Abstract

We demonstrated experimentally a method to generate the sum-frequency Nonlinear Cherenkov radiation (NCR) on the boundary of bulk medium by using two synchronized laser beam with wavelength of 1300nm and 800nm. It is also an evidence that the polarization wave is always confined to the boundary. Critical conditions of surface sum-frequency NCR under normal and anomalous dispersion condition is discussed.

© 2015 Optical Society of America

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References

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  1. P. A. Cherenkov, “Visible emission of clean liquids by action of γ radiation,” Dokl. Akad. Nauk SSSR 2, 451–454 (1934).
  2. 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]
  3. A. S. Aleksandrovsky, A. M. Vyunishev, A. I. Zaitsev, A. A. Ikonnikov, and G. I. Pospelov, “Ultrashort pulses characterization by nonlinear diffraction from virtual beam,” Appl. Phys. Lett. 98(6), 061104 (2011).
    [Crossref]
  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]
  5. Y. Sheng, W. J. Wang, R. Shiloh, V. Roppo, Y. F. Kong, A. Arie, and W. Krolikowski, “Cerenkov third-harmonic generation in chi((2)) nonlinear photonic crystal,” Appl. Phys. Lett. 98(24), 241114 (2011).
    [Crossref]
  6. N. An, H. J. Ren, Y. L. Zheng, X. W. Deng, and X. F. Chen, “Cherenkov high-order harmonic generation by multistep cascading in chi((2)) nonlinear photonic crystal,” Appl. Phys. Lett. 100(22), 221103 (2012).
    [Crossref]
  7. C. D. Chen, X. P. Hu, Y. L. Xu, P. Xu, G. Zhao, and S. N. Zhu, “Čerenkov difference frequency generation in a two-dimensional nonlinear photonic crystal,” Appl. Phys. Lett. 101, 071113 (2012).
  8. Y. Sheng, A. Best, H. J. Butt, W. Krolikowski, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualization by Cerenkov-type second harmonic generation,” Opt. Express 18(16), 16539–16545 (2010).
    [Crossref] [PubMed]
  9. A. Fragemann, V. Pasiskevicius, and F. Laurell, “Second-order nonlinearities in the domain walls of periodically poled KTiOPO4,” Appl. Phys. Lett. 85(3), 375–377 (2004).
    [Crossref]
  10. X. Deng, H. Ren, H. Lao, and X. Chen, “Research on Cherenkov second harmonic generation in periodically poled lithium niobate by femtosecond pulses,” J. Opt. Soc. Am. B 27(7), 1475–1480 (2010).
    [Crossref]
  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. Y. Sheng, V. Roppo, K. Kalinowski, and W. Krolikowski, “Role of a localized modulation of χ(2) in Čerenkov second-harmonic generation in nonlinear bulk medium,” Opt. Lett. 37(18), 3864–3866 (2012).
    [Crossref] [PubMed]
  13. 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]
  14. X. Wang, H. Ren, N. An, X. Zhao, Y. Zheng, and X. Chen, “Large acceptance of non-collinear phase-matching second harmonic generation on the surface of an anomalous-like bulk dispersion medium,” Opt. Express 22(23), 28234–28239 (2014).
    [Crossref] [PubMed]
  15. 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]
  16. H. Ren, X. Deng, Y. Zheng, and X. Chen, “Single Domain Wall Effect on Parametric Processes via Cherenkov-Type Phase Matching,” J. Nonlinear Opt. Phys. Mater. 20(04), 459–466 (2011).
    [Crossref]
  17. H. J. Ren, X. W. Deng, Y. L. Zheng, N. An, and X. F. Chen, “Surface phase-matched harmonic enhancement in a bulk anomalous dispersion medium,” Appl. Phys. Lett. 103(2), 021110 (2013).
    [Crossref]

2014 (1)

2013 (3)

2012 (4)

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]

Y. Sheng, V. Roppo, K. Kalinowski, and W. Krolikowski, “Role of a localized modulation of χ(2) in Čerenkov second-harmonic generation in nonlinear bulk medium,” Opt. Lett. 37(18), 3864–3866 (2012).
[Crossref] [PubMed]

N. An, H. J. Ren, Y. L. Zheng, X. W. Deng, and X. F. Chen, “Cherenkov high-order harmonic generation by multistep cascading in chi((2)) nonlinear photonic crystal,” Appl. Phys. Lett. 100(22), 221103 (2012).
[Crossref]

C. D. Chen, X. P. Hu, Y. L. Xu, P. Xu, G. Zhao, and S. N. Zhu, “Čerenkov difference frequency generation in a two-dimensional nonlinear photonic crystal,” Appl. Phys. Lett. 101, 071113 (2012).

2011 (3)

A. S. Aleksandrovsky, A. M. Vyunishev, A. I. Zaitsev, A. A. Ikonnikov, and G. I. Pospelov, “Ultrashort pulses characterization by nonlinear diffraction from virtual beam,” Appl. Phys. Lett. 98(6), 061104 (2011).
[Crossref]

Y. Sheng, W. J. Wang, R. Shiloh, V. Roppo, Y. F. Kong, A. Arie, and W. Krolikowski, “Cerenkov third-harmonic generation in chi((2)) nonlinear photonic crystal,” Appl. Phys. Lett. 98(24), 241114 (2011).
[Crossref]

H. Ren, X. Deng, Y. Zheng, and X. Chen, “Single Domain Wall Effect on Parametric Processes via Cherenkov-Type Phase Matching,” J. Nonlinear Opt. Phys. Mater. 20(04), 459–466 (2011).
[Crossref]

2010 (3)

2008 (1)

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]

2004 (1)

A. Fragemann, V. Pasiskevicius, and F. Laurell, “Second-order nonlinearities in the domain walls of periodically poled KTiOPO4,” Appl. Phys. Lett. 85(3), 375–377 (2004).
[Crossref]

1934 (1)

P. A. Cherenkov, “Visible emission of clean liquids by action of γ radiation,” Dokl. Akad. Nauk SSSR 2, 451–454 (1934).

Aleksandrovsky, A. S.

A. S. Aleksandrovsky, A. M. Vyunishev, A. I. Zaitsev, A. A. Ikonnikov, and G. I. Pospelov, “Ultrashort pulses characterization by nonlinear diffraction from virtual beam,” Appl. Phys. Lett. 98(6), 061104 (2011).
[Crossref]

An, N.

X. Wang, H. Ren, N. An, X. Zhao, Y. Zheng, and X. Chen, “Large acceptance of non-collinear phase-matching second harmonic generation on the surface of an anomalous-like bulk dispersion medium,” Opt. Express 22(23), 28234–28239 (2014).
[Crossref] [PubMed]

H. J. Ren, X. W. Deng, Y. L. Zheng, N. An, and X. F. Chen, “Surface phase-matched harmonic enhancement in a bulk anomalous dispersion medium,” Appl. Phys. Lett. 103(2), 021110 (2013).
[Crossref]

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]

N. An, H. J. Ren, Y. L. Zheng, X. W. Deng, and X. F. Chen, “Cherenkov high-order harmonic generation by multistep cascading in chi((2)) nonlinear photonic crystal,” Appl. Phys. Lett. 100(22), 221103 (2012).
[Crossref]

Arie, A.

Y. Sheng, W. J. Wang, R. Shiloh, V. Roppo, Y. F. Kong, A. Arie, and W. Krolikowski, “Cerenkov third-harmonic generation in chi((2)) nonlinear photonic crystal,” Appl. Phys. Lett. 98(24), 241114 (2011).
[Crossref]

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]

Y. Sheng, A. Best, H. J. Butt, W. Krolikowski, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualization by Cerenkov-type second harmonic generation,” Opt. Express 18(16), 16539–16545 (2010).
[Crossref] [PubMed]

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]

Best, A.

Butt, H. J.

Chen, C. D.

C. D. Chen, X. P. Hu, Y. L. Xu, P. Xu, G. Zhao, and S. N. Zhu, “Čerenkov difference frequency generation in a two-dimensional nonlinear photonic crystal,” Appl. Phys. Lett. 101, 071113 (2012).

Chen, X.

Chen, X. F.

H. J. Ren, X. W. Deng, Y. L. Zheng, N. An, and X. F. Chen, “Surface phase-matched harmonic enhancement in a bulk anomalous dispersion medium,” Appl. Phys. Lett. 103(2), 021110 (2013).
[Crossref]

N. An, H. J. Ren, Y. L. Zheng, X. W. Deng, and X. F. Chen, “Cherenkov high-order harmonic generation by multistep cascading in chi((2)) nonlinear photonic crystal,” Appl. Phys. Lett. 100(22), 221103 (2012).
[Crossref]

Cherenkov, P. A.

P. A. Cherenkov, “Visible emission of clean liquids by action of γ radiation,” Dokl. Akad. Nauk SSSR 2, 451–454 (1934).

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]

H. Ren, X. Deng, Y. Zheng, and X. Chen, “Single Domain Wall Effect on Parametric Processes via Cherenkov-Type Phase Matching,” J. Nonlinear Opt. Phys. Mater. 20(04), 459–466 (2011).
[Crossref]

X. Deng, H. Ren, H. Lao, and X. Chen, “Research on Cherenkov second harmonic generation in periodically poled lithium niobate by femtosecond pulses,” J. Opt. Soc. Am. B 27(7), 1475–1480 (2010).
[Crossref]

Deng, X. W.

H. J. Ren, X. W. Deng, Y. L. Zheng, N. An, and X. F. Chen, “Surface phase-matched harmonic enhancement in a bulk anomalous dispersion medium,” Appl. Phys. Lett. 103(2), 021110 (2013).
[Crossref]

N. An, H. J. Ren, Y. L. Zheng, X. W. Deng, and X. F. Chen, “Cherenkov high-order harmonic generation by multistep cascading in chi((2)) nonlinear photonic crystal,” Appl. Phys. Lett. 100(22), 221103 (2012).
[Crossref]

Fragemann, A.

A. Fragemann, V. Pasiskevicius, and F. Laurell, “Second-order nonlinearities in the domain walls of periodically poled KTiOPO4,” Appl. Phys. Lett. 85(3), 375–377 (2004).
[Crossref]

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]

Hu, X. P.

C. D. Chen, X. P. Hu, Y. L. Xu, P. Xu, G. Zhao, and S. N. Zhu, “Čerenkov difference frequency generation in a two-dimensional nonlinear photonic crystal,” Appl. Phys. Lett. 101, 071113 (2012).

Ikonnikov, A. A.

A. S. Aleksandrovsky, A. M. Vyunishev, A. I. Zaitsev, A. A. Ikonnikov, and G. I. Pospelov, “Ultrashort pulses characterization by nonlinear diffraction from virtual beam,” Appl. Phys. Lett. 98(6), 061104 (2011).
[Crossref]

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]

Kong, Y. F.

Y. Sheng, W. J. Wang, R. Shiloh, V. Roppo, Y. F. Kong, A. Arie, and W. Krolikowski, “Cerenkov third-harmonic generation in chi((2)) nonlinear photonic crystal,” Appl. Phys. Lett. 98(24), 241114 (2011).
[Crossref]

Koynov, K.

Krolikowski, W.

Lao, H.

Laurell, F.

A. Fragemann, V. Pasiskevicius, and F. Laurell, “Second-order nonlinearities in the domain walls of periodically poled KTiOPO4,” Appl. Phys. Lett. 85(3), 375–377 (2004).
[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]

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]

Pasiskevicius, V.

A. Fragemann, V. Pasiskevicius, and F. Laurell, “Second-order nonlinearities in the domain walls of periodically poled KTiOPO4,” Appl. Phys. Lett. 85(3), 375–377 (2004).
[Crossref]

Pospelov, G. I.

A. S. Aleksandrovsky, A. M. Vyunishev, A. I. Zaitsev, A. A. Ikonnikov, and G. I. Pospelov, “Ultrashort pulses characterization by nonlinear diffraction from virtual beam,” Appl. Phys. Lett. 98(6), 061104 (2011).
[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]

Ren, H.

Ren, H. J.

H. J. Ren, X. W. Deng, Y. L. Zheng, N. An, and X. F. Chen, “Surface phase-matched harmonic enhancement in a bulk anomalous dispersion medium,” Appl. Phys. Lett. 103(2), 021110 (2013).
[Crossref]

N. An, H. J. Ren, Y. L. Zheng, X. W. Deng, and X. F. Chen, “Cherenkov high-order harmonic generation by multistep cascading in chi((2)) nonlinear photonic crystal,” Appl. Phys. Lett. 100(22), 221103 (2012).
[Crossref]

Roppo, V.

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]

Sheng, Y.

Shiloh, R.

Y. Sheng, W. J. Wang, R. Shiloh, V. Roppo, Y. F. Kong, A. Arie, and W. Krolikowski, “Cerenkov third-harmonic generation in chi((2)) nonlinear photonic crystal,” Appl. Phys. Lett. 98(24), 241114 (2011).
[Crossref]

Trull, J.

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]

Vyunishev, A. M.

A. S. Aleksandrovsky, A. M. Vyunishev, A. I. Zaitsev, A. A. Ikonnikov, and G. I. Pospelov, “Ultrashort pulses characterization by nonlinear diffraction from virtual beam,” Appl. Phys. Lett. 98(6), 061104 (2011).
[Crossref]

Wang, W. J.

Y. Sheng, W. J. Wang, R. Shiloh, V. Roppo, Y. F. Kong, A. Arie, and W. Krolikowski, “Cerenkov third-harmonic generation in chi((2)) nonlinear photonic crystal,” Appl. Phys. Lett. 98(24), 241114 (2011).
[Crossref]

Wang, X.

Xu, P.

C. D. Chen, X. P. Hu, Y. L. Xu, P. Xu, G. Zhao, and S. N. Zhu, “Čerenkov difference frequency generation in a two-dimensional nonlinear photonic crystal,” Appl. Phys. Lett. 101, 071113 (2012).

Xu, Y. L.

C. D. Chen, X. P. Hu, Y. L. Xu, P. Xu, G. Zhao, and S. N. Zhu, “Čerenkov difference frequency generation in a two-dimensional nonlinear photonic crystal,” Appl. Phys. Lett. 101, 071113 (2012).

Zaitsev, A. I.

A. S. Aleksandrovsky, A. M. Vyunishev, A. I. Zaitsev, A. A. Ikonnikov, and G. I. Pospelov, “Ultrashort pulses characterization by nonlinear diffraction from virtual beam,” Appl. Phys. Lett. 98(6), 061104 (2011).
[Crossref]

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.

C. D. Chen, X. P. Hu, Y. L. Xu, P. Xu, G. Zhao, and S. N. Zhu, “Čerenkov difference frequency generation in a two-dimensional nonlinear photonic crystal,” Appl. Phys. Lett. 101, 071113 (2012).

Zhao, X.

Zheng, Y.

X. Wang, H. Ren, N. An, X. Zhao, Y. Zheng, and X. Chen, “Large acceptance of non-collinear phase-matching second harmonic generation on the surface of an anomalous-like bulk dispersion medium,” Opt. Express 22(23), 28234–28239 (2014).
[Crossref] [PubMed]

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]

H. Ren, X. Deng, Y. Zheng, and X. Chen, “Single Domain Wall Effect on Parametric Processes via Cherenkov-Type Phase Matching,” J. Nonlinear Opt. Phys. Mater. 20(04), 459–466 (2011).
[Crossref]

Zheng, Y. L.

H. J. Ren, X. W. Deng, Y. L. Zheng, N. An, and X. F. Chen, “Surface phase-matched harmonic enhancement in a bulk anomalous dispersion medium,” Appl. Phys. Lett. 103(2), 021110 (2013).
[Crossref]

N. An, H. J. Ren, Y. L. Zheng, X. W. Deng, and X. F. Chen, “Cherenkov high-order harmonic generation by multistep cascading in chi((2)) nonlinear photonic crystal,” Appl. Phys. Lett. 100(22), 221103 (2012).
[Crossref]

Zhu, S. N.

C. D. Chen, X. P. Hu, Y. L. Xu, P. Xu, G. Zhao, and S. N. Zhu, “Čerenkov difference frequency generation in a two-dimensional nonlinear photonic crystal,” Appl. Phys. Lett. 101, 071113 (2012).

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]

Appl. Phys. Lett. (6)

A. S. Aleksandrovsky, A. M. Vyunishev, A. I. Zaitsev, A. A. Ikonnikov, and G. I. Pospelov, “Ultrashort pulses characterization by nonlinear diffraction from virtual beam,” Appl. Phys. Lett. 98(6), 061104 (2011).
[Crossref]

Y. Sheng, W. J. Wang, R. Shiloh, V. Roppo, Y. F. Kong, A. Arie, and W. Krolikowski, “Cerenkov third-harmonic generation in chi((2)) nonlinear photonic crystal,” Appl. Phys. Lett. 98(24), 241114 (2011).
[Crossref]

N. An, H. J. Ren, Y. L. Zheng, X. W. Deng, and X. F. Chen, “Cherenkov high-order harmonic generation by multistep cascading in chi((2)) nonlinear photonic crystal,” Appl. Phys. Lett. 100(22), 221103 (2012).
[Crossref]

C. D. Chen, X. P. Hu, Y. L. Xu, P. Xu, G. Zhao, and S. N. Zhu, “Čerenkov difference frequency generation in a two-dimensional nonlinear photonic crystal,” Appl. Phys. Lett. 101, 071113 (2012).

H. J. Ren, X. W. Deng, Y. L. Zheng, N. An, and X. F. Chen, “Surface phase-matched harmonic enhancement in a bulk anomalous dispersion medium,” Appl. Phys. Lett. 103(2), 021110 (2013).
[Crossref]

A. Fragemann, V. Pasiskevicius, and F. Laurell, “Second-order nonlinearities in the domain walls of periodically poled KTiOPO4,” Appl. Phys. Lett. 85(3), 375–377 (2004).
[Crossref]

Dokl. Akad. Nauk SSSR (1)

P. A. Cherenkov, “Visible emission of clean liquids by action of γ radiation,” Dokl. Akad. Nauk SSSR 2, 451–454 (1934).

J. Nonlinear Opt. Phys. Mater. (1)

H. Ren, X. Deng, Y. Zheng, and X. Chen, “Single Domain Wall Effect on Parametric Processes via Cherenkov-Type Phase Matching,” J. Nonlinear Opt. Phys. Mater. 20(04), 459–466 (2011).
[Crossref]

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

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. Lett. (3)

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, 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]

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]

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Figures (4)

Fig. 1
Fig. 1 (a) Schematic of the experimental setup. (b)-(c) Photographs of NCR with different incident angles.
Fig. 2
Fig. 2 (a) Through internal reflection on the crystal boundary, NCR can be generated by sum-frequency polarization waves. (b) Phase-matching geometries of generation of NCR 650nm with the fundamental wave 1300nm. (c) Phase-matching geometries of NCR 400nm generated by the fundamental wave 800nm. (d) Phase-matching geometries of NCR 495nm generated by the fundamental wave 1300nm and 800nm.
Fig. 3
Fig. 3 (a) Theoretical calculation curve and experimental measured data of three emergence angles of NCR with the wavelength of 400nm, 495nm and 650nm. (b) The photographs of the collinear phase-mismatched SHG and sum-frequency wave with the o-polarized fundamental wave incident at four different angles (7.5°, 10°, 12.5°, 15°).
Fig. 4
Fig. 4 Theoretical calculation of criterion for cut-off angle with different fundamental waves under the oo-e type phase-matching condition.

Equations (12)

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P 1 N L = 4 ε 0 d e f f E 1 2 e i [ ( k 1 + k 1 ' ) r 2 ω 1 t ]
P 2 N L = 4 ε 0 d e f f E 2 2 e i [ ( k 2 + k 2 ' ) r 2 ω 2 t ]
P 3 N L = 4 ε 0 d e f f E 1 E 2 e i [ ( k 1 + k 2 ' ) r ( ω 1 + ω 2 ) t ]
P 3 N L = 4 ε 0 d e f f E 1 E 2 e i [ k p 3 r cos γ ( ω 1 + ω 2 ) t ]
n 1300 e ( π / 2 θ ) cos θ = n 650 e ( π / 2 α 1 ) cos α 1
n 800 e ( π / 2 θ ) cos θ = n 400 e ( π / 2 α 2 ) cos α 2
ω 1 n 1300 e ( π / 2 θ ) cos θ + ω 2 n 800 e ( π / 2 θ ) = ( ω 1 + ω 2 ) n 495 e ( π / 2 α 3 ) cos α 3
n 650 o n 650 e n 650 o 2 + n 650 e 2 tan 2 α 1 = n 1300 o n 1300 e n 1300 o 2 + n 1300 e 2 tan 2 θ
n 400 o n 400 e n 400 o 2 + n 400 e 2 tan 2 α 2 = n 800 o n 800 e n 800 o 2 + n 800 e 2 tan 2 θ
( ω 1 + ω 2 ) n 495 o n 495 e n 495 o 2 + n 495 e 2 tan 2 α 3 = ω 1 n 1300 o n 1300 e n 1300 o 2 + n 1300 e 2 tan 2 θ + ω 2 n 800 o n 800 e n 800 o 2 + n 800 e 2 tan 2 θ
ee e ω 1 n 1 e + ω 2 n 2 e < ( ω 1 + ω 2 ) n 3 e
oo e ω 1 n 1 o + ω 2 n 2 o < ( ω 1 + ω 2 ) n 3 e

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