Abstract

We discuss the nonlinear response due to the spatial modulation of the second-order susceptibility at the interface between two nonlinear media, and experimentally demonstrate that the nonlinear Cherenkov radiation is enhanced by the interface of two nonlinear crystals with a large disparity in χ(2). In our experiment, the intensity of the nonlinear Cherenkov radiation generated at the nonlinear interface was approximately 4 to 10 times that at the crystal boundary. This result suggests potential applications to efficient frequency conversion.

© 2016 Optical Society of America

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References

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  1. A. Zembrod, H. Puell, and J. Giordmaine, “Surface radiation from non-linear optical polarisation,” Opt. Quantum Electron. 1, 64 (1969).
  2. H. Ren, X. Deng, Y. Zheng, N. An, and X. Chen, “Nonlinear Cherenkov radiation in an anomalous dispersive medium,” Phys. Rev. Lett. 108, 223901 (2012).
    [Crossref] [PubMed]
  3. Y. Zhang, Z. Gao, Z. Qi, S. Zhu, and N. Ming, “Nonlinear Čerenkov radiation in nonlinear photonic crystal waveguides,” Phys. Rev. Lett. 100, 163904 (2008).
    [Crossref]
  4. C. Chen, J. Lu, Y. Liu, X. Hu, L. Zhao, Y. Zhang, G. Zhao, Y. Yuan, and S. Zhu, “Cerenkov third-harmonic generation via cascaded χ(2) processes in a periodic-poled LiTaO3 waveguide,” Opt. Lett. 36, 1227 (2011).
    [Crossref] [PubMed]
  5. Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in 2 nonlinear photonic crystal,” Appl. Phys. Lett. 98, 241114 (2011).
    [Crossref]
  6. N. An, H. Ren, Y. Zheng, X. Deng, and X. Chen, “Cherenkov high-order harmonic generation by multistep cascading in χ(2) nonlinear photonic crystal,” Appl. Phys. Lett. 100, 221103 (2012).
    [Crossref]
  7. N. An, Y. Zheng, H. Ren, X. Zhao, X. Deng, and X. Chen, “Normal, degenerated, and anomalous-dispersion-like Cerenkov sum-frequency generation in one nonlinear medium,” Photonics Res. 3, 106 (2015).
    [Crossref]
  8. C. Chen, X. Hu, Y. Xu, P. Xu, G. Zhao, and S. Zhu, “Čerenkov difference frequency generation in a two-dimensional nonlinear photonic crystal,” Appl. Phys. Lett. 101, 071113 (2012).
    [Crossref]
  9. H. Ren, X. Deng, Y. Zheng, N. An, and X. Chen, “Surface phase-matched harmonic enhancement in a bulk anomalous dispersion medium,” Appl. Phys. Lett. 103, 021110 (2013).
    [Crossref]
  10. W. Shi, Y. J. Ding, N. Fernelius, and K. Vodopyanov, “Efficient, tunable, and coherent 0.18–5.27-THz source based on GaSe crystal,” Opt. Lett. 27, 1454 (2002).
    [Crossref]
  11. A. Aleksandrovsky, A. Vyunishev, A. Zaitsev, A. Ikonnikov, and G. Pospelov, “Ultrashort pulses characterization by nonlinear diffraction from virtual beam,” Appl. Phys. Lett. 98, 061104 (2011).
    [Crossref]
  12. 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 (2010).
    [Crossref] [PubMed]
  13. X. Zhao, Y. Zheng, H. Ren, N. An, and X. Chen, “Cherenkov second-harmonic Talbot effect in one-dimension nonlinear photonic crystal,” Opt. Lett. 39, 5885 (2014).
    [Crossref] [PubMed]
  14. S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Cerenkov-type second-harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum Electron. 45, 1465 (2009).
    [Crossref]
  15. M. Ayoub, P. Roedig, J. Imbrock, and C. Denz, “Cascaded Čerenkov third-harmonic generation in random quadratic media,” Appl. Phys. Lett. 99, 241109 (2011).
    [Crossref]
  16. P. Tien, R. Ulrich, and R. Martin, “optical second harmonic generation in form of coherent cerenkov radiation from a thin-film waveguide,” Appl. Phys. Lett. 17, 447 (1970).
    [Crossref]
  17. M.-J. Li, M. De Micheli, Q. He, and D. Ostrowsky, “Cerenkov configuration second harmonic generation in proton-exchanged lithium niobate guides,” IEEE. J. Quantum Electron. 26, 1384 (1990).
    [Crossref]
  18. 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, 3864 (2012).
    [Crossref] [PubMed]
  19. H. Ren, X. Deng, Y. Zheng, N. An, and X. Chen, “Enhanced nonlinear Cherenkov radiation on the crystal boundary,” Opt. Lett. 38, 1993 (2013).
    [Crossref] [PubMed]
  20. R. W. Boyd, Nonlinear Optics (Academic, 2003).
  21. Y. Sheng, Q. Kong, V. Roppo, K. Kalinowski, Q. Wang, C. Cojocaru, and W. Krolikowski, “Theoretical study of Čerenkov-type second-harmonic generation in periodically poled ferroelectric crystals,” J Opt. Soc. Am. B 29, 312 (2012).
    [Crossref]
  22. A. Sugiyama, H. Fukuyama, T. Sasuga, T. Arisawa, and H. Takuma, “Direct bonding of Ti: sapphire laser crystals,” Appl. Opt. 37, 12 (1998).
    [Crossref]

2015 (1)

N. An, Y. Zheng, H. Ren, X. Zhao, X. Deng, and X. Chen, “Normal, degenerated, and anomalous-dispersion-like Cerenkov sum-frequency generation in one nonlinear medium,” Photonics Res. 3, 106 (2015).
[Crossref]

2014 (1)

2013 (2)

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

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

2012 (5)

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

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

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

Y. Sheng, Q. Kong, V. Roppo, K. Kalinowski, Q. Wang, C. Cojocaru, and W. Krolikowski, “Theoretical study of Čerenkov-type second-harmonic generation in periodically poled ferroelectric crystals,” J Opt. Soc. Am. B 29, 312 (2012).
[Crossref]

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, 3864 (2012).
[Crossref] [PubMed]

2011 (4)

C. Chen, J. Lu, Y. Liu, X. Hu, L. Zhao, Y. Zhang, G. Zhao, Y. Yuan, and S. Zhu, “Cerenkov third-harmonic generation via cascaded χ(2) processes in a periodic-poled LiTaO3 waveguide,” Opt. Lett. 36, 1227 (2011).
[Crossref] [PubMed]

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

M. Ayoub, P. Roedig, J. Imbrock, and C. Denz, “Cascaded Čerenkov third-harmonic generation in random quadratic media,” Appl. Phys. Lett. 99, 241109 (2011).
[Crossref]

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

2010 (1)

2009 (1)

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Cerenkov-type second-harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum Electron. 45, 1465 (2009).
[Crossref]

2008 (1)

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

2002 (1)

1998 (1)

A. Sugiyama, H. Fukuyama, T. Sasuga, T. Arisawa, and H. Takuma, “Direct bonding of Ti: sapphire laser crystals,” Appl. Opt. 37, 12 (1998).
[Crossref]

1990 (1)

M.-J. Li, M. De Micheli, Q. He, and D. Ostrowsky, “Cerenkov configuration second harmonic generation in proton-exchanged lithium niobate guides,” IEEE. J. Quantum Electron. 26, 1384 (1990).
[Crossref]

1970 (1)

P. Tien, R. Ulrich, and R. Martin, “optical second harmonic generation in form of coherent cerenkov radiation from a thin-film waveguide,” Appl. Phys. Lett. 17, 447 (1970).
[Crossref]

1969 (1)

A. Zembrod, H. Puell, and J. Giordmaine, “Surface radiation from non-linear optical polarisation,” Opt. Quantum Electron. 1, 64 (1969).

Aleksandrovsky, A.

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

An, N.

N. An, Y. Zheng, H. Ren, X. Zhao, X. Deng, and X. Chen, “Normal, degenerated, and anomalous-dispersion-like Cerenkov sum-frequency generation in one nonlinear medium,” Photonics Res. 3, 106 (2015).
[Crossref]

X. Zhao, Y. Zheng, H. Ren, N. An, and X. Chen, “Cherenkov second-harmonic Talbot effect in one-dimension nonlinear photonic crystal,” Opt. Lett. 39, 5885 (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, 1993 (2013).
[Crossref] [PubMed]

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

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

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

Arie, A.

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in 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 (2010).
[Crossref] [PubMed]

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Cerenkov-type second-harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum Electron. 45, 1465 (2009).
[Crossref]

Arisawa, T.

A. Sugiyama, H. Fukuyama, T. Sasuga, T. Arisawa, and H. Takuma, “Direct bonding of Ti: sapphire laser crystals,” Appl. Opt. 37, 12 (1998).
[Crossref]

Ayoub, M.

M. Ayoub, P. Roedig, J. Imbrock, and C. Denz, “Cascaded Čerenkov third-harmonic generation in random quadratic media,” Appl. Phys. Lett. 99, 241109 (2011).
[Crossref]

Best, A.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 2003).

Butt, H.-J.

Chen, C.

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

C. Chen, J. Lu, Y. Liu, X. Hu, L. Zhao, Y. Zhang, G. Zhao, Y. Yuan, and S. Zhu, “Cerenkov third-harmonic generation via cascaded χ(2) processes in a periodic-poled LiTaO3 waveguide,” Opt. Lett. 36, 1227 (2011).
[Crossref] [PubMed]

Chen, X.

N. An, Y. Zheng, H. Ren, X. Zhao, X. Deng, and X. Chen, “Normal, degenerated, and anomalous-dispersion-like Cerenkov sum-frequency generation in one nonlinear medium,” Photonics Res. 3, 106 (2015).
[Crossref]

X. Zhao, Y. Zheng, H. Ren, N. An, and X. Chen, “Cherenkov second-harmonic Talbot effect in one-dimension nonlinear photonic crystal,” Opt. Lett. 39, 5885 (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, 1993 (2013).
[Crossref] [PubMed]

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

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

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

Cojocaru, C.

Y. Sheng, Q. Kong, V. Roppo, K. Kalinowski, Q. Wang, C. Cojocaru, and W. Krolikowski, “Theoretical study of Čerenkov-type second-harmonic generation in periodically poled ferroelectric crystals,” J Opt. Soc. Am. B 29, 312 (2012).
[Crossref]

De Micheli, M.

M.-J. Li, M. De Micheli, Q. He, and D. Ostrowsky, “Cerenkov configuration second harmonic generation in proton-exchanged lithium niobate guides,” IEEE. J. Quantum Electron. 26, 1384 (1990).
[Crossref]

Deng, X.

N. An, Y. Zheng, H. Ren, X. Zhao, X. Deng, and X. Chen, “Normal, degenerated, and anomalous-dispersion-like Cerenkov sum-frequency generation in one nonlinear medium,” Photonics Res. 3, 106 (2015).
[Crossref]

H. Ren, X. Deng, Y. Zheng, N. An, and X. Chen, “Surface phase-matched harmonic enhancement in a bulk anomalous dispersion medium,” Appl. Phys. Lett. 103, 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, 1993 (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, 223901 (2012).
[Crossref] [PubMed]

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

Denz, C.

M. Ayoub, P. Roedig, J. Imbrock, and C. Denz, “Cascaded Čerenkov third-harmonic generation in random quadratic media,” Appl. Phys. Lett. 99, 241109 (2011).
[Crossref]

Ding, Y. J.

Fernelius, N.

Fukuyama, H.

A. Sugiyama, H. Fukuyama, T. Sasuga, T. Arisawa, and H. Takuma, “Direct bonding of Ti: sapphire laser crystals,” Appl. Opt. 37, 12 (1998).
[Crossref]

Gao, Z.

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

Giordmaine, J.

A. Zembrod, H. Puell, and J. Giordmaine, “Surface radiation from non-linear optical polarisation,” Opt. Quantum Electron. 1, 64 (1969).

He, Q.

M.-J. Li, M. De Micheli, Q. He, and D. Ostrowsky, “Cerenkov configuration second harmonic generation in proton-exchanged lithium niobate guides,” IEEE. J. Quantum Electron. 26, 1384 (1990).
[Crossref]

Hu, X.

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

C. Chen, J. Lu, Y. Liu, X. Hu, L. Zhao, Y. Zhang, G. Zhao, Y. Yuan, and S. Zhu, “Cerenkov third-harmonic generation via cascaded χ(2) processes in a periodic-poled LiTaO3 waveguide,” Opt. Lett. 36, 1227 (2011).
[Crossref] [PubMed]

Ikonnikov, A.

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

Imbrock, J.

M. Ayoub, P. Roedig, J. Imbrock, and C. Denz, “Cascaded Čerenkov third-harmonic generation in random quadratic media,” Appl. Phys. Lett. 99, 241109 (2011).
[Crossref]

Kalinowski, K.

Y. Sheng, Q. Kong, V. Roppo, K. Kalinowski, Q. Wang, C. Cojocaru, and W. Krolikowski, “Theoretical study of Čerenkov-type second-harmonic generation in periodically poled ferroelectric crystals,” J Opt. Soc. Am. B 29, 312 (2012).
[Crossref]

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, 3864 (2012).
[Crossref] [PubMed]

Kivshar, Y. S.

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Cerenkov-type second-harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum Electron. 45, 1465 (2009).
[Crossref]

Kong, Q.

Y. Sheng, Q. Kong, V. Roppo, K. Kalinowski, Q. Wang, C. Cojocaru, and W. Krolikowski, “Theoretical study of Čerenkov-type second-harmonic generation in periodically poled ferroelectric crystals,” J Opt. Soc. Am. B 29, 312 (2012).
[Crossref]

Kong, Y.

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

Koynov, K.

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 (2010).
[Crossref] [PubMed]

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Cerenkov-type second-harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum Electron. 45, 1465 (2009).
[Crossref]

Krolikowski, W.

Y. Sheng, Q. Kong, V. Roppo, K. Kalinowski, Q. Wang, C. Cojocaru, and W. Krolikowski, “Theoretical study of Čerenkov-type second-harmonic generation in periodically poled ferroelectric crystals,” J Opt. Soc. Am. B 29, 312 (2012).
[Crossref]

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, 3864 (2012).
[Crossref] [PubMed]

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in 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 (2010).
[Crossref] [PubMed]

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Cerenkov-type second-harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum Electron. 45, 1465 (2009).
[Crossref]

Li, M.-J.

M.-J. Li, M. De Micheli, Q. He, and D. Ostrowsky, “Cerenkov configuration second harmonic generation in proton-exchanged lithium niobate guides,” IEEE. J. Quantum Electron. 26, 1384 (1990).
[Crossref]

Liu, Y.

Lu, J.

Martin, R.

P. Tien, R. Ulrich, and R. Martin, “optical second harmonic generation in form of coherent cerenkov radiation from a thin-film waveguide,” Appl. Phys. Lett. 17, 447 (1970).
[Crossref]

Ming, N.

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

Neshev, D. N.

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Cerenkov-type second-harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum Electron. 45, 1465 (2009).
[Crossref]

Ostrowsky, D.

M.-J. Li, M. De Micheli, Q. He, and D. Ostrowsky, “Cerenkov configuration second harmonic generation in proton-exchanged lithium niobate guides,” IEEE. J. Quantum Electron. 26, 1384 (1990).
[Crossref]

Pospelov, G.

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

Puell, H.

A. Zembrod, H. Puell, and J. Giordmaine, “Surface radiation from non-linear optical polarisation,” Opt. Quantum Electron. 1, 64 (1969).

Qi, Z.

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

Ren, H.

N. An, Y. Zheng, H. Ren, X. Zhao, X. Deng, and X. Chen, “Normal, degenerated, and anomalous-dispersion-like Cerenkov sum-frequency generation in one nonlinear medium,” Photonics Res. 3, 106 (2015).
[Crossref]

X. Zhao, Y. Zheng, H. Ren, N. An, and X. Chen, “Cherenkov second-harmonic Talbot effect in one-dimension nonlinear photonic crystal,” Opt. Lett. 39, 5885 (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, 1993 (2013).
[Crossref] [PubMed]

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

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

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

Roedig, P.

M. Ayoub, P. Roedig, J. Imbrock, and C. Denz, “Cascaded Čerenkov third-harmonic generation in random quadratic media,” Appl. Phys. Lett. 99, 241109 (2011).
[Crossref]

Roppo, V.

Y. Sheng, Q. Kong, V. Roppo, K. Kalinowski, Q. Wang, C. Cojocaru, and W. Krolikowski, “Theoretical study of Čerenkov-type second-harmonic generation in periodically poled ferroelectric crystals,” J Opt. Soc. Am. B 29, 312 (2012).
[Crossref]

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, 3864 (2012).
[Crossref] [PubMed]

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

Saltiel, S. M.

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Cerenkov-type second-harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum Electron. 45, 1465 (2009).
[Crossref]

Sasuga, T.

A. Sugiyama, H. Fukuyama, T. Sasuga, T. Arisawa, and H. Takuma, “Direct bonding of Ti: sapphire laser crystals,” Appl. Opt. 37, 12 (1998).
[Crossref]

Sheng, Y.

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, 3864 (2012).
[Crossref] [PubMed]

Y. Sheng, Q. Kong, V. Roppo, K. Kalinowski, Q. Wang, C. Cojocaru, and W. Krolikowski, “Theoretical study of Čerenkov-type second-harmonic generation in periodically poled ferroelectric crystals,” J Opt. Soc. Am. B 29, 312 (2012).
[Crossref]

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in 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 (2010).
[Crossref] [PubMed]

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Cerenkov-type second-harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum Electron. 45, 1465 (2009).
[Crossref]

Shi, W.

Shiloh, R.

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

Sugiyama, A.

A. Sugiyama, H. Fukuyama, T. Sasuga, T. Arisawa, and H. Takuma, “Direct bonding of Ti: sapphire laser crystals,” Appl. Opt. 37, 12 (1998).
[Crossref]

Takuma, H.

A. Sugiyama, H. Fukuyama, T. Sasuga, T. Arisawa, and H. Takuma, “Direct bonding of Ti: sapphire laser crystals,” Appl. Opt. 37, 12 (1998).
[Crossref]

Tien, P.

P. Tien, R. Ulrich, and R. Martin, “optical second harmonic generation in form of coherent cerenkov radiation from a thin-film waveguide,” Appl. Phys. Lett. 17, 447 (1970).
[Crossref]

Ulrich, R.

P. Tien, R. Ulrich, and R. Martin, “optical second harmonic generation in form of coherent cerenkov radiation from a thin-film waveguide,” Appl. Phys. Lett. 17, 447 (1970).
[Crossref]

Vodopyanov, K.

Voloch-Bloch, N.

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Cerenkov-type second-harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum Electron. 45, 1465 (2009).
[Crossref]

Vyunishev, A.

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

Wang, Q.

Y. Sheng, Q. Kong, V. Roppo, K. Kalinowski, Q. Wang, C. Cojocaru, and W. Krolikowski, “Theoretical study of Čerenkov-type second-harmonic generation in periodically poled ferroelectric crystals,” J Opt. Soc. Am. B 29, 312 (2012).
[Crossref]

Wang, W.

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

Xu, P.

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

Xu, Y.

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

Yuan, Y.

Zaitsev, A.

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

Zembrod, A.

A. Zembrod, H. Puell, and J. Giordmaine, “Surface radiation from non-linear optical polarisation,” Opt. Quantum Electron. 1, 64 (1969).

Zhang, Y.

Zhao, G.

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

C. Chen, J. Lu, Y. Liu, X. Hu, L. Zhao, Y. Zhang, G. Zhao, Y. Yuan, and S. Zhu, “Cerenkov third-harmonic generation via cascaded χ(2) processes in a periodic-poled LiTaO3 waveguide,” Opt. Lett. 36, 1227 (2011).
[Crossref] [PubMed]

Zhao, L.

Zhao, X.

N. An, Y. Zheng, H. Ren, X. Zhao, X. Deng, and X. Chen, “Normal, degenerated, and anomalous-dispersion-like Cerenkov sum-frequency generation in one nonlinear medium,” Photonics Res. 3, 106 (2015).
[Crossref]

X. Zhao, Y. Zheng, H. Ren, N. An, and X. Chen, “Cherenkov second-harmonic Talbot effect in one-dimension nonlinear photonic crystal,” Opt. Lett. 39, 5885 (2014).
[Crossref] [PubMed]

Zheng, Y.

N. An, Y. Zheng, H. Ren, X. Zhao, X. Deng, and X. Chen, “Normal, degenerated, and anomalous-dispersion-like Cerenkov sum-frequency generation in one nonlinear medium,” Photonics Res. 3, 106 (2015).
[Crossref]

X. Zhao, Y. Zheng, H. Ren, N. An, and X. Chen, “Cherenkov second-harmonic Talbot effect in one-dimension nonlinear photonic crystal,” Opt. Lett. 39, 5885 (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, 1993 (2013).
[Crossref] [PubMed]

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

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

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

Zhu, S.

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

C. Chen, J. Lu, Y. Liu, X. Hu, L. Zhao, Y. Zhang, G. Zhao, Y. Yuan, and S. Zhu, “Cerenkov third-harmonic generation via cascaded χ(2) processes in a periodic-poled LiTaO3 waveguide,” Opt. Lett. 36, 1227 (2011).
[Crossref] [PubMed]

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

Appl. Opt. (1)

A. Sugiyama, H. Fukuyama, T. Sasuga, T. Arisawa, and H. Takuma, “Direct bonding of Ti: sapphire laser crystals,” Appl. Opt. 37, 12 (1998).
[Crossref]

Appl. Phys. Lett. (7)

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

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

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

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

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

M. Ayoub, P. Roedig, J. Imbrock, and C. Denz, “Cascaded Čerenkov third-harmonic generation in random quadratic media,” Appl. Phys. Lett. 99, 241109 (2011).
[Crossref]

P. Tien, R. Ulrich, and R. Martin, “optical second harmonic generation in form of coherent cerenkov radiation from a thin-film waveguide,” Appl. Phys. Lett. 17, 447 (1970).
[Crossref]

IEEE J. Quantum Electron. (1)

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Cerenkov-type second-harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum Electron. 45, 1465 (2009).
[Crossref]

IEEE. J. Quantum Electron. (1)

M.-J. Li, M. De Micheli, Q. He, and D. Ostrowsky, “Cerenkov configuration second harmonic generation in proton-exchanged lithium niobate guides,” IEEE. J. Quantum Electron. 26, 1384 (1990).
[Crossref]

J Opt. Soc. Am. B (1)

Y. Sheng, Q. Kong, V. Roppo, K. Kalinowski, Q. Wang, C. Cojocaru, and W. Krolikowski, “Theoretical study of Čerenkov-type second-harmonic generation in periodically poled ferroelectric crystals,” J Opt. Soc. Am. B 29, 312 (2012).
[Crossref]

Opt. Express (1)

Opt. Lett. (5)

Opt. Quantum Electron. (1)

A. Zembrod, H. Puell, and J. Giordmaine, “Surface radiation from non-linear optical polarisation,” Opt. Quantum Electron. 1, 64 (1969).

Photonics Res. (1)

N. An, Y. Zheng, H. Ren, X. Zhao, X. Deng, and X. Chen, “Normal, degenerated, and anomalous-dispersion-like Cerenkov sum-frequency generation in one nonlinear medium,” Photonics Res. 3, 106 (2015).
[Crossref]

Phys. Rev. Lett. (2)

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

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

Other (1)

R. W. Boyd, Nonlinear Optics (Academic, 2003).

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Figures (4)

Fig. 1
Fig. 1 NCR Simulation at an interface. (a) Structure of a nonlinear medium. The y = 0 plane is the interface between media 1 and 2, which have different second nonlinear coefficients C1χ(2) and C2χ(2), respectively. The FW is incident along the x axis. (b), (c) and (d) are the simulation results under the conditions C1 = 1, C2 = 1; C1 = 1, C2 = 0; C1 = 1, C2 = 10, respectively.
Fig. 2
Fig. 2 Schematic experimental samples viewed from the top. (a) Sample 1: z-cut BBO and y-cut LN. (b) Sample 2: z-cut BBO and z-cut LN.
Fig. 3
Fig. 3 (a) Schematic experimental setup. (b) Internal NCR angle θ under normal dispersion versus FW incident angle α. Theoretical prediction (solid curve) and experimental results (symbols) are in good agreement. (c) Measured intensity and enhancement factor of SH generated at the BBO-LN interface and boundary of BBO crystal. (d), (f) and (h) are the recorded patterns with varying FW incident angle at the BBO-LN interface. (e), (g) and (i) are the recorded patterns of the FW incident on the BBO crystal boundary with the same angle as in (d), (f) and (h), respectively.
Fig. 4
Fig. 4 (a) The internal NCR angle θ under anomalous dispersion versus the incident angle of FW α. (b)–(e) are the recorded patterns varying with the incident angle of FW.

Equations (3)

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( x + i 2 k 2 2 y 2 ) A 2 ( x , y ) = i k 2 2 n 2 2 g ( y ) χ ( 2 ) ( A 1 e y 2 / a 2 ) 2 e i Δ k x ,
g ( y ) = { C 1 y 0 C 2 y < 0 .
I 2 ( x , k y ) = [ k 2 2 n 2 2 χ ( 2 ) ] I 1 2 x 2 sin c 2 [ ( Δ k k y / 2 k 2 ) x 2 ] | ( C 1 + C 2 ) π 8 a e a 2 k y 2 8 + i ( C 1 C 2 ) π 2 a D ( a k y 2 2 ) | 2 ,

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