. Shapira, L. Naor, and A. Arie, “Nonlinear optical holograms for spatial and spectral shaping of light waves,” Sci. Bull. 60, 1403–1415 (2015).
[Crossref]

A. Libster-Hershko, S. Trajtenberg-Mills, and A. Arie, “Dynamic control of light beams in second harmonic generation,” Opt. Lett. 40, 1944–1947 (2015).
[Crossref] [PubMed]

N. V. Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting light by nonlinear photonic crystals,” Phys. Rev. Lett. 108, 233902 (2012).
[Crossref] [PubMed]

A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Two-dimensional nonlinear beam shaping,” Opt. Lett. 37, 2136–2138 (2012).
[Crossref] [PubMed]

A. Shapira, I. Juwiler, and A. Arie, “Nonlinear computer-generated holograms,” Opt. Lett. 36, 3015–3017 (2011).
[Crossref] [PubMed]

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, “Cerenkov third-harmonic generation in χ(2) nonlinear photonic crystal,” Appl. Phys. Lett. 98, 241114 (2011).
[Crossref]

Y. Sheng, A. Best, H.-J. Butt, W. Krolikowski, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualization by čerenkov-type second harmonic generation,” Opt. Express 18, 16539–16545 (2010).
[Crossref] [PubMed]

W. Wang, Y. Sheng, Y. Kong, A. Arie, and W. Krolikowski, “Multiple čerenkov second-harmonic waves in a two-dimensional nonlinear photonic structure,” Opt. Lett. 35, 3790–3792 (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]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic bessel beams by transverse phase-matching in annular periodically poled structures,” Jpn. J. Appl. Phys. 47, 6777 (2008).
[Crossref]

Armstrong, J.

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

Bausa, L.

P. Molina, M. Ramírez, B. García, and L. Bausa, “Directional dependence of the second harmonic response in two-dimensional nonlinear photonic crystals,” Appl. Phys. Lett. 96, 261111 (2010).
[Crossref]

Best, A.

Bloch, N. V.

N. V. Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting light by nonlinear photonic crystals,” Phys. Rev. Lett. 108, 233902 (2012).
[Crossref] [PubMed]

Bloembergen, N.

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

Butt, H.-J.

Chen, X.

Chen, Y.

Cojocaru, C.

Deng, X.

N. An, Y. Zheng, H. Ren, X. Deng, and X. Chen, “Conical second harmonic generation in one-dimension nonlinear photonic crystal,” Appl. Phys. Lett. 102, 201112 (2013).
[Crossref]

Ducuing, J.

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

Ellenbogen, T.

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]

Fischer, R.

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic bessel beams by transverse phase-matching in annular periodically poled structures,” Jpn. J. Appl. Phys. 47, 6777 (2008).
[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]

Gao, Z.

Z. Xie, G. Zhao, P. Xu, Z. Gao, and S. Zhu, “Study of optical elastic scattering in a quasiperiodically poled LiTaO3 crystal,” J. Appl. Phys. 101, 056104 (2007).
[Crossref]

P. Xu, S. Zhu, X. Yu, S. Ji, Z. Gao, G. Zhao, Y. Zhu, and N. Ming, “Experimental studies of enhanced raman scattering from a hexagonally poled LiTaO3 crystal,” Phys. Rev. B 72, 064307 (2005).
[Crossref]

García, B.

P. Molina, M. Ramírez, B. García, and L. Bausa, “Directional dependence of the second harmonic response in two-dimensional nonlinear photonic crystals,” Appl. Phys. Lett. 96, 261111 (2010).
[Crossref]

He, J.

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

Hong, X.

X. Hong, B. Yang, C. Zhang, Y. Qin, and Y. Zhu, “Nonlinear volume holography for wave-front engineering,” Phys. Rev. Lett. 113, 163902 (2014).
[Crossref] [PubMed]

H. Huang, C. Huang, C. Zhang, D. Zhu, X. Hong, J. Lu, J. Jiang, Q. Wang, and Y. Zhu, “Second-harmonic generation in a periodically poled congruent LiTaO3 sample with phase-tuned nonlinear cherenkov radiation,” Appl. Phys. Lett. 100, 022905 (2012).
[Crossref]

Huang, C.

H. Huang, C. Huang, C. Zhang, D. Zhu, X. Hong, J. Lu, J. Jiang, Q. Wang, and Y. Zhu, “Second-harmonic generation in a periodically poled congruent LiTaO3 sample with phase-tuned nonlinear cherenkov radiation,” Appl. Phys. Lett. 100, 022905 (2012).
[Crossref]

Huang, H.

H. Huang, C. Huang, C. Zhang, D. Zhu, X. Hong, J. Lu, J. Jiang, Q. Wang, and Y. Zhu, “Second-harmonic generation in a periodically poled congruent LiTaO3 sample with phase-tuned nonlinear cherenkov radiation,” Appl. Phys. Lett. 100, 022905 (2012).
[Crossref]

Huang, K.

Ji, S.

P. Xu, S. Zhu, X. Yu, S. Ji, Z. Gao, G. Zhao, Y. Zhu, and N. Ming, “Experimental studies of enhanced raman scattering from a hexagonally poled LiTaO3 crystal,” Phys. Rev. B 72, 064307 (2005).
[Crossref]

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

Jiang, J.

H. Huang, C. Huang, C. Zhang, D. Zhu, X. Hong, J. Lu, J. Jiang, Q. Wang, and Y. Zhu, “Second-harmonic generation in a periodically poled congruent LiTaO3 sample with phase-tuned nonlinear cherenkov radiation,” Appl. Phys. Lett. 100, 022905 (2012).
[Crossref]

Juwiler, I.

S. Trajtenberg-Mills, I. Juwiler, and A. Arie, “On-axis shaping of second-harmonic beams,” Laser Photon. Rev. 9, L40–L44 (2015).
[Crossref]

A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Two-dimensional nonlinear beam shaping,” Opt. Lett. 37, 2136–2138 (2012).
[Crossref] [PubMed]

N. V. Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting light by nonlinear photonic crystals,” Phys. Rev. Lett. 108, 233902 (2012).
[Crossref] [PubMed]

A. Shapira, I. Juwiler, and A. Arie, “Nonlinear computer-generated holograms,” Opt. Lett. 36, 3015–3017 (2011).
[Crossref] [PubMed]

Kalinowski, K.

Kivshar, Y. S.

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic bessel beams by transverse phase-matching in annular periodically poled structures,” Jpn. J. Appl. Phys. 47, 6777 (2008).
[Crossref]

Kong, Y.

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, “Cerenkov third-harmonic generation in χ(2) nonlinear photonic crystal,” Appl. Phys. Lett. 98, 241114 (2011).
[Crossref]

W. Wang, Y. Sheng, Y. Kong, A. Arie, and W. Krolikowski, “Multiple čerenkov second-harmonic waves in a two-dimensional nonlinear photonic structure,” Opt. Lett. 35, 3790–3792 (2010).
[Crossref] [PubMed]

Koynov, K.

Krolikowski, W.

V. Roppo, K. Kalinowski, Y. Sheng, W. Krolikowski, C. Cojocaru, and J. Trull, “Unified approach to Cerenkov second harmonic generation,” Opt. Express 21, 25715–25726 (2013).
[Crossref] [PubMed]

Y. Sheng, D. Ma, and W. Krolikowski, “Randomized nonlinear photonic crystal for broadband optical frequency conversion,” J. Phys. At. Mol. Opt. Phys. 46, 215401 (2013).
[Crossref]

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, “Cerenkov third-harmonic generation in χ(2) nonlinear photonic crystal,” Appl. Phys. Lett. 98, 241114 (2011).
[Crossref]

Y. Sheng, A. Best, H.-J. Butt, W. Krolikowski, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualization by čerenkov-type second harmonic generation,” Opt. Express 18, 16539–16545 (2010).
[Crossref] [PubMed]

W. Wang, Y. Sheng, Y. Kong, A. Arie, and W. Krolikowski, “Multiple čerenkov second-harmonic waves in a two-dimensional nonlinear photonic structure,” Opt. Lett. 35, 3790–3792 (2010).
[Crossref] [PubMed]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic bessel beams by transverse phase-matching in annular periodically poled structures,” Jpn. J. Appl. Phys. 47, 6777 (2008).
[Crossref]

Li, J.

Li, T.

Libster-Hershko, A.

Lin, Y.

Liu, H.

Lu, J.

H. Huang, C. Huang, C. Zhang, D. Zhu, X. Hong, J. Lu, J. Jiang, Q. Wang, and Y. Zhu, “Second-harmonic generation in a periodically poled congruent LiTaO3 sample with phase-tuned nonlinear cherenkov radiation,” Appl. Phys. Lett. 100, 022905 (2012).
[Crossref]

Ma, D.

Y. Sheng, D. Ma, and W. Krolikowski, “Randomized nonlinear photonic crystal for broadband optical frequency conversion,” J. Phys. At. Mol. Opt. Phys. 46, 215401 (2013).
[Crossref]

Ming, N.

P. Xu, S. Zhu, X. Yu, S. Ji, Z. Gao, G. Zhao, Y. Zhu, and N. Ming, “Experimental studies of enhanced raman scattering from a hexagonally poled LiTaO3 crystal,” Phys. Rev. B 72, 064307 (2005).
[Crossref]

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

Molina, P.

P. Molina, M. Ramírez, B. García, and L. Bausa, “Directional dependence of the second harmonic response in two-dimensional nonlinear photonic crystals,” Appl. Phys. Lett. 96, 261111 (2010).
[Crossref]

Naor, L.

A. Shapira, L. Naor, and A. Arie, “Nonlinear optical holograms for spatial and spectral shaping of light waves,” Sci. Bull. 60, 1403–1415 (2015).
[Crossref]

Neshev, D. N.

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic bessel beams by transverse phase-matching in annular periodically poled structures,” Jpn. J. Appl. Phys. 47, 6777 (2008).
[Crossref]

Pershan, P.

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

Qin, Y.

X. Hong, B. Yang, C. Zhang, Y. Qin, and Y. Zhu, “Nonlinear volume holography for wave-front engineering,” Phys. Rev. Lett. 113, 163902 (2014).
[Crossref] [PubMed]

Ramírez, M.

P. Molina, M. Ramírez, B. García, and L. Bausa, “Directional dependence of the second harmonic response in two-dimensional nonlinear photonic crystals,” Appl. Phys. Lett. 96, 261111 (2010).
[Crossref]

Ren, H.

N. An, Y. Zheng, H. Ren, X. Deng, and X. Chen, “Conical second harmonic generation in one-dimension nonlinear photonic crystal,” Appl. Phys. Lett. 102, 201112 (2013).
[Crossref]

Roppo, V.

V. Roppo, K. Kalinowski, Y. Sheng, W. Krolikowski, C. Cojocaru, and J. Trull, “Unified approach to Cerenkov second harmonic generation,” Opt. Express 21, 25715–25726 (2013).
[Crossref] [PubMed]

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, “Cerenkov third-harmonic generation in χ(2) nonlinear photonic crystal,” Appl. Phys. Lett. 98, 241114 (2011).
[Crossref]

Saltiel, S. M.

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic bessel beams by transverse phase-matching in annular periodically poled structures,” Jpn. J. Appl. Phys. 47, 6777 (2008).
[Crossref]

Shapira, A.

A. Shapira, L. Naor, and A. Arie, “Nonlinear optical holograms for spatial and spectral shaping of light waves,” Sci. Bull. 60, 1403–1415 (2015).
[Crossref]

A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Two-dimensional nonlinear beam shaping,” Opt. Lett. 37, 2136–2138 (2012).
[Crossref] [PubMed]

N. V. Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting light by nonlinear photonic crystals,” Phys. Rev. Lett. 108, 233902 (2012).
[Crossref] [PubMed]

A. Shapira, I. Juwiler, and A. Arie, “Nonlinear computer-generated holograms,” Opt. Lett. 36, 3015–3017 (2011).
[Crossref] [PubMed]

Shemer, K.

N. V. Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting light by nonlinear photonic crystals,” Phys. Rev. Lett. 108, 233902 (2012).
[Crossref] [PubMed]

Sheng, Y.

Shiloh, R.

A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Two-dimensional nonlinear beam shaping,” Opt. Lett. 37, 2136–2138 (2012).
[Crossref] [PubMed]

N. V. Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting light by nonlinear photonic crystals,” Phys. Rev. Lett. 108, 233902 (2012).
[Crossref] [PubMed]

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, “Cerenkov third-harmonic generation in χ(2) nonlinear photonic crystal,” Appl. Phys. Lett. 98, 241114 (2011).
[Crossref]

Su, K.

Sun, J.

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

Trajtenberg-Mills, S.

A. Libster-Hershko, S. Trajtenberg-Mills, and A. Arie, “Dynamic control of light beams in second harmonic generation,” Opt. Lett. 40, 1944–1947 (2015).
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S. Trajtenberg-Mills, I. Juwiler, and A. Arie, “On-axis shaping of second-harmonic beams,” Laser Photon. Rev. 9, L40–L44 (2015).
[Crossref]

Trull, J.

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.

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

Wang, Q.

H. Huang, C. Huang, C. Zhang, D. Zhu, X. Hong, J. Lu, J. Jiang, Q. Wang, and Y. Zhu, “Second-harmonic generation in a periodically poled congruent LiTaO3 sample with phase-tuned nonlinear cherenkov radiation,” Appl. Phys. Lett. 100, 022905 (2012).
[Crossref]

Wang, W.

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, “Cerenkov third-harmonic generation in χ(2) nonlinear photonic crystal,” Appl. Phys. Lett. 98, 241114 (2011).
[Crossref]

W. Wang, Y. Sheng, Y. Kong, A. Arie, and W. Krolikowski, “Multiple čerenkov second-harmonic waves in a two-dimensional nonlinear photonic structure,” Opt. Lett. 35, 3790–3792 (2010).
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Wen, J.

Y. Zhang, J. Wen, S. Zhu, and M. Xiao, “Nonlinear talbot effect,” Phys. Rev. Lett. 104, 183901 (2010).
[Crossref] [PubMed]

Xiao, M.

Y. Zhang, J. Wen, S. Zhu, and M. Xiao, “Nonlinear talbot effect,” Phys. Rev. Lett. 104, 183901 (2010).
[Crossref] [PubMed]

Xie, Z.

Z. Xie, G. Zhao, P. Xu, Z. Gao, and S. Zhu, “Study of optical elastic scattering in a quasiperiodically poled LiTaO3 crystal,” J. Appl. Phys. 101, 056104 (2007).
[Crossref]

Xu, P.

Z. Xie, G. Zhao, P. Xu, Z. Gao, and S. Zhu, “Study of optical elastic scattering in a quasiperiodically poled LiTaO3 crystal,” J. Appl. Phys. 101, 056104 (2007).
[Crossref]

P. Xu, S. Zhu, X. Yu, S. Ji, Z. Gao, G. Zhao, Y. Zhu, and N. Ming, “Experimental studies of enhanced raman scattering from a hexagonally poled LiTaO3 crystal,” Phys. Rev. B 72, 064307 (2005).
[Crossref]

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

Yang, B.

X. Hong, B. Yang, C. Zhang, Y. Qin, and Y. Zhu, “Nonlinear volume holography for wave-front engineering,” Phys. Rev. Lett. 113, 163902 (2014).
[Crossref] [PubMed]

Yu, X.

P. Xu, S. Zhu, X. Yu, S. Ji, Z. Gao, G. Zhao, Y. Zhu, and N. Ming, “Experimental studies of enhanced raman scattering from a hexagonally poled LiTaO3 crystal,” Phys. Rev. B 72, 064307 (2005).
[Crossref]

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

Zhang, C.

X. Hong, B. Yang, C. Zhang, Y. Qin, and Y. Zhu, “Nonlinear volume holography for wave-front engineering,” Phys. Rev. Lett. 113, 163902 (2014).
[Crossref] [PubMed]

H. Huang, C. Huang, C. Zhang, D. Zhu, X. Hong, J. Lu, J. Jiang, Q. Wang, and Y. Zhu, “Second-harmonic generation in a periodically poled congruent LiTaO3 sample with phase-tuned nonlinear cherenkov radiation,” Appl. Phys. Lett. 100, 022905 (2012).
[Crossref]

Zhang, Y.

Y. Zhang, J. Wen, S. Zhu, and M. Xiao, “Nonlinear talbot effect,” Phys. Rev. Lett. 104, 183901 (2010).
[Crossref] [PubMed]

Zhao, G.

Z. Xie, G. Zhao, P. Xu, Z. Gao, and S. Zhu, “Study of optical elastic scattering in a quasiperiodically poled LiTaO3 crystal,” J. Appl. Phys. 101, 056104 (2007).
[Crossref]

P. Xu, S. Zhu, X. Yu, S. Ji, Z. Gao, G. Zhao, Y. Zhu, and N. Ming, “Experimental studies of enhanced raman scattering from a hexagonally poled LiTaO3 crystal,” Phys. Rev. B 72, 064307 (2005).
[Crossref]

Zhao, X.

Zheng, Y.

Zhu, D.

H. Huang, C. Huang, C. Zhang, D. Zhu, X. Hong, J. Lu, J. Jiang, Q. Wang, and Y. Zhu, “Second-harmonic generation in a periodically poled congruent LiTaO3 sample with phase-tuned nonlinear cherenkov radiation,” Appl. Phys. Lett. 100, 022905 (2012).
[Crossref]

Zhu, S.

Y. Zhang, J. Wen, S. Zhu, and M. Xiao, “Nonlinear talbot effect,” Phys. Rev. Lett. 104, 183901 (2010).
[Crossref] [PubMed]

Z. Xie, G. Zhao, P. Xu, Z. Gao, and S. Zhu, “Study of optical elastic scattering in a quasiperiodically poled LiTaO3 crystal,” J. Appl. Phys. 101, 056104 (2007).
[Crossref]

P. Xu, S. Zhu, X. Yu, S. Ji, Z. Gao, G. Zhao, Y. Zhu, and N. Ming, “Experimental studies of enhanced raman scattering from a hexagonally poled LiTaO3 crystal,” Phys. Rev. B 72, 064307 (2005).
[Crossref]

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

Zhu, Y.

X. Hong, B. Yang, C. Zhang, Y. Qin, and Y. Zhu, “Nonlinear volume holography for wave-front engineering,” Phys. Rev. Lett. 113, 163902 (2014).
[Crossref] [PubMed]

H. Huang, C. Huang, C. Zhang, D. Zhu, X. Hong, J. Lu, J. Jiang, Q. Wang, and Y. Zhu, “Second-harmonic generation in a periodically poled congruent LiTaO3 sample with phase-tuned nonlinear cherenkov radiation,” Appl. Phys. Lett. 100, 022905 (2012).
[Crossref]

P. Xu, S. Zhu, X. Yu, S. Ji, Z. Gao, G. Zhao, Y. Zhu, and N. Ming, “Experimental studies of enhanced raman scattering from a hexagonally poled LiTaO3 crystal,” Phys. Rev. B 72, 064307 (2005).
[Crossref]

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

Appl. Phys. Lett. (4)

N. An, Y. Zheng, H. Ren, X. Deng, and X. Chen, “Conical second harmonic generation in one-dimension nonlinear photonic crystal,” Appl. Phys. Lett. 102, 201112 (2013).
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H. Huang, C. Huang, C. Zhang, D. Zhu, X. Hong, J. Lu, J. Jiang, Q. Wang, and Y. Zhu, “Second-harmonic generation in a periodically poled congruent LiTaO3 sample with phase-tuned nonlinear cherenkov radiation,” Appl. Phys. Lett. 100, 022905 (2012).
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P. Molina, M. Ramírez, B. García, and L. Bausa, “Directional dependence of the second harmonic response in two-dimensional nonlinear photonic crystals,” Appl. Phys. Lett. 96, 261111 (2010).
[Crossref]

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, “Cerenkov third-harmonic generation in χ(2) nonlinear photonic crystal,” Appl. Phys. Lett. 98, 241114 (2011).
[Crossref]

J. Appl. Phys. (1)

Z. Xie, G. Zhao, P. Xu, Z. Gao, and S. Zhu, “Study of optical elastic scattering in a quasiperiodically poled LiTaO3 crystal,” J. Appl. Phys. 101, 056104 (2007).
[Crossref]

J. Phys. At. Mol. Opt. Phys. (1)

Y. Sheng, D. Ma, and W. Krolikowski, “Randomized nonlinear photonic crystal for broadband optical frequency conversion,” J. Phys. At. Mol. Opt. Phys. 46, 215401 (2013).
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Jpn. J. Appl. Phys. (1)

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic bessel beams by transverse phase-matching in annular periodically poled structures,” Jpn. J. Appl. Phys. 47, 6777 (2008).
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Laser Photon. Rev. (1)

S. Trajtenberg-Mills, I. Juwiler, and A. Arie, “On-axis shaping of second-harmonic beams,” Laser Photon. Rev. 9, L40–L44 (2015).
[Crossref]

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. Express (5)

Opt. Lett. (4)

Phys. Rev. (1)

J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918 (1962).
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Phys. Rev. B (1)

P. Xu, S. Zhu, X. Yu, S. Ji, Z. Gao, G. Zhao, Y. Zhu, and N. Ming, “Experimental studies of enhanced raman scattering from a hexagonally poled LiTaO3 crystal,” Phys. Rev. B 72, 064307 (2005).
[Crossref]

Phys. Rev. Lett. (4)

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

X. Hong, B. Yang, C. Zhang, Y. Qin, and Y. Zhu, “Nonlinear volume holography for wave-front engineering,” Phys. Rev. Lett. 113, 163902 (2014).
[Crossref] [PubMed]

N. V. Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting light by nonlinear photonic crystals,” Phys. Rev. Lett. 108, 233902 (2012).
[Crossref] [PubMed]

Y. Zhang, J. Wen, S. Zhu, and M. Xiao, “Nonlinear talbot effect,” Phys. Rev. Lett. 104, 183901 (2010).
[Crossref] [PubMed]

Sci. Bull. (1)

A. Shapira, L. Naor, and A. Arie, “Nonlinear optical holograms for spatial and spectral shaping of light waves,” Sci. Bull. 60, 1403–1415 (2015).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1 (a)(d) The phase structure of the FW. (b)(e) Phase-matching geometries of scattering-assisted conical SHG process with different structure of FW corresponding to (a)(d), respectively. (c)(f) Observed SH patterns in experiment corresponding to (a)(d), respectively.

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Fig. 2
Fig. 2 Photos of SH evolving with periods of the FW. (a–d) 125 μm, 83.3 μm, 62.5 μm and 50 μm, respectively.

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Fig. 3
Fig. 3 (a) Angles α and β as a function of the FW period. Theoretical prediction (solid curves) and measured ones (signs) are in well agreement with each other. (b) SHG in case of FW periodic modulated from 0 to π and D=0.6. (c) FW periodic modulated from 0 to π/2 in 1D structure. (d) SHG corresponding to (c).

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Fig. 4
Fig. 4 (a) The annular phase structure of the FW. (b) Phase-matching geometries of scattering-assisted conical SHG process with annular structure of FW. (c) Observed SH belts in experiment.

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Equations (4)

Equations on this page are rendered with MathJax. Learn more.

E → 1 = A 1 ⋅ ∑ C m exp ( − i G → m ⋅ r → ) exp [ − i ( k → y m ⋅ r → − ω t ) ]
P → 2 = ∊ 0 χ ( 2 ) E → 1 E → 1 ′ = ∊ 0 χ ( 2 ) A 1 A 1 ′ ∑ C m exp [ − i ( k → y m + k → 1 ′ + G → m ) ⋅ r → + i 2 ω t ) ]
C 0 = 1 2 ( 1 + e i ϕ ) ,           C m = i [ cos ( m π ) − 1 ] 2 m π ( 1 − e i ϕ )
α = arc   sin ( G → m | k → 1 , o | ) ,     β = arc   cos ( | k → 2 , e | 2 | k → 1 , o | ) + α

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