Abstract

We study the configuration of efficient nonlinear Cherenkov radiation generated at the inner surface of a one-dimensional nonlinear photonic crystal, which utilizes the combination of both quasi-phase matching and total internal reflection by the crystal surface. Multi-directional nonlinear Cherenkov radiation assisted by different orders of reciprocal vectors is demonstrated experimentally. At specific angles, by associating with quasi-phase matching, the incident fundamental wave and total internal reflection wave format completely the phase-matching scheme, leading to great enhancement of harmonic wave intensity.

© 2017 Optical Society of America

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  1. A. Zembrod, H. Puell, and J. Giordmaine, “Surface radiation from non-linear optical polarisation,” Opt. Quant. Electron. 1, 64–66 (1969).
    [Crossref]
  2. 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]
  3. 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, 447–450 (1970).
    [Crossref]
  4. 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, 1384–1393 (1990).
    [Crossref]
  5. 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).
  6. L. Mateos, P. Molina, J. Galisteo, C. López, L. E. Bausá, and M. O. Ramírez, “Simultaneous generation of second to fifth harmonic conical beams in a two dimensional nonlinear photonic crystal,” Opt. Express 20, 29940–29948 (2012).
    [Crossref]
  7. 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, 1227–1229 (2011).
    [Crossref] [PubMed]
  8. Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in χ(2) nonlinear photonic crystal,” Appl. Phys. Lett. 98, 241114 (2011).
    [Crossref]
  9. 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]
  10. P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
    [Crossref] [PubMed]
  11. 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, 1475–1480 (2010).
    [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, 16539–16545 (2010).
    [Crossref] [PubMed]
  13. Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Nonlinear Talbot Effect,” Phys. Rev. Lett. 104, 183901 (2010).
    [Crossref] [PubMed]
  14. 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, 3864–3866 (2012).
    [Crossref] [PubMed]
  15. X. Zhao, Y. Zheng, H. Ren, N. An, X. Deng, and X. Chen, “Nonlinear Cherenkov radiation at the interface of two different nonlinear media,” Opt. Express 24, 12825–12830 (2016).
    [Crossref] [PubMed]
  16. 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]
  17. H. Ren, X. Deng, Y. Zheng, N. An, and X. Chen, “Enhanced nonlinear Cherenkov radiation on the crystal boundary,” Opt. Lett. 38, 1993–1995 (2013).
    [Crossref] [PubMed]
  18. V. Roppo, K. Kalinowski, W. Krolikowski, K. Wieslaw, C. Cojocaru, and J. Trull, “Unified approach to Čerenkov second harmonic generation,” Opt. Express 21, 25715–25726 (2013).
    [Crossref] [PubMed]
  19. O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91, 343–348 (2008).
    [Crossref]
  20. 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]
  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, 312–318 (2012).
    [Crossref]

2016 (1)

2013 (3)

2012 (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]

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).

L. Mateos, P. Molina, J. Galisteo, C. López, L. E. Bausá, and M. O. Ramírez, “Simultaneous generation of second to fifth harmonic conical beams in a two dimensional nonlinear photonic crystal,” Opt. Express 20, 29940–29948 (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]

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, 312–318 (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, 3864–3866 (2012).
[Crossref] [PubMed]

2011 (2)

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, 1227–1229 (2011).
[Crossref] [PubMed]

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

2010 (3)

2008 (2)

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91, 343–348 (2008).
[Crossref]

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]

2001 (1)

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref] [PubMed]

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, 1384–1393 (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, 447–450 (1970).
[Crossref]

1969 (1)

A. Zembrod, H. Puell, and J. Giordmaine, “Surface radiation from non-linear optical polarisation,” Opt. Quant. Electron. 1, 64–66 (1969).
[Crossref]

Agostini, P.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref] [PubMed]

An, N.

X. Zhao, Y. Zheng, H. Ren, N. An, X. Deng, and X. Chen, “Nonlinear Cherenkov radiation at the interface of two different nonlinear media,” Opt. Express 24, 12825–12830 (2016).
[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, “Enhanced nonlinear Cherenkov radiation on the crystal boundary,” Opt. Lett. 38, 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, 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 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]

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91, 343–348 (2008).
[Crossref]

Auge, F.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref] [PubMed]

Balcou, P.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref] [PubMed]

Bausá, L. E.

Best, A.

Breger, P.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref] [PubMed]

Butt, H.-J.

Chen, C.

Chen, X.

X. Zhao, Y. Zheng, H. Ren, N. An, X. Deng, and X. Chen, “Nonlinear Cherenkov radiation at the interface of two different nonlinear media,” Opt. Express 24, 12825–12830 (2016).
[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, “Enhanced nonlinear Cherenkov radiation on the crystal boundary,” Opt. Lett. 38, 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, 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]

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, 1475–1480 (2010).
[Crossref]

Cojocaru, C.

Deng, X.

X. Zhao, Y. Zheng, H. Ren, N. An, X. Deng, and X. Chen, “Nonlinear Cherenkov radiation at the interface of two different nonlinear media,” Opt. Express 24, 12825–12830 (2016).
[Crossref] [PubMed]

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

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, 1475–1480 (2010).
[Crossref]

Galisteo, J.

Galun, E.

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91, 343–348 (2008).
[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]

Gayer, O.

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91, 343–348 (2008).
[Crossref]

Giordmaine, J.

A. Zembrod, H. Puell, and J. Giordmaine, “Surface radiation from non-linear optical polarisation,” Opt. Quant. Electron. 1, 64–66 (1969).
[Crossref]

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, 1384–1393 (1990).
[Crossref]

Hong, X.

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).

Hu, X.

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).

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).

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).

Kalinowski, K.

Kong, Q.

Kong, Y.

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

Koynov, K.

Krolikowski, W.

Lao, H.

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, 1384–1393 (1990).
[Crossref]

Liu, Y.

López, C.

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).

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, 1227–1229 (2011).
[Crossref] [PubMed]

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, 447–450 (1970).
[Crossref]

Mateos, L.

Micheli, M. De

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, 1384–1393 (1990).
[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]

Molina, P.

Muller, H. G.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref] [PubMed]

Mullot, G.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref] [PubMed]

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, 1384–1393 (1990).
[Crossref]

Paul, P. M.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref] [PubMed]

Puell, H.

A. Zembrod, H. Puell, and J. Giordmaine, “Surface radiation from non-linear optical polarisation,” Opt. Quant. Electron. 1, 64–66 (1969).
[Crossref]

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]

Ramírez, M. O.

Ren, H.

X. Zhao, Y. Zheng, H. Ren, N. An, X. Deng, and X. Chen, “Nonlinear Cherenkov radiation at the interface of two different nonlinear media,” Opt. Express 24, 12825–12830 (2016).
[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, “Enhanced nonlinear Cherenkov radiation on the crystal boundary,” Opt. Lett. 38, 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, 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]

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, 1475–1480 (2010).
[Crossref]

Roppo, V.

Sacks, Z.

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91, 343–348 (2008).
[Crossref]

Sheng, Y.

Shiloh, R.

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in χ(2) nonlinear photonic crystal,” Appl. Phys. Lett. 98, 241114 (2011).
[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, 447–450 (1970).
[Crossref]

Toma, E. S.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref] [PubMed]

Trull, J.

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, 447–450 (1970).
[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).

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, 312–318 (2012).
[Crossref]

Wang, W.

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

Wen, J.

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

Wieslaw, K.

Xiao, M.

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

Yuan, Y.

Zembrod, A.

A. Zembrod, H. Puell, and J. Giordmaine, “Surface radiation from non-linear optical polarisation,” Opt. Quant. Electron. 1, 64–66 (1969).
[Crossref]

Zhang, 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).

Zhang, Y.

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, 1227–1229 (2011).
[Crossref] [PubMed]

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

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[Crossref]

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[Crossref] [PubMed]

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[Crossref] [PubMed]

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Figures (4)

Fig. 1
Fig. 1 (a) The diagram of experimental setup; (b) Multiple nonlinear Cherenkov diffraction pattern recorded in the experiment.
Fig. 2
Fig. 2 (a) Simulation result of SH distribution with a FW incident angle of α = 20°; (b) Phase-matching geometry.
Fig. 3
Fig. 3 The external angles along z-axis of different order NCRs versus the incident wavelength of FW (a) and external incident angle (b). The relationship of external angles along x-axis of 1-order NCR varying with the incident wavelength (c) and the poling period of PPLN (d). Theoretical prediction (solid curves) and experimental results (signs) are in well agreement with each other.
Fig. 4
Fig. 4 (a) Recorded pattern of enhanced 0-order NCR. (b) The external FW angles of enhanced 0-order NCR versus the incident wavelength of FW.

Equations (4)

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I 2 ( k x , k z ) = [ k 2 2 n 2 2 χ ( 2 ) ] 2 I 1 2 L 2 sinc 2 [ ( k 2 2 k 1 cos α k x 2 + k z 2 2 k 2 ) L 2 ] | F ( k x ) | 2 | G ( k z ) | 2 ,
g n = { 2 sin ( n π d ) / ( n π ) n 0 2 d 1 n = 0 ,
φ n = arctan n G 0 2 k 1 cos α ,
θ n arccos ( n G 0 ) 2 + ( 2 k 1 cos α ) 2 k 2 .

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