Abstract

Nonlinear Cherenkov radiation plays an important role in detecting the internal structure of the ferroelectric crystal. However, linear Cherenkov radiation in the ferroelectric crystal was not observed before. Based on mirror symmetry reduction at the domain walls, we theoretically predicted that the linear Cherenkov radiation could be generated in periodically poled ferroelectric crystals according to the coupled wave equation. Then, we experimentally demonstrated the generation of such Cherenkov radiation in domain walls. Compared with the domain region, new nonzero elements χ13, χ23, χ31 and χ32 appear in the linear susceptibility tensor. The experimental results are consistent with our theoretical prediction.

© 2017 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 (1934).
  2. A. Zembrod, H. Puell, and J. Giordmaine, “Surface radiation from non-linear optical polarisation,” Opto-electronics 1(1), 64–66 (1969).
  3. 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).
    [PubMed]
  4. P. Molina, M. O. Ramírez, B. J. García, and L. E. Bausá, “Directional dependence of the second harmonic response in two-dimensional nonlinear photonic crystals,” Appl. Phys. Lett. 96(26), 261111 (2010).
  5. S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of secondharmonic bessel beams by transverse phase-matching in annular periodically poled structures,” Jpn. J. Appl. Phys. 47 (8S1), 6777– 6783 (2008).
  6. 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).
    [PubMed]
  7. 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).
  8. S. J. Holmgren, C. Canalias, and V. Pasiskevicius, “Ultrashort single-shot pulse characterization with high spatial resolution using localized nonlinearities in ferroelectric domain walls,” Opt. Lett. 32(11), 1545–1547 (2007).
    [PubMed]
  9. 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(16), 16539–16545 (2010).
    [PubMed]
  10. 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(7), 1227–1229 (2011).
    [PubMed]
  11. 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).
    [PubMed]
  12. 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(4), 106–109 (2015).
  13. 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).
  14. 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).
  15. G. Catalan, J. Seidel, R. Ramesh, and J. F. Scott, “Domain wall nanoelectronics,” Rev. Mod. Phys. 84(1), 119–156 (2012).
  16. 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).
  17. 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).
    [PubMed]
  18. B. Liu, Y. Zheng, X. Zhao, H. Liu, and X. Chen, “Probe of symmetry reduction at domain walls by nonlinear Cherenkov measurement,” Opt. Express 24(26), 29459–29464 (2016).
    [PubMed]
  19. X. Deng and X. Chen, “Domain wall characterization in ferroelectrics by using localized nonlinearities,” Opt. Express 18(15), 15597–15602 (2010).
    [PubMed]
  20. D. A. Scrymgeour, V. Gopalan, A. Itagi, A. Saxena, and P. J. Swart, “Phenomenological theory of a single domain wall in uniaxial trigonal ferroelectrics: Lithium niobate and lithium tantalate,” Phys. Rev. B 71(18), 184110 (2005).

2016 (1)

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(4), 106–109 (2015).

2013 (2)

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).

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).
[PubMed]

2012 (2)

G. Catalan, J. Seidel, R. Ramesh, and J. F. Scott, “Domain wall nanoelectronics,” Rev. Mod. Phys. 84(1), 119–156 (2012).

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).
[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(7), 1227–1229 (2011).
[PubMed]

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).

2010 (5)

2008 (2)

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of secondharmonic bessel beams by transverse phase-matching in annular periodically poled structures,” Jpn. J. Appl. Phys. 47 (8S1), 6777– 6783 (2008).

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).
[PubMed]

2007 (1)

2005 (1)

D. A. Scrymgeour, V. Gopalan, A. Itagi, A. Saxena, and P. J. Swart, “Phenomenological theory of a single domain wall in uniaxial trigonal ferroelectrics: Lithium niobate and lithium tantalate,” Phys. Rev. B 71(18), 184110 (2005).

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).

1969 (1)

A. Zembrod, H. Puell, and J. Giordmaine, “Surface radiation from non-linear optical polarisation,” Opto-electronics 1(1), 64–66 (1969).

1934 (1)

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

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(4), 106–109 (2015).

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).
[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).
[PubMed]

Arie, A.

Bausá, L. E.

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

Best, A.

Butt, H. J.

Canalias, C.

Catalan, G.

G. Catalan, J. Seidel, R. Ramesh, and J. F. Scott, “Domain wall nanoelectronics,” Rev. Mod. Phys. 84(1), 119–156 (2012).

Chen, C.

Chen, X.

Cherenkov, P. A.

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

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(4), 106–109 (2015).

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).
[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).
[PubMed]

X. Deng and X. Chen, “Domain wall characterization in ferroelectrics by using localized nonlinearities,” Opt. Express 18(15), 15597–15602 (2010).
[PubMed]

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).

Fischer, R.

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of secondharmonic bessel beams by transverse phase-matching in annular periodically poled structures,” Jpn. J. Appl. Phys. 47 (8S1), 6777– 6783 (2008).

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).

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).
[PubMed]

García, B. J.

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

Giordmaine, J.

A. Zembrod, H. Puell, and J. Giordmaine, “Surface radiation from non-linear optical polarisation,” Opto-electronics 1(1), 64–66 (1969).

Gopalan, V.

D. A. Scrymgeour, V. Gopalan, A. Itagi, A. Saxena, and P. J. Swart, “Phenomenological theory of a single domain wall in uniaxial trigonal ferroelectrics: Lithium niobate and lithium tantalate,” Phys. Rev. B 71(18), 184110 (2005).

Holmgren, S. J.

Hu, X.

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).

Itagi, A.

D. A. Scrymgeour, V. Gopalan, A. Itagi, A. Saxena, and P. J. Swart, “Phenomenological theory of a single domain wall in uniaxial trigonal ferroelectrics: Lithium niobate and lithium tantalate,” Phys. Rev. B 71(18), 184110 (2005).

Kivshar, Y. S.

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of secondharmonic bessel beams by transverse phase-matching in annular periodically poled structures,” Jpn. J. Appl. Phys. 47 (8S1), 6777– 6783 (2008).

Kong, Y.

Koynov, K.

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).

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).

Liu, B.

Liu, H.

Liu, Y.

Lu, J.

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).

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).
[PubMed]

Molina, P.

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

Neshev, D. N.

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of secondharmonic bessel beams by transverse phase-matching in annular periodically poled structures,” Jpn. J. Appl. Phys. 47 (8S1), 6777– 6783 (2008).

Pasiskevicius, V.

S. J. Holmgren, C. Canalias, and V. Pasiskevicius, “Ultrashort single-shot pulse characterization with high spatial resolution using localized nonlinearities in ferroelectric domain walls,” Opt. Lett. 32(11), 1545–1547 (2007).
[PubMed]

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).

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).

Puell, H.

A. Zembrod, H. Puell, and J. Giordmaine, “Surface radiation from non-linear optical polarisation,” Opto-electronics 1(1), 64–66 (1969).

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).
[PubMed]

Ramesh, R.

G. Catalan, J. Seidel, R. Ramesh, and J. F. Scott, “Domain wall nanoelectronics,” Rev. Mod. Phys. 84(1), 119–156 (2012).

Ramírez, M. O.

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

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(4), 106–109 (2015).

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).
[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).
[PubMed]

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).

Saltiel, S. M.

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of secondharmonic bessel beams by transverse phase-matching in annular periodically poled structures,” Jpn. J. Appl. Phys. 47 (8S1), 6777– 6783 (2008).

Saxena, A.

D. A. Scrymgeour, V. Gopalan, A. Itagi, A. Saxena, and P. J. Swart, “Phenomenological theory of a single domain wall in uniaxial trigonal ferroelectrics: Lithium niobate and lithium tantalate,” Phys. Rev. B 71(18), 184110 (2005).

Scott, J. F.

G. Catalan, J. Seidel, R. Ramesh, and J. F. Scott, “Domain wall nanoelectronics,” Rev. Mod. Phys. 84(1), 119–156 (2012).

Scrymgeour, D. A.

D. A. Scrymgeour, V. Gopalan, A. Itagi, A. Saxena, and P. J. Swart, “Phenomenological theory of a single domain wall in uniaxial trigonal ferroelectrics: Lithium niobate and lithium tantalate,” Phys. Rev. B 71(18), 184110 (2005).

Seidel, J.

G. Catalan, J. Seidel, R. Ramesh, and J. F. Scott, “Domain wall nanoelectronics,” Rev. Mod. Phys. 84(1), 119–156 (2012).

Sheng, Y.

Swart, P. J.

D. A. Scrymgeour, V. Gopalan, A. Itagi, A. Saxena, and P. J. Swart, “Phenomenological theory of a single domain wall in uniaxial trigonal ferroelectrics: Lithium niobate and lithium tantalate,” Phys. Rev. B 71(18), 184110 (2005).

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).

Wang, W.

Yuan, Y.

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).

Zembrod, A.

A. Zembrod, H. Puell, and J. Giordmaine, “Surface radiation from non-linear optical polarisation,” Opto-electronics 1(1), 64–66 (1969).

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(7), 1227–1229 (2011).
[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).
[PubMed]

Zhao, G.

Zhao, L.

Zhao, X.

B. Liu, Y. Zheng, X. Zhao, H. Liu, and X. Chen, “Probe of symmetry reduction at domain walls by nonlinear Cherenkov measurement,” Opt. Express 24(26), 29459–29464 (2016).
[PubMed]

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(4), 106–109 (2015).

Zheng, Y.

B. Liu, Y. Zheng, X. Zhao, H. Liu, and X. Chen, “Probe of symmetry reduction at domain walls by nonlinear Cherenkov measurement,” Opt. Express 24(26), 29459–29464 (2016).
[PubMed]

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(4), 106–109 (2015).

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).
[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).
[PubMed]

Zhu, S.

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).
[PubMed]

Appl. Phys. Lett. (3)

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

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).

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).

Dokl. Akad. Nauk SSSR (1)

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

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

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).

Jpn. J. Appl. Phys. (1)

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of secondharmonic bessel beams by transverse phase-matching in annular periodically poled structures,” Jpn. J. Appl. Phys. 47 (8S1), 6777– 6783 (2008).

Opt. Express (3)

Opt. Lett. (4)

Opto-electronics (1)

A. Zembrod, H. Puell, and J. Giordmaine, “Surface radiation from non-linear optical polarisation,” Opto-electronics 1(1), 64–66 (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(4), 106–109 (2015).

Phys. Rev. B (1)

D. A. Scrymgeour, V. Gopalan, A. Itagi, A. Saxena, and P. J. Swart, “Phenomenological theory of a single domain wall in uniaxial trigonal ferroelectrics: Lithium niobate and lithium tantalate,” Phys. Rev. B 71(18), 184110 (2005).

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(22), 223901 (2012).
[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).
[PubMed]

Rev. Mod. Phys. (1)

G. Catalan, J. Seidel, R. Ramesh, and J. F. Scott, “Domain wall nanoelectronics,” Rev. Mod. Phys. 84(1), 119–156 (2012).

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Figures (4)

Fig. 1
Fig. 1 (a) The distributed function of χ 13 modulated by domain walls. (b) Phasing matching diagram of k , k and κ x . (c) Diagram of Cherenkov radiation.
Fig. 2
Fig. 2 (a) Angular distribution of emitting light for the incident wavelength of 532 nm. (b) The relationship between the intensity of LCR and the thickness of domain wall ( a = 50 μ m ).
Fig. 3
Fig. 3 (a) Schematic of the experimental setup. (b) LCR on the screen with the e-polarized incidence. (c) The relationship between external LCR angle and external incident angle. Theoretical calculation (the solid line) and experimental results (symbols) are in well agreement with each other.
Fig. 4
Fig. 4 (a) The experimental results of LCR with varying incident angles. (b) The phase-matching geometry of different stage. (c) The relationship between external CR angle θ and external incident angle.

Equations (5)

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( P x P y P z ) = ε 0 ( χ 11 0 0 _ 0 χ 22 0 _ 0 _ 0 _ χ 33 ) ( E x E y E z ) ,
D x = ε 0 E x + P x = ε 0 E x + ε 0 [ χ 11 E x + χ 13 g ( x ) E z ] .
( y + i 2 k 2 2 x ) A ( x , y ) = i μ 0 ε 0 ω 2 2 k χ 13 g ( x ) A e i ( k k ) y F ( x ) ,
S ( κ x , y ) = ( y χ 13 A π μ 0 ε 0 ω 2 2 k ) 2 { sin c [ ( Δ k κ x 2 2 k ) y 2 ] } 2 { a m 0 g n e a 2 ( m G 0 κ x ) 2 4 + a e a 2 κ x 2 4 2 [ e r f ( d i a 2 κ x 2 a ) + e r f ( d + i a 2 κ x 2 a ) ] } 2 ,
cos γ = k p / k = k cos β / k = n cos β / n ,

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