Abstract

We proposed and experimentally demonstrated that nonlinear Raman-Nath second harmonic can be achieved in real time when a fundamental wave with the phase periodically modulated, termed as structured fundamental wave, incident in a homogeneous nonlinear medium. The diffraction of second harmonic originates from the structured fundamental wave, rather than the grating of a nonlinear photonic crystal. Nonlinear second harmonic generation, in forms of both one- and two-dimensional, was investigated in our experiment. This method circumvents the limitation of nonlinear photonic crystals in some extend and has potential applications in nonlinear frequency conversion, optical signal processing and beam shaping, etc.

© 2016 Optical Society of America

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References

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  1. A. Arie and N. Voloch, “Periodic, quasi-periodic, and random quadratic nonlinear photonic crystals,” Laser Photonics Rev. 4(3), 355–373 (2010).
    [Crossref]
  2. 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]
  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]
  4. K. Fradkin-Kashi, A. Arie, P. Urenski, and G. Rosenman, “Multiple nonlinear optical interactions with arbitrary wave vector differences,” Phys. Rev. Lett. 88(2), 023903 (2001).
    [Crossref] [PubMed]
  5. T. Ellenbogen, N. V. Bloch, A. G. Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3(7), 395–398 (2009).
    [Crossref]
  6. 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]
  7. Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Cerenkov radiation in nonlinear photonic crystal waveguides,” Phys. Rev. Lett. 100(16), 163904 (2008).
    [Crossref] [PubMed]
  8. A. R. Tunyagi, M. Ulex, and K. Betzler, “Noncollinear optical frequency doubling in strontium barium niobate,” Phys. Rev. Lett. 90(24), 243901 (2003).
    [Crossref] [PubMed]
  9. S. M. Saltiel, D. N. Neshev, W. Krolikowski, A. Arie, O. Bang, and Y. S. Kivshar, “Multiorder nonlinear diffraction in frequency doubling processes,” Opt. Lett. 34(6), 848–850 (2009).
    [Crossref] [PubMed]
  10. K. Kalinowski, P. Roedig, Y. Sheng, M. Ayoub, J. Imbrock, C. Denz, and W. Krolikowski, “Enhanced Čerenkov second-harmonic emission in nonlinear photonic structures,” Opt. Lett. 37(11), 1832–1834 (2012).
    [Crossref] [PubMed]
  11. H. Ren, X. Deng, Y. Zheng, N. An, and X. Chen, “Nonlinear Cherenkov radiation in an anomalous dispersive medium,” Phys. Rev. Lett. 108(22), 223901 (2012).
    [Crossref] [PubMed]
  12. H. Ren, X. Deng, Y. Zheng, N. An, and X. Chen, “Enhanced nonlinear Cherenkov radiation on the crystal boundary,” Opt. Lett. 38(11), 1993–1995 (2013).
    [Crossref] [PubMed]
  13. V. Roppo, K. Kalinowski, Y. Sheng, W. Krolikowski, C. Cojocaru, and J. Trull, “Unified approach to Čerenkov second harmonic generation,” Opt. Express 21(22), 25715–25726 (2013).
    [Crossref] [PubMed]
  14. S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
    [Crossref] [PubMed]
  15. A. Shapira and A. Arie, “Phase-matched nonlinear diffraction,” Opt. Lett. 36(10), 1933–1935 (2011).
    [Crossref] [PubMed]
  16. S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Y. S. Kivshar, “Nonlinear diffraction from a virtual beam,” Phys. Rev. Lett. 104(8), 083902 (2010).
    [Crossref] [PubMed]
  17. 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(8), 6777 (2008).
  18. 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(22), 3790–3792 (2010).
    [Crossref] [PubMed]
  19. P. Molina, M. O. Ramirez, B. J. Garcia, and L. E. Bausa, “Directional dependence of the second harmonic response in two-dimensional nonlinear photonic crystals,” Appl. Phys. Lett. 96(26), 261111 (2010).
    [Crossref]
  20. Y. Sheng, D. L. Ma, and A. Krolikowski, “Randomized nonlinear photonic crystal for broadband optical frequency conversion,” J. Phys. At. Mol. Opt. Phys. 46(21), 215401 (2013).
    [Crossref]
  21. Y. Sheng, W. J. Wang, R. Shiloh, V. Roppo, Y. F. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in χ2, ” Appl. Phys. Lett. 98(24), 241114 (2011).
    [Crossref]
  22. X. H. Hong, B. Yang, C. Zhang, Y. Q. Qin, and Y. Y. Zhu, “Nonlinear volume holography for wave-front engineering,” Phys. Rev. Lett. 113(16), 163902 (2014).
    [Crossref] [PubMed]
  23. N. V. Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting light by nonlinear photonic crystals,” Phys. Rev. Lett. 108(23), 233902 (2012).
    [Crossref] [PubMed]
  24. A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Two-dimensional nonlinear beam shaping,” Opt. Lett. 37(11), 2136–2138 (2012).
    [Crossref] [PubMed]
  25. T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. 70(10), 1401–1404 (1993).
    [Crossref] [PubMed]
  26. A. Libster-Hershko, S. Trajtenberg-Mills, and A. Arie, “Dynamic control of light beams in second harmonic generation,” Opt. Lett. 40(9), 1944–1947 (2015).
    [Crossref] [PubMed]

2015 (1)

2014 (1)

X. H. Hong, B. Yang, C. Zhang, Y. Q. Qin, and Y. Y. Zhu, “Nonlinear volume holography for wave-front engineering,” Phys. Rev. Lett. 113(16), 163902 (2014).
[Crossref] [PubMed]

2013 (3)

2012 (4)

K. Kalinowski, P. Roedig, Y. Sheng, M. Ayoub, J. Imbrock, C. Denz, and W. Krolikowski, “Enhanced Čerenkov second-harmonic emission in nonlinear photonic structures,” Opt. Lett. 37(11), 1832–1834 (2012).
[Crossref] [PubMed]

H. Ren, X. Deng, Y. Zheng, N. An, and X. Chen, “Nonlinear Cherenkov radiation in an anomalous dispersive medium,” Phys. Rev. Lett. 108(22), 223901 (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(23), 233902 (2012).
[Crossref] [PubMed]

A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Two-dimensional nonlinear beam shaping,” Opt. Lett. 37(11), 2136–2138 (2012).
[Crossref] [PubMed]

2011 (2)

Y. Sheng, W. J. Wang, R. Shiloh, V. Roppo, Y. F. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in χ2, ” Appl. Phys. Lett. 98(24), 241114 (2011).
[Crossref]

A. Shapira and A. Arie, “Phase-matched nonlinear diffraction,” Opt. Lett. 36(10), 1933–1935 (2011).
[Crossref] [PubMed]

2010 (4)

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Y. S. Kivshar, “Nonlinear diffraction from a virtual beam,” Phys. Rev. Lett. 104(8), 083902 (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(22), 3790–3792 (2010).
[Crossref] [PubMed]

P. Molina, M. O. Ramirez, B. J. Garcia, and L. E. Bausa, “Directional dependence of the second harmonic response in two-dimensional nonlinear photonic crystals,” Appl. Phys. Lett. 96(26), 261111 (2010).
[Crossref]

A. Arie and N. Voloch, “Periodic, quasi-periodic, and random quadratic nonlinear photonic crystals,” Laser Photonics Rev. 4(3), 355–373 (2010).
[Crossref]

2009 (2)

T. Ellenbogen, N. V. Bloch, A. G. Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3(7), 395–398 (2009).
[Crossref]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, A. Arie, O. Bang, and Y. S. Kivshar, “Multiorder nonlinear diffraction in frequency doubling processes,” Opt. Lett. 34(6), 848–850 (2009).
[Crossref] [PubMed]

2008 (4)

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]

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Cerenkov radiation in nonlinear photonic crystal waveguides,” Phys. Rev. Lett. 100(16), 163904 (2008).
[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(8), 6777 (2008).

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
[Crossref] [PubMed]

2003 (1)

A. R. Tunyagi, M. Ulex, and K. Betzler, “Noncollinear optical frequency doubling in strontium barium niobate,” Phys. Rev. Lett. 90(24), 243901 (2003).
[Crossref] [PubMed]

2001 (1)

K. Fradkin-Kashi, A. Arie, P. Urenski, and G. Rosenman, “Multiple nonlinear optical interactions with arbitrary wave vector differences,” Phys. Rev. Lett. 88(2), 023903 (2001).
[Crossref] [PubMed]

1997 (1)

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]

1993 (1)

T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. 70(10), 1401–1404 (1993).
[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]

An, N.

H. Ren, X. Deng, Y. Zheng, N. An, and X. Chen, “Enhanced nonlinear Cherenkov radiation on the crystal boundary,” Opt. Lett. 38(11), 1993–1995 (2013).
[Crossref] [PubMed]

H. Ren, X. Deng, Y. Zheng, N. An, and X. Chen, “Nonlinear Cherenkov radiation in an anomalous dispersive medium,” Phys. Rev. Lett. 108(22), 223901 (2012).
[Crossref] [PubMed]

Arie, A.

A. Libster-Hershko, S. Trajtenberg-Mills, and A. Arie, “Dynamic control of light beams in second harmonic generation,” Opt. Lett. 40(9), 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(23), 233902 (2012).
[Crossref] [PubMed]

A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Two-dimensional nonlinear beam shaping,” Opt. Lett. 37(11), 2136–2138 (2012).
[Crossref] [PubMed]

Y. Sheng, W. J. Wang, R. Shiloh, V. Roppo, Y. F. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in χ2, ” Appl. Phys. Lett. 98(24), 241114 (2011).
[Crossref]

A. Shapira and A. Arie, “Phase-matched nonlinear diffraction,” Opt. Lett. 36(10), 1933–1935 (2011).
[Crossref] [PubMed]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Y. S. Kivshar, “Nonlinear diffraction from a virtual beam,” Phys. Rev. Lett. 104(8), 083902 (2010).
[Crossref] [PubMed]

A. Arie and N. Voloch, “Periodic, quasi-periodic, and random quadratic nonlinear photonic crystals,” Laser Photonics Rev. 4(3), 355–373 (2010).
[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(22), 3790–3792 (2010).
[Crossref] [PubMed]

T. Ellenbogen, N. V. Bloch, A. G. Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3(7), 395–398 (2009).
[Crossref]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, A. Arie, O. Bang, and Y. S. Kivshar, “Multiorder nonlinear diffraction in frequency doubling processes,” Opt. Lett. 34(6), 848–850 (2009).
[Crossref] [PubMed]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
[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(8), 6777 (2008).

K. Fradkin-Kashi, A. Arie, P. Urenski, and G. Rosenman, “Multiple nonlinear optical interactions with arbitrary wave vector differences,” Phys. Rev. Lett. 88(2), 023903 (2001).
[Crossref] [PubMed]

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]

Ayoub, M.

Bang, O.

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Y. S. Kivshar, “Nonlinear diffraction from a virtual beam,” Phys. Rev. Lett. 104(8), 083902 (2010).
[Crossref] [PubMed]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, A. Arie, O. Bang, and Y. S. Kivshar, “Multiorder nonlinear diffraction in frequency doubling processes,” Opt. Lett. 34(6), 848–850 (2009).
[Crossref] [PubMed]

Bausa, L. E.

P. Molina, M. O. Ramirez, B. J. Garcia, and L. E. Bausa, “Directional dependence of the second harmonic response in two-dimensional nonlinear photonic crystals,” Appl. Phys. Lett. 96(26), 261111 (2010).
[Crossref]

Betzler, K.

A. R. Tunyagi, M. Ulex, and K. Betzler, “Noncollinear optical frequency doubling in strontium barium niobate,” Phys. Rev. Lett. 90(24), 243901 (2003).
[Crossref] [PubMed]

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(23), 233902 (2012).
[Crossref] [PubMed]

T. Ellenbogen, N. V. Bloch, A. G. Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3(7), 395–398 (2009).
[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]

Chen, X.

H. Ren, X. Deng, Y. Zheng, N. An, and X. Chen, “Enhanced nonlinear Cherenkov radiation on the crystal boundary,” Opt. Lett. 38(11), 1993–1995 (2013).
[Crossref] [PubMed]

H. Ren, X. Deng, Y. Zheng, N. An, and X. Chen, “Nonlinear Cherenkov radiation in an anomalous dispersive medium,” Phys. Rev. Lett. 108(22), 223901 (2012).
[Crossref] [PubMed]

Cojocaru, C.

Deng, X.

H. Ren, X. Deng, Y. Zheng, N. An, and X. Chen, “Enhanced nonlinear Cherenkov radiation on the crystal boundary,” Opt. Lett. 38(11), 1993–1995 (2013).
[Crossref] [PubMed]

H. Ren, X. Deng, Y. Zheng, N. An, and X. Chen, “Nonlinear Cherenkov radiation in an anomalous dispersive medium,” Phys. Rev. Lett. 108(22), 223901 (2012).
[Crossref] [PubMed]

Denz, C.

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]

Ellenbogen, T.

T. Ellenbogen, N. V. Bloch, A. G. Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3(7), 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 conical waves via nonlinear bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
[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(8), 6777 (2008).

Fradkin-Kashi, K.

K. Fradkin-Kashi, A. Arie, P. Urenski, and G. Rosenman, “Multiple nonlinear optical interactions with arbitrary wave vector differences,” Phys. Rev. Lett. 88(2), 023903 (2001).
[Crossref] [PubMed]

Gao, Z. D.

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Cerenkov radiation in nonlinear photonic crystal waveguides,” Phys. Rev. Lett. 100(16), 163904 (2008).
[Crossref] [PubMed]

Garcia, B. J.

P. Molina, M. O. Ramirez, B. J. Garcia, and L. E. Bausa, “Directional dependence of the second harmonic response in two-dimensional nonlinear photonic crystals,” Appl. Phys. Lett. 96(26), 261111 (2010).
[Crossref]

Herminghaus, S.

T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. 70(10), 1401–1404 (1993).
[Crossref] [PubMed]

Hong, X. H.

X. H. Hong, B. Yang, C. Zhang, Y. Q. Qin, and Y. Y. Zhu, “Nonlinear volume holography for wave-front engineering,” Phys. Rev. Lett. 113(16), 163902 (2014).
[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]

Imbrock, J.

Juwiler, I.

N. V. Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting light by nonlinear photonic crystals,” Phys. Rev. Lett. 108(23), 233902 (2012).
[Crossref] [PubMed]

A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Two-dimensional nonlinear beam shaping,” Opt. Lett. 37(11), 2136–2138 (2012).
[Crossref] [PubMed]

Kalinowski, K.

Kivshar, Y. S.

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Y. S. Kivshar, “Nonlinear diffraction from a virtual beam,” Phys. Rev. Lett. 104(8), 083902 (2010).
[Crossref] [PubMed]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, A. Arie, O. Bang, and Y. S. Kivshar, “Multiorder nonlinear diffraction in frequency doubling processes,” Opt. Lett. 34(6), 848–850 (2009).
[Crossref] [PubMed]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
[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(8), 6777 (2008).

Kong, Y.

Kong, Y. F.

Y. Sheng, W. J. Wang, R. Shiloh, V. Roppo, Y. F. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in χ2, ” Appl. Phys. Lett. 98(24), 241114 (2011).
[Crossref]

Krolikowski, A.

Y. Sheng, D. L. Ma, and A. Krolikowski, “Randomized nonlinear photonic crystal for broadband optical frequency conversion,” J. Phys. At. Mol. Opt. Phys. 46(21), 215401 (2013).
[Crossref]

Krolikowski, W.

V. Roppo, K. Kalinowski, Y. Sheng, W. Krolikowski, C. Cojocaru, and J. Trull, “Unified approach to Čerenkov second harmonic generation,” Opt. Express 21(22), 25715–25726 (2013).
[Crossref] [PubMed]

K. Kalinowski, P. Roedig, Y. Sheng, M. Ayoub, J. Imbrock, C. Denz, and W. Krolikowski, “Enhanced Čerenkov second-harmonic emission in nonlinear photonic structures,” Opt. Lett. 37(11), 1832–1834 (2012).
[Crossref] [PubMed]

Y. Sheng, W. J. Wang, R. Shiloh, V. Roppo, Y. F. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in χ2, ” Appl. Phys. Lett. 98(24), 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(22), 3790–3792 (2010).
[Crossref] [PubMed]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Y. S. Kivshar, “Nonlinear diffraction from a virtual beam,” Phys. Rev. Lett. 104(8), 083902 (2010).
[Crossref] [PubMed]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, A. Arie, O. Bang, and Y. S. Kivshar, “Multiorder nonlinear diffraction in frequency doubling processes,” Opt. Lett. 34(6), 848–850 (2009).
[Crossref] [PubMed]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
[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(8), 6777 (2008).

Libster-Hershko, A.

Ma, D. L.

Y. Sheng, D. L. Ma, and A. Krolikowski, “Randomized nonlinear photonic crystal for broadband optical frequency conversion,” J. Phys. At. Mol. Opt. Phys. 46(21), 215401 (2013).
[Crossref]

Ming, N. B.

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Cerenkov radiation in nonlinear photonic crystal waveguides,” Phys. Rev. Lett. 100(16), 163904 (2008).
[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]

Molina, P.

P. Molina, M. O. Ramirez, B. J. Garcia, and L. E. Bausa, “Directional dependence of the second harmonic response in two-dimensional nonlinear photonic crystals,” Appl. Phys. Lett. 96(26), 261111 (2010).
[Crossref]

Neshev, D. N.

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Y. S. Kivshar, “Nonlinear diffraction from a virtual beam,” Phys. Rev. Lett. 104(8), 083902 (2010).
[Crossref] [PubMed]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, A. Arie, O. Bang, and Y. S. Kivshar, “Multiorder nonlinear diffraction in frequency doubling processes,” Opt. Lett. 34(6), 848–850 (2009).
[Crossref] [PubMed]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
[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(8), 6777 (2008).

Padowicz, A. G.

T. Ellenbogen, N. V. Bloch, A. G. Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3(7), 395–398 (2009).
[Crossref]

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]

Qi, Z.

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Cerenkov radiation in nonlinear photonic crystal waveguides,” Phys. Rev. Lett. 100(16), 163904 (2008).
[Crossref] [PubMed]

Qin, Y. Q.

X. H. Hong, B. Yang, C. Zhang, Y. Q. Qin, and Y. Y. Zhu, “Nonlinear volume holography for wave-front engineering,” Phys. Rev. Lett. 113(16), 163902 (2014).
[Crossref] [PubMed]

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]

Ramirez, M. O.

P. Molina, M. O. Ramirez, B. J. Garcia, and L. E. Bausa, “Directional dependence of the second harmonic response in two-dimensional nonlinear photonic crystals,” Appl. Phys. Lett. 96(26), 261111 (2010).
[Crossref]

Ren, H.

H. Ren, X. Deng, Y. Zheng, N. An, and X. Chen, “Enhanced nonlinear Cherenkov radiation on the crystal boundary,” Opt. Lett. 38(11), 1993–1995 (2013).
[Crossref] [PubMed]

H. Ren, X. Deng, Y. Zheng, N. An, and X. Chen, “Nonlinear Cherenkov radiation in an anomalous dispersive medium,” Phys. Rev. Lett. 108(22), 223901 (2012).
[Crossref] [PubMed]

Roedig, P.

Roppo, V.

V. Roppo, K. Kalinowski, Y. Sheng, W. Krolikowski, C. Cojocaru, and J. Trull, “Unified approach to Čerenkov second harmonic generation,” Opt. Express 21(22), 25715–25726 (2013).
[Crossref] [PubMed]

Y. Sheng, W. J. Wang, R. Shiloh, V. Roppo, Y. F. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in χ2, ” Appl. Phys. Lett. 98(24), 241114 (2011).
[Crossref]

Rosenman, G.

K. Fradkin-Kashi, A. Arie, P. Urenski, and G. Rosenman, “Multiple nonlinear optical interactions with arbitrary wave vector differences,” Phys. Rev. Lett. 88(2), 023903 (2001).
[Crossref] [PubMed]

Saltiel, S. M.

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Y. S. Kivshar, “Nonlinear diffraction from a virtual beam,” Phys. Rev. Lett. 104(8), 083902 (2010).
[Crossref] [PubMed]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, A. Arie, O. Bang, and Y. S. Kivshar, “Multiorder nonlinear diffraction in frequency doubling processes,” Opt. Lett. 34(6), 848–850 (2009).
[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(8), 6777 (2008).

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
[Crossref] [PubMed]

Shapira, A.

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(23), 233902 (2012).
[Crossref] [PubMed]

Sheng, Y.

Shiloh, R.

N. V. Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting light by nonlinear photonic crystals,” Phys. Rev. Lett. 108(23), 233902 (2012).
[Crossref] [PubMed]

A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Two-dimensional nonlinear beam shaping,” Opt. Lett. 37(11), 2136–2138 (2012).
[Crossref] [PubMed]

Y. Sheng, W. J. Wang, R. Shiloh, V. Roppo, Y. F. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in χ2, ” Appl. Phys. Lett. 98(24), 241114 (2011).
[Crossref]

Trajtenberg-Mills, S.

Trull, J.

Tunyagi, A. R.

A. R. Tunyagi, M. Ulex, and K. Betzler, “Noncollinear optical frequency doubling in strontium barium niobate,” Phys. Rev. Lett. 90(24), 243901 (2003).
[Crossref] [PubMed]

Ulex, M.

A. R. Tunyagi, M. Ulex, and K. Betzler, “Noncollinear optical frequency doubling in strontium barium niobate,” Phys. Rev. Lett. 90(24), 243901 (2003).
[Crossref] [PubMed]

Urenski, P.

K. Fradkin-Kashi, A. Arie, P. Urenski, and G. Rosenman, “Multiple nonlinear optical interactions with arbitrary wave vector differences,” Phys. Rev. Lett. 88(2), 023903 (2001).
[Crossref] [PubMed]

Voloch, N.

A. Arie and N. Voloch, “Periodic, quasi-periodic, and random quadratic nonlinear photonic crystals,” Laser Photonics Rev. 4(3), 355–373 (2010).
[Crossref]

Voloch-Bloch, N.

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Y. S. Kivshar, “Nonlinear diffraction from a virtual beam,” Phys. Rev. Lett. 104(8), 083902 (2010).
[Crossref] [PubMed]

Wang, W.

Wang, W. J.

Y. Sheng, W. J. Wang, R. Shiloh, V. Roppo, Y. F. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in χ2, ” Appl. Phys. Lett. 98(24), 241114 (2011).
[Crossref]

Wulle, T.

T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. 70(10), 1401–1404 (1993).
[Crossref] [PubMed]

Yang, B.

X. H. Hong, B. Yang, C. Zhang, Y. Q. Qin, and Y. Y. Zhu, “Nonlinear volume holography for wave-front engineering,” Phys. Rev. Lett. 113(16), 163902 (2014).
[Crossref] [PubMed]

Zhang, C.

X. H. Hong, B. Yang, C. Zhang, Y. Q. Qin, and Y. Y. Zhu, “Nonlinear volume holography for wave-front engineering,” Phys. Rev. Lett. 113(16), 163902 (2014).
[Crossref] [PubMed]

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]

Zhang, Y.

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Cerenkov radiation in nonlinear photonic crystal waveguides,” Phys. Rev. Lett. 100(16), 163904 (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]

Zheng, Y.

H. Ren, X. Deng, Y. Zheng, N. An, and X. Chen, “Enhanced nonlinear Cherenkov radiation on the crystal boundary,” Opt. Lett. 38(11), 1993–1995 (2013).
[Crossref] [PubMed]

H. Ren, X. Deng, Y. Zheng, N. An, and X. Chen, “Nonlinear Cherenkov radiation in an anomalous dispersive medium,” Phys. Rev. Lett. 108(22), 223901 (2012).
[Crossref] [PubMed]

Zhu, S. N.

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Cerenkov radiation in nonlinear photonic crystal waveguides,” Phys. Rev. Lett. 100(16), 163904 (2008).
[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.

X. H. Hong, B. Yang, C. Zhang, Y. Q. Qin, and Y. Y. Zhu, “Nonlinear volume holography for wave-front engineering,” Phys. Rev. Lett. 113(16), 163902 (2014).
[Crossref] [PubMed]

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]

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. (2)

Y. Sheng, W. J. Wang, R. Shiloh, V. Roppo, Y. F. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in χ2, ” Appl. Phys. Lett. 98(24), 241114 (2011).
[Crossref]

P. Molina, M. O. Ramirez, B. J. Garcia, and L. E. Bausa, “Directional dependence of the second harmonic response in two-dimensional nonlinear photonic crystals,” Appl. Phys. Lett. 96(26), 261111 (2010).
[Crossref]

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

Y. Sheng, D. L. Ma, and A. Krolikowski, “Randomized nonlinear photonic crystal for broadband optical frequency conversion,” J. Phys. At. Mol. Opt. Phys. 46(21), 215401 (2013).
[Crossref]

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(8), 6777 (2008).

Laser Photonics Rev. (1)

A. Arie and N. Voloch, “Periodic, quasi-periodic, and random quadratic nonlinear photonic crystals,” Laser Photonics Rev. 4(3), 355–373 (2010).
[Crossref]

Nat. Photonics (1)

T. Ellenbogen, N. V. Bloch, A. G. Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams,” Nat. Photonics 3(7), 395–398 (2009).
[Crossref]

Opt. Express (1)

Opt. Lett. (7)

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. Lett. (10)

K. Fradkin-Kashi, A. Arie, P. Urenski, and G. Rosenman, “Multiple nonlinear optical interactions with arbitrary wave vector differences,” Phys. Rev. Lett. 88(2), 023903 (2001).
[Crossref] [PubMed]

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]

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Cerenkov radiation in nonlinear photonic crystal waveguides,” Phys. Rev. Lett. 100(16), 163904 (2008).
[Crossref] [PubMed]

A. R. Tunyagi, M. Ulex, and K. Betzler, “Noncollinear optical frequency doubling in strontium barium niobate,” Phys. Rev. Lett. 90(24), 243901 (2003).
[Crossref] [PubMed]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
[Crossref] [PubMed]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Y. S. Kivshar, “Nonlinear diffraction from a virtual beam,” Phys. Rev. Lett. 104(8), 083902 (2010).
[Crossref] [PubMed]

X. H. Hong, B. Yang, C. Zhang, Y. Q. Qin, and Y. Y. Zhu, “Nonlinear volume holography for wave-front engineering,” Phys. Rev. Lett. 113(16), 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(23), 233902 (2012).
[Crossref] [PubMed]

T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. 70(10), 1401–1404 (1993).
[Crossref] [PubMed]

H. Ren, X. Deng, Y. Zheng, N. An, and X. Chen, “Nonlinear Cherenkov radiation in an anomalous dispersive medium,” Phys. Rev. Lett. 108(22), 223901 (2012).
[Crossref] [PubMed]

Science (1)

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]

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Figures (3)

Fig. 1
Fig. 1 (a)(d) Holograms loaded on SLM representing the phase structure of the FW. (b)(e) Phase-matching geometries of the nonlinear Raman-Nath diffraction SHG process, corresponding to (a) and (d) under the assumption of nondiffraction of FW, respectively. (c)(f) Observed SH diffraction patterns of (a) and (d), respectively. (g) The experimental image of the FW from the output end of the nonlinear crystal.
Fig. 2
Fig. 2 (a) The external angles of + 1, + 2, and + 3 order SH as a function of the FW modulation period. Theoretical prediction (solid curves) and measured ones (signs) are in well agreement with each other. (b) Observed SH pattern with D = 0.5 and ϕ = π in 1D structure.
Fig. 3
Fig. 3 (a)(d) Holograms loaded on SLM representing the phase structure of the FW. (b)(e) The phase-matching geometries of the nonlinear Raman-Nath diffraction SHG process with different structures of the FW, corresponding to (a) and (d) under the assumption of nondiffraction of FW, respectively. (c)(f) SH pattern observed in experiment, corresponding to (a) and (d), respectively.

Equations (5)

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

P 2 ω ( r , t ) = ε 0 χ ( 2 ) ( r ) E ω ( r , t ) 2 ,
E 1 = A 1 C m exp ( i G m r ) exp [ i ( k y m r ω t ) ]
E 1 = A 1 exp [ i ( k 1 r ω t ) ] C m exp ( i G m r )
d A 2 d y = κ A 1 2 b q exp [ i ( k 2 y 2 k 1 ) y ] exp [ i ( k 2 t G q ) r ] ,
{ C 0 = 1 + e i ϕ C m = i [ cos ( m π ) 1 ] 2 m π ( 1 e i ϕ ) . m = 0 , ± 1 , ± 2 ,

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