Abstract

We experimentally investigate ferroelectric domains close to the phase transition in a nonlinear photonic crystal exhibiting disordered domain distribution implementing Čerenkov second-harmonic generation. The interplay of domain structures and the second-harmonic signal is studied exemplarily in strontium barium niobate measuring the far-field distribution as well as imaging domain structures microscopically.

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  1. S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, “Second-harmonic generation from needlelike ferroelectric domains in Sr0.6Ba0.4Nd2O6 single crystals,” Appl. Phys. Lett. 73, 768–770 (1998).
    [Crossref]
  2. E. Y. Morozov, A. A. Kaminskii, A. S. Chirkin, and D. B. Yusupov, “Second optical harmonic generation in nonlinear crystals with a disordered domain structure,” JETP Lett. 73, 647–650 (2001).
    [Crossref]
  3. M. Baudrier-Raybaut, R. Haidar, P. Kupecek, P. Lemasson, and E. Rosencher, “Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials,” Nature 432, 374–376 (2004).
    [Crossref] [PubMed]
  4. K. A. Kuznetsov, G. K. Kitaeva, A. V. Shevlyuga, L. I. Ivleva, and T. R. Volk, “Second harmonic generation in a strontium barium niobate crystal with a random domain structure,” JETP Letters 87, 98–102 (2008).
    [Crossref]
  5. X. Vidal and J. Martorell, “Generation of light in media with a random distribution of nonlinear domains,” Phys. Rev. Lett. 97, 013902 (2006).
    [Crossref] [PubMed]
  6. A. R. Tunyagi, M. Ulex, and K. Betzler, “Noncollinear optical frequency doubling in strontium barium niobate,” Phys. Rev. Lett. 90, 243901 (2003).
    [Crossref] [PubMed]
  7. P. Molina, M. de la O Ramírez, and L. E. Bausá, “Strontium barium niobate as a multifunctional two-dimensional nonlinear “photonic glass”,” Adv. Funct. Mater. 18, 709–715 (2008).
    [Crossref]
  8. Y. Zhang, X. P. Hu, G. Zhao, S. N. Zhu, and M. Xiao, “Čerenkov second-harmonic arc from a hexagonally poled LiTaO3 planar waveguide,” J. Phys. D 42, 215103 (2009).
    [Crossref]
  9. V. Roppo, K. Kalinowski, Y. Sheng, W. Krolikowski, C. Cojocaru, and J. Trull, “Unified approach to Čerenkov second harmonic generation,” Opt. Express 21, 25715–25726 (2013).
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    [Crossref]
  12. M. Ayoub, P. Roedig, J. Imbrock, and C. Denz, “Domain-shape-based modulation of Čerenkov second-harmonic generation in multidomain strontium barium niobate,” Opt. Lett. 36, 4371–4373 (2011).
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    [Crossref]
  15. A. Arie and N. Voloch, “Periodic, quasi-periodic, and random quadratic nonlinear photonic crystals,” Laser and Photon. Rev. 4, 355–373 (2010).
    [Crossref]
  16. Y. Sheng, S. M. Saltiel, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Čerenkov-type second-harmonic generation with fundamental beams of different polarizations,” Opt. Lett. 35, 1317–1319 (2010).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  20. 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]
  21. M. Ayoub, H. Futterlieb, J. Imbrock, and C. Denz, “3d imaging of ferroelectric kinetics during electrically driven switching,” Adv. Mater. 29, 1603325 (2017).
    [Crossref]
  22. L. Tian, D. A. Scrymgeour, and V. Gopalan, “Real-time study of domain dynamics in ferroelectric Sr0.61Ba0.39Nb2O6,” Journal of Applied Physics 97, 114111 (2005).
    [Crossref]
  23. K. Terabe, S. Takekawa, M. Nakamura, K. Kitamura, S. Higuchi, Y. Gotoh, and A. Gruverman, “Imaging and engineering the nanoscale-domain structure of a Sr0.61Ba0.39Nb2O6 crystal using a scanning force microscope,” Appl. Phys. Lett. 81, 2044–2046 (2002).
    [Crossref]
  24. V. V. Shvartsman, W. Kleemann, T. Łukasiewicz, and J. Dec, “Nanopolar structure in Srx Ba1−x Nb2O6 single crystals tuned by Sr/Ba ratio and investigated by piezoelectric force microscopy,” Phys. Rev. B. 77, 054105 (2008).
    [Crossref]
  25. M. Ayoub, J. Imbrock, and C. Denz, “Second harmonic generation in multi-domain χ(2) media: from disorder to order,” Opt. Express 19, 11340–11354 (2011).
    [Crossref] [PubMed]
  26. M. Horowitz, A. Bekker, and B. Fischer, “Broadband second-harmonic generation in Srx Ba1−x Nb2O6 by spread spectrum phase matching with controllable domain gratings,” Appl. Phys. Lett. 62, 2619–2621 (1993).
    [Crossref]
  27. W. Wang, V. Roppo, K. Kalinowski, Y. Kong, D. N. Neshev, C. Cojocaru, J. Trull, R. Vilaseca, K. Staliunas, W. Krolikowski, S. M. Saltiel, and Y. Kivshar, “Third-harmonic generation via broadband cascading in disordered quadratic nonlinear media,” Opt. Express 17, 20117 (2009).
    [Crossref] [PubMed]
  28. L. E. Cross, “Relaxor ferroelectrics,” Ferroelectrics 76, 241–267 (1987).
    [Crossref]
  29. J. R. Oliver, R. R. Neurgaonkar, and L. E. Cross, “A thermodynamic phenomenology for ferroelectric tungsten bronze Sr0.6Ba0.4Nb2O6 (SBN:60),” Journal of Applied Physics 64, 37–47 (1988).
    [Crossref]
  30. T. Granzow, U. Dörfler, T. Woike, M. Wöhlecke, R. Pankrath, M. Imlau, and W. Kleemann, “Local electric-field-driven repoling reflected in the ferroelectric polarization of ce-doped Sr0.61Ba0.39Nb2O6,” Appl. Phys. Lett. 80, 470–472 (2002).
    [Crossref]
  31. U. Voelker and K. Betzler, “Domain morphology from k-space spectroscopy of ferroelectric crystals,” Phys. Rev. B 74, 132104 (2006).
    [Crossref]

2017 (1)

M. Ayoub, H. Futterlieb, J. Imbrock, and C. Denz, “3d imaging of ferroelectric kinetics during electrically driven switching,” Adv. Mater. 29, 1603325 (2017).
[Crossref]

2016 (1)

2013 (2)

2012 (1)

A. M. Vyunishev, A. S. Aleksandrovsky, A. I. Zaitsev, and V. V. Slabko, “Čerenkov nonlinear diffraction in random nonlinear photonic crystal of strontium tetraborate,” Appl. Phys. Lett. 101, 211114 (2012).
[Crossref]

2011 (3)

2010 (5)

2009 (3)

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, 1465–1472 (2009).
[Crossref]

Y. Zhang, X. P. Hu, G. Zhao, S. N. Zhu, and M. Xiao, “Čerenkov second-harmonic arc from a hexagonally poled LiTaO3 planar waveguide,” J. Phys. D 42, 215103 (2009).
[Crossref]

W. Wang, V. Roppo, K. Kalinowski, Y. Kong, D. N. Neshev, C. Cojocaru, J. Trull, R. Vilaseca, K. Staliunas, W. Krolikowski, S. M. Saltiel, and Y. Kivshar, “Third-harmonic generation via broadband cascading in disordered quadratic nonlinear media,” Opt. Express 17, 20117 (2009).
[Crossref] [PubMed]

2008 (3)

V. V. Shvartsman, W. Kleemann, T. Łukasiewicz, and J. Dec, “Nanopolar structure in Srx Ba1−x Nb2O6 single crystals tuned by Sr/Ba ratio and investigated by piezoelectric force microscopy,” Phys. Rev. B. 77, 054105 (2008).
[Crossref]

P. Molina, M. de la O Ramírez, and L. E. Bausá, “Strontium barium niobate as a multifunctional two-dimensional nonlinear “photonic glass”,” Adv. Funct. Mater. 18, 709–715 (2008).
[Crossref]

K. A. Kuznetsov, G. K. Kitaeva, A. V. Shevlyuga, L. I. Ivleva, and T. R. Volk, “Second harmonic generation in a strontium barium niobate crystal with a random domain structure,” JETP Letters 87, 98–102 (2008).
[Crossref]

2006 (2)

X. Vidal and J. Martorell, “Generation of light in media with a random distribution of nonlinear domains,” Phys. Rev. Lett. 97, 013902 (2006).
[Crossref] [PubMed]

U. Voelker and K. Betzler, “Domain morphology from k-space spectroscopy of ferroelectric crystals,” Phys. Rev. B 74, 132104 (2006).
[Crossref]

2005 (1)

L. Tian, D. A. Scrymgeour, and V. Gopalan, “Real-time study of domain dynamics in ferroelectric Sr0.61Ba0.39Nb2O6,” Journal of Applied Physics 97, 114111 (2005).
[Crossref]

2004 (1)

M. Baudrier-Raybaut, R. Haidar, P. Kupecek, P. Lemasson, and E. Rosencher, “Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials,” Nature 432, 374–376 (2004).
[Crossref] [PubMed]

2003 (1)

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

2002 (2)

K. Terabe, S. Takekawa, M. Nakamura, K. Kitamura, S. Higuchi, Y. Gotoh, and A. Gruverman, “Imaging and engineering the nanoscale-domain structure of a Sr0.61Ba0.39Nb2O6 crystal using a scanning force microscope,” Appl. Phys. Lett. 81, 2044–2046 (2002).
[Crossref]

T. Granzow, U. Dörfler, T. Woike, M. Wöhlecke, R. Pankrath, M. Imlau, and W. Kleemann, “Local electric-field-driven repoling reflected in the ferroelectric polarization of ce-doped Sr0.61Ba0.39Nb2O6,” Appl. Phys. Lett. 80, 470–472 (2002).
[Crossref]

2001 (1)

E. Y. Morozov, A. A. Kaminskii, A. S. Chirkin, and D. B. Yusupov, “Second optical harmonic generation in nonlinear crystals with a disordered domain structure,” JETP Lett. 73, 647–650 (2001).
[Crossref]

1998 (1)

S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, “Second-harmonic generation from needlelike ferroelectric domains in Sr0.6Ba0.4Nd2O6 single crystals,” Appl. Phys. Lett. 73, 768–770 (1998).
[Crossref]

1993 (1)

M. Horowitz, A. Bekker, and B. Fischer, “Broadband second-harmonic generation in Srx Ba1−x Nb2O6 by spread spectrum phase matching with controllable domain gratings,” Appl. Phys. Lett. 62, 2619–2621 (1993).
[Crossref]

1988 (1)

J. R. Oliver, R. R. Neurgaonkar, and L. E. Cross, “A thermodynamic phenomenology for ferroelectric tungsten bronze Sr0.6Ba0.4Nb2O6 (SBN:60),” Journal of Applied Physics 64, 37–47 (1988).
[Crossref]

1987 (1)

L. E. Cross, “Relaxor ferroelectrics,” Ferroelectrics 76, 241–267 (1987).
[Crossref]

Aleksandrovsky, A. S.

A. M. Vyunishev, A. S. Aleksandrovsky, A. I. Zaitsev, and V. V. Slabko, “Čerenkov nonlinear diffraction in random nonlinear photonic crystal of strontium tetraborate,” Appl. Phys. Lett. 101, 211114 (2012).
[Crossref]

An, N.

Arie, A.

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

Y. Sheng, S. M. Saltiel, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Čerenkov-type second-harmonic generation with fundamental beams of different polarizations,” Opt. Lett. 35, 1317–1319 (2010).
[Crossref] [PubMed]

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]

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, 1465–1472 (2009).
[Crossref]

Ayoub, M.

Baudrier-Raybaut, M.

M. Baudrier-Raybaut, R. Haidar, P. Kupecek, P. Lemasson, and E. Rosencher, “Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials,” Nature 432, 374–376 (2004).
[Crossref] [PubMed]

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, 261111 (2010).
[Crossref]

P. Molina, M. de la O Ramírez, and L. E. Bausá, “Strontium barium niobate as a multifunctional two-dimensional nonlinear “photonic glass”,” Adv. Funct. Mater. 18, 709–715 (2008).
[Crossref]

Bekker, A.

M. Horowitz, A. Bekker, and B. Fischer, “Broadband second-harmonic generation in Srx Ba1−x Nb2O6 by spread spectrum phase matching with controllable domain gratings,” Appl. Phys. Lett. 62, 2619–2621 (1993).
[Crossref]

Best, A.

Betzler, K.

U. Voelker and K. Betzler, “Domain morphology from k-space spectroscopy of ferroelectric crystals,” Phys. Rev. B 74, 132104 (2006).
[Crossref]

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

Butt, H.-J.

Chen, X.

Chirkin, A. S.

E. Y. Morozov, A. A. Kaminskii, A. S. Chirkin, and D. B. Yusupov, “Second optical harmonic generation in nonlinear crystals with a disordered domain structure,” JETP Lett. 73, 647–650 (2001).
[Crossref]

Cojocaru, C.

Cross, L. E.

J. R. Oliver, R. R. Neurgaonkar, and L. E. Cross, “A thermodynamic phenomenology for ferroelectric tungsten bronze Sr0.6Ba0.4Nb2O6 (SBN:60),” Journal of Applied Physics 64, 37–47 (1988).
[Crossref]

L. E. Cross, “Relaxor ferroelectrics,” Ferroelectrics 76, 241–267 (1987).
[Crossref]

de la O Ramírez, M.

P. Molina, M. de la O Ramírez, and L. E. Bausá, “Strontium barium niobate as a multifunctional two-dimensional nonlinear “photonic glass”,” Adv. Funct. Mater. 18, 709–715 (2008).
[Crossref]

Dec, J.

V. V. Shvartsman, W. Kleemann, T. Łukasiewicz, and J. Dec, “Nanopolar structure in Srx Ba1−x Nb2O6 single crystals tuned by Sr/Ba ratio and investigated by piezoelectric force microscopy,” Phys. Rev. B. 77, 054105 (2008).
[Crossref]

DeMattei, R. C.

S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, “Second-harmonic generation from needlelike ferroelectric domains in Sr0.6Ba0.4Nd2O6 single crystals,” Appl. Phys. Lett. 73, 768–770 (1998).
[Crossref]

Deng, X.

Denz, C.

Dörfler, U.

T. Granzow, U. Dörfler, T. Woike, M. Wöhlecke, R. Pankrath, M. Imlau, and W. Kleemann, “Local electric-field-driven repoling reflected in the ferroelectric polarization of ce-doped Sr0.61Ba0.39Nb2O6,” Appl. Phys. Lett. 80, 470–472 (2002).
[Crossref]

Feigelson, R. S.

S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, “Second-harmonic generation from needlelike ferroelectric domains in Sr0.6Ba0.4Nd2O6 single crystals,” Appl. Phys. Lett. 73, 768–770 (1998).
[Crossref]

Fischer, B.

M. Horowitz, A. Bekker, and B. Fischer, “Broadband second-harmonic generation in Srx Ba1−x Nb2O6 by spread spectrum phase matching with controllable domain gratings,” Appl. Phys. Lett. 62, 2619–2621 (1993).
[Crossref]

Futterlieb, H.

M. Ayoub, H. Futterlieb, J. Imbrock, and C. Denz, “3d imaging of ferroelectric kinetics during electrically driven switching,” Adv. Mater. 29, 1603325 (2017).
[Crossref]

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, 261111 (2010).
[Crossref]

Geren, K.

Gopalan, V.

L. Tian, D. A. Scrymgeour, and V. Gopalan, “Real-time study of domain dynamics in ferroelectric Sr0.61Ba0.39Nb2O6,” Journal of Applied Physics 97, 114111 (2005).
[Crossref]

Gotoh, Y.

K. Terabe, S. Takekawa, M. Nakamura, K. Kitamura, S. Higuchi, Y. Gotoh, and A. Gruverman, “Imaging and engineering the nanoscale-domain structure of a Sr0.61Ba0.39Nb2O6 crystal using a scanning force microscope,” Appl. Phys. Lett. 81, 2044–2046 (2002).
[Crossref]

Granzow, T.

T. Granzow, U. Dörfler, T. Woike, M. Wöhlecke, R. Pankrath, M. Imlau, and W. Kleemann, “Local electric-field-driven repoling reflected in the ferroelectric polarization of ce-doped Sr0.61Ba0.39Nb2O6,” Appl. Phys. Lett. 80, 470–472 (2002).
[Crossref]

Gruverman, A.

K. Terabe, S. Takekawa, M. Nakamura, K. Kitamura, S. Higuchi, Y. Gotoh, and A. Gruverman, “Imaging and engineering the nanoscale-domain structure of a Sr0.61Ba0.39Nb2O6 crystal using a scanning force microscope,” Appl. Phys. Lett. 81, 2044–2046 (2002).
[Crossref]

Haidar, R.

M. Baudrier-Raybaut, R. Haidar, P. Kupecek, P. Lemasson, and E. Rosencher, “Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials,” Nature 432, 374–376 (2004).
[Crossref] [PubMed]

Higuchi, S.

K. Terabe, S. Takekawa, M. Nakamura, K. Kitamura, S. Higuchi, Y. Gotoh, and A. Gruverman, “Imaging and engineering the nanoscale-domain structure of a Sr0.61Ba0.39Nb2O6 crystal using a scanning force microscope,” Appl. Phys. Lett. 81, 2044–2046 (2002).
[Crossref]

Horowitz, M.

M. Horowitz, A. Bekker, and B. Fischer, “Broadband second-harmonic generation in Srx Ba1−x Nb2O6 by spread spectrum phase matching with controllable domain gratings,” Appl. Phys. Lett. 62, 2619–2621 (1993).
[Crossref]

Hu, X. P.

Y. Zhang, X. P. Hu, G. Zhao, S. N. Zhu, and M. Xiao, “Čerenkov second-harmonic arc from a hexagonally poled LiTaO3 planar waveguide,” J. Phys. D 42, 215103 (2009).
[Crossref]

Imbrock, J.

Imlau, M.

T. Granzow, U. Dörfler, T. Woike, M. Wöhlecke, R. Pankrath, M. Imlau, and W. Kleemann, “Local electric-field-driven repoling reflected in the ferroelectric polarization of ce-doped Sr0.61Ba0.39Nb2O6,” Appl. Phys. Lett. 80, 470–472 (2002).
[Crossref]

Ivleva, L. I.

K. A. Kuznetsov, G. K. Kitaeva, A. V. Shevlyuga, L. I. Ivleva, and T. R. Volk, “Second harmonic generation in a strontium barium niobate crystal with a random domain structure,” JETP Letters 87, 98–102 (2008).
[Crossref]

Kalinowski, K.

Kaminskii, A. A.

E. Y. Morozov, A. A. Kaminskii, A. S. Chirkin, and D. B. Yusupov, “Second optical harmonic generation in nonlinear crystals with a disordered domain structure,” JETP Lett. 73, 647–650 (2001).
[Crossref]

Kawai, S.

S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, “Second-harmonic generation from needlelike ferroelectric domains in Sr0.6Ba0.4Nd2O6 single crystals,” Appl. Phys. Lett. 73, 768–770 (1998).
[Crossref]

Kitaeva, G. K.

K. A. Kuznetsov, G. K. Kitaeva, A. V. Shevlyuga, L. I. Ivleva, and T. R. Volk, “Second harmonic generation in a strontium barium niobate crystal with a random domain structure,” JETP Letters 87, 98–102 (2008).
[Crossref]

Kitamura, K.

K. Terabe, S. Takekawa, M. Nakamura, K. Kitamura, S. Higuchi, Y. Gotoh, and A. Gruverman, “Imaging and engineering the nanoscale-domain structure of a Sr0.61Ba0.39Nb2O6 crystal using a scanning force microscope,” Appl. Phys. Lett. 81, 2044–2046 (2002).
[Crossref]

Kivshar, Y.

Kivshar, Y. S.

Y. Sheng, S. M. Saltiel, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Čerenkov-type second-harmonic generation with fundamental beams of different polarizations,” Opt. Lett. 35, 1317–1319 (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, 1465–1472 (2009).
[Crossref]

Kleemann, W.

V. V. Shvartsman, W. Kleemann, T. Łukasiewicz, and J. Dec, “Nanopolar structure in Srx Ba1−x Nb2O6 single crystals tuned by Sr/Ba ratio and investigated by piezoelectric force microscopy,” Phys. Rev. B. 77, 054105 (2008).
[Crossref]

T. Granzow, U. Dörfler, T. Woike, M. Wöhlecke, R. Pankrath, M. Imlau, and W. Kleemann, “Local electric-field-driven repoling reflected in the ferroelectric polarization of ce-doped Sr0.61Ba0.39Nb2O6,” Appl. Phys. Lett. 80, 470–472 (2002).
[Crossref]

Kong, Y.

Koynov, K.

Krolikowski, W.

Kupecek, P.

M. Baudrier-Raybaut, R. Haidar, P. Kupecek, P. Lemasson, and E. Rosencher, “Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials,” Nature 432, 374–376 (2004).
[Crossref] [PubMed]

Kuznetsov, K. A.

K. A. Kuznetsov, G. K. Kitaeva, A. V. Shevlyuga, L. I. Ivleva, and T. R. Volk, “Second harmonic generation in a strontium barium niobate crystal with a random domain structure,” JETP Letters 87, 98–102 (2008).
[Crossref]

Lee, H. S.

S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, “Second-harmonic generation from needlelike ferroelectric domains in Sr0.6Ba0.4Nd2O6 single crystals,” Appl. Phys. Lett. 73, 768–770 (1998).
[Crossref]

Lemasson, P.

M. Baudrier-Raybaut, R. Haidar, P. Kupecek, P. Lemasson, and E. Rosencher, “Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials,” Nature 432, 374–376 (2004).
[Crossref] [PubMed]

Lukasiewicz, T.

V. V. Shvartsman, W. Kleemann, T. Łukasiewicz, and J. Dec, “Nanopolar structure in Srx Ba1−x Nb2O6 single crystals tuned by Sr/Ba ratio and investigated by piezoelectric force microscopy,” Phys. Rev. B. 77, 054105 (2008).
[Crossref]

Martorell, J.

X. Vidal and J. Martorell, “Generation of light in media with a random distribution of nonlinear domains,” Phys. Rev. Lett. 97, 013902 (2006).
[Crossref] [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, 261111 (2010).
[Crossref]

P. Molina, M. de la O Ramírez, and L. E. Bausá, “Strontium barium niobate as a multifunctional two-dimensional nonlinear “photonic glass”,” Adv. Funct. Mater. 18, 709–715 (2008).
[Crossref]

Morozov, E. Y.

E. Y. Morozov, A. A. Kaminskii, A. S. Chirkin, and D. B. Yusupov, “Second optical harmonic generation in nonlinear crystals with a disordered domain structure,” JETP Lett. 73, 647–650 (2001).
[Crossref]

Nakamura, M.

K. Terabe, S. Takekawa, M. Nakamura, K. Kitamura, S. Higuchi, Y. Gotoh, and A. Gruverman, “Imaging and engineering the nanoscale-domain structure of a Sr0.61Ba0.39Nb2O6 crystal using a scanning force microscope,” Appl. Phys. Lett. 81, 2044–2046 (2002).
[Crossref]

Neshev, D. N.

W. Wang, V. Roppo, K. Kalinowski, Y. Kong, D. N. Neshev, C. Cojocaru, J. Trull, R. Vilaseca, K. Staliunas, W. Krolikowski, S. M. Saltiel, and Y. Kivshar, “Third-harmonic generation via broadband cascading in disordered quadratic nonlinear media,” Opt. Express 17, 20117 (2009).
[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, 1465–1472 (2009).
[Crossref]

Neurgaonkar, R. R.

J. R. Oliver, R. R. Neurgaonkar, and L. E. Cross, “A thermodynamic phenomenology for ferroelectric tungsten bronze Sr0.6Ba0.4Nb2O6 (SBN:60),” Journal of Applied Physics 64, 37–47 (1988).
[Crossref]

Ogawa, T.

S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, “Second-harmonic generation from needlelike ferroelectric domains in Sr0.6Ba0.4Nd2O6 single crystals,” Appl. Phys. Lett. 73, 768–770 (1998).
[Crossref]

Oliver, J. R.

J. R. Oliver, R. R. Neurgaonkar, and L. E. Cross, “A thermodynamic phenomenology for ferroelectric tungsten bronze Sr0.6Ba0.4Nb2O6 (SBN:60),” Journal of Applied Physics 64, 37–47 (1988).
[Crossref]

Pankrath, R.

T. Granzow, U. Dörfler, T. Woike, M. Wöhlecke, R. Pankrath, M. Imlau, and W. Kleemann, “Local electric-field-driven repoling reflected in the ferroelectric polarization of ce-doped Sr0.61Ba0.39Nb2O6,” Appl. Phys. Lett. 80, 470–472 (2002).
[Crossref]

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, 261111 (2010).
[Crossref]

Ren, H.

Roedig, P.

Roppo, V.

Rosencher, E.

M. Baudrier-Raybaut, R. Haidar, P. Kupecek, P. Lemasson, and E. Rosencher, “Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials,” Nature 432, 374–376 (2004).
[Crossref] [PubMed]

Saltiel, S. M.

Scrymgeour, D. A.

L. Tian, D. A. Scrymgeour, and V. Gopalan, “Real-time study of domain dynamics in ferroelectric Sr0.61Ba0.39Nb2O6,” Journal of Applied Physics 97, 114111 (2005).
[Crossref]

Sheng, Y.

Shevlyuga, A. V.

K. A. Kuznetsov, G. K. Kitaeva, A. V. Shevlyuga, L. I. Ivleva, and T. R. Volk, “Second harmonic generation in a strontium barium niobate crystal with a random domain structure,” JETP Letters 87, 98–102 (2008).
[Crossref]

Shvartsman, V. V.

V. V. Shvartsman, W. Kleemann, T. Łukasiewicz, and J. Dec, “Nanopolar structure in Srx Ba1−x Nb2O6 single crystals tuned by Sr/Ba ratio and investigated by piezoelectric force microscopy,” Phys. Rev. B. 77, 054105 (2008).
[Crossref]

Slabko, V. V.

A. M. Vyunishev, A. S. Aleksandrovsky, A. I. Zaitsev, and V. V. Slabko, “Čerenkov nonlinear diffraction in random nonlinear photonic crystal of strontium tetraborate,” Appl. Phys. Lett. 101, 211114 (2012).
[Crossref]

Staliunas, K.

Takekawa, S.

K. Terabe, S. Takekawa, M. Nakamura, K. Kitamura, S. Higuchi, Y. Gotoh, and A. Gruverman, “Imaging and engineering the nanoscale-domain structure of a Sr0.61Ba0.39Nb2O6 crystal using a scanning force microscope,” Appl. Phys. Lett. 81, 2044–2046 (2002).
[Crossref]

Terabe, K.

K. Terabe, S. Takekawa, M. Nakamura, K. Kitamura, S. Higuchi, Y. Gotoh, and A. Gruverman, “Imaging and engineering the nanoscale-domain structure of a Sr0.61Ba0.39Nb2O6 crystal using a scanning force microscope,” Appl. Phys. Lett. 81, 2044–2046 (2002).
[Crossref]

Tian, L.

L. Tian, D. A. Scrymgeour, and V. Gopalan, “Real-time study of domain dynamics in ferroelectric Sr0.61Ba0.39Nb2O6,” Journal of Applied Physics 97, 114111 (2005).
[Crossref]

Trull, J.

Tunyagi, A. R.

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

Ulex, M.

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

Vidal, X.

X. Vidal and J. Martorell, “Generation of light in media with a random distribution of nonlinear domains,” Phys. Rev. Lett. 97, 013902 (2006).
[Crossref] [PubMed]

Vilaseca, R.

Voelker, U.

U. Voelker and K. Betzler, “Domain morphology from k-space spectroscopy of ferroelectric crystals,” Phys. Rev. B 74, 132104 (2006).
[Crossref]

Volk, T. R.

K. A. Kuznetsov, G. K. Kitaeva, A. V. Shevlyuga, L. I. Ivleva, and T. R. Volk, “Second harmonic generation in a strontium barium niobate crystal with a random domain structure,” JETP Letters 87, 98–102 (2008).
[Crossref]

Voloch, N.

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

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, 1465–1472 (2009).
[Crossref]

Vyunishev, A. M.

A. M. Vyunishev, A. S. Aleksandrovsky, A. I. Zaitsev, and V. V. Slabko, “Čerenkov nonlinear diffraction in random nonlinear photonic crystal of strontium tetraborate,” Appl. Phys. Lett. 101, 211114 (2012).
[Crossref]

Wang, F.

Wang, W.

Wöhlecke, M.

T. Granzow, U. Dörfler, T. Woike, M. Wöhlecke, R. Pankrath, M. Imlau, and W. Kleemann, “Local electric-field-driven repoling reflected in the ferroelectric polarization of ce-doped Sr0.61Ba0.39Nb2O6,” Appl. Phys. Lett. 80, 470–472 (2002).
[Crossref]

Woike, T.

T. Granzow, U. Dörfler, T. Woike, M. Wöhlecke, R. Pankrath, M. Imlau, and W. Kleemann, “Local electric-field-driven repoling reflected in the ferroelectric polarization of ce-doped Sr0.61Ba0.39Nb2O6,” Appl. Phys. Lett. 80, 470–472 (2002).
[Crossref]

Xiao, M.

Y. Zhang, F. Wang, K. Geren, S. N. Zhu, and M. Xiao, “Second-harmonic imaging from a modulated domain structure,” Opt. Lett. 35, 178–180 (2010).
[Crossref] [PubMed]

Y. Zhang, X. P. Hu, G. Zhao, S. N. Zhu, and M. Xiao, “Čerenkov second-harmonic arc from a hexagonally poled LiTaO3 planar waveguide,” J. Phys. D 42, 215103 (2009).
[Crossref]

Yusupov, D. B.

E. Y. Morozov, A. A. Kaminskii, A. S. Chirkin, and D. B. Yusupov, “Second optical harmonic generation in nonlinear crystals with a disordered domain structure,” JETP Lett. 73, 647–650 (2001).
[Crossref]

Zaitsev, A. I.

A. M. Vyunishev, A. S. Aleksandrovsky, A. I. Zaitsev, and V. V. Slabko, “Čerenkov nonlinear diffraction in random nonlinear photonic crystal of strontium tetraborate,” Appl. Phys. Lett. 101, 211114 (2012).
[Crossref]

Zhang, Y.

Y. Zhang, F. Wang, K. Geren, S. N. Zhu, and M. Xiao, “Second-harmonic imaging from a modulated domain structure,” Opt. Lett. 35, 178–180 (2010).
[Crossref] [PubMed]

Y. Zhang, X. P. Hu, G. Zhao, S. N. Zhu, and M. Xiao, “Čerenkov second-harmonic arc from a hexagonally poled LiTaO3 planar waveguide,” J. Phys. D 42, 215103 (2009).
[Crossref]

Zhao, G.

Y. Zhang, X. P. Hu, G. Zhao, S. N. Zhu, and M. Xiao, “Čerenkov second-harmonic arc from a hexagonally poled LiTaO3 planar waveguide,” J. Phys. D 42, 215103 (2009).
[Crossref]

Zhao, X.

Zheng, Y.

Zhu, S. N.

Y. Zhang, F. Wang, K. Geren, S. N. Zhu, and M. Xiao, “Second-harmonic imaging from a modulated domain structure,” Opt. Lett. 35, 178–180 (2010).
[Crossref] [PubMed]

Y. Zhang, X. P. Hu, G. Zhao, S. N. Zhu, and M. Xiao, “Čerenkov second-harmonic arc from a hexagonally poled LiTaO3 planar waveguide,” J. Phys. D 42, 215103 (2009).
[Crossref]

Adv. Funct. Mater. (1)

P. Molina, M. de la O Ramírez, and L. E. Bausá, “Strontium barium niobate as a multifunctional two-dimensional nonlinear “photonic glass”,” Adv. Funct. Mater. 18, 709–715 (2008).
[Crossref]

Adv. Mater. (1)

M. Ayoub, H. Futterlieb, J. Imbrock, and C. Denz, “3d imaging of ferroelectric kinetics during electrically driven switching,” Adv. Mater. 29, 1603325 (2017).
[Crossref]

Appl. Phys. Lett. (7)

K. Terabe, S. Takekawa, M. Nakamura, K. Kitamura, S. Higuchi, Y. Gotoh, and A. Gruverman, “Imaging and engineering the nanoscale-domain structure of a Sr0.61Ba0.39Nb2O6 crystal using a scanning force microscope,” Appl. Phys. Lett. 81, 2044–2046 (2002).
[Crossref]

M. Horowitz, A. Bekker, and B. Fischer, “Broadband second-harmonic generation in Srx Ba1−x Nb2O6 by spread spectrum phase matching with controllable domain gratings,” Appl. Phys. Lett. 62, 2619–2621 (1993).
[Crossref]

T. Granzow, U. Dörfler, T. Woike, M. Wöhlecke, R. Pankrath, M. Imlau, and W. Kleemann, “Local electric-field-driven repoling reflected in the ferroelectric polarization of ce-doped Sr0.61Ba0.39Nb2O6,” Appl. Phys. Lett. 80, 470–472 (2002).
[Crossref]

S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, “Second-harmonic generation from needlelike ferroelectric domains in Sr0.6Ba0.4Nd2O6 single crystals,” Appl. Phys. Lett. 73, 768–770 (1998).
[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]

A. M. Vyunishev, A. S. Aleksandrovsky, A. I. Zaitsev, and V. V. Slabko, “Čerenkov nonlinear diffraction in random nonlinear photonic crystal of strontium tetraborate,” Appl. Phys. Lett. 101, 211114 (2012).
[Crossref]

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, 261111 (2010).
[Crossref]

Ferroelectrics (1)

L. E. Cross, “Relaxor ferroelectrics,” Ferroelectrics 76, 241–267 (1987).
[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, 1465–1472 (2009).
[Crossref]

J. Phys. D (1)

Y. Zhang, X. P. Hu, G. Zhao, S. N. Zhu, and M. Xiao, “Čerenkov second-harmonic arc from a hexagonally poled LiTaO3 planar waveguide,” J. Phys. D 42, 215103 (2009).
[Crossref]

JETP Lett. (1)

E. Y. Morozov, A. A. Kaminskii, A. S. Chirkin, and D. B. Yusupov, “Second optical harmonic generation in nonlinear crystals with a disordered domain structure,” JETP Lett. 73, 647–650 (2001).
[Crossref]

JETP Letters (1)

K. A. Kuznetsov, G. K. Kitaeva, A. V. Shevlyuga, L. I. Ivleva, and T. R. Volk, “Second harmonic generation in a strontium barium niobate crystal with a random domain structure,” JETP Letters 87, 98–102 (2008).
[Crossref]

Journal of Applied Physics (2)

J. R. Oliver, R. R. Neurgaonkar, and L. E. Cross, “A thermodynamic phenomenology for ferroelectric tungsten bronze Sr0.6Ba0.4Nb2O6 (SBN:60),” Journal of Applied Physics 64, 37–47 (1988).
[Crossref]

L. Tian, D. A. Scrymgeour, and V. Gopalan, “Real-time study of domain dynamics in ferroelectric Sr0.61Ba0.39Nb2O6,” Journal of Applied Physics 97, 114111 (2005).
[Crossref]

Laser and Photon. Rev. (1)

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

Nature (1)

M. Baudrier-Raybaut, R. Haidar, P. Kupecek, P. Lemasson, and E. Rosencher, “Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials,” Nature 432, 374–376 (2004).
[Crossref] [PubMed]

Opt. Express (6)

Opt. Lett. (3)

Phys. Rev. B (1)

U. Voelker and K. Betzler, “Domain morphology from k-space spectroscopy of ferroelectric crystals,” Phys. Rev. B 74, 132104 (2006).
[Crossref]

Phys. Rev. B. (1)

V. V. Shvartsman, W. Kleemann, T. Łukasiewicz, and J. Dec, “Nanopolar structure in Srx Ba1−x Nb2O6 single crystals tuned by Sr/Ba ratio and investigated by piezoelectric force microscopy,” Phys. Rev. B. 77, 054105 (2008).
[Crossref]

Phys. Rev. Lett. (2)

X. Vidal and J. Martorell, “Generation of light in media with a random distribution of nonlinear domains,” Phys. Rev. Lett. 97, 013902 (2006).
[Crossref] [PubMed]

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

Supplementary Material (1)

NameDescription
» Visualization 1       Farfield CSHG Temperautre dependency

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Figures (5)

Fig. 1
Fig. 1

Illustration of the Čerenkov-type phase-matching condition. The ring-shaped emission in a disordered 2D nonlinear structure, and the point-shaped emission on a domain wall.

Fig. 2
Fig. 2

(a) and (b): Čerenkov-type SHG microscopic images of ferroelectric domains in SBN perpendicular to the optical axis with different averaged domain sizes, respectively; (c) a three-dimensional visualization of needle-like ferroelectric domains. Insets show the corresponding far-field Čerenkov SHG. Schematic of the experimental setup (d): The fundamental wave λFW = 1200 nm propagates along the optical axis of the crystal, and the Čerenkov SH ring is emitted at λSH = 600 nm. The crystal is sandwiched between thermo electrical coolers (TEC).

Fig. 3
Fig. 3

Experimental images of Čerenkov SH emission in the far-field recorded for an SBN of micro-scaled squircle-shaped domain, heated above Curie temperature and then cooled down at the fundamental wavelength 1200 nm. (see Visualization 1)

Fig. 4
Fig. 4

Images of ferroelectric domain structures in SBN using Čerenkov SHG microscopy. Green signals represent domain walls. The temperature is increased from 22 °C (a) up to 85 °C (i). First, the crystal has undergone some poling cycles to start with micro-scaled domains (a). In (i) only background noise is detected.

Fig. 5
Fig. 5

Far-field ČSHG intensities (cfg. Fig. 3) and mean domain diameters determined from the microscope images (cfg. Fig. 4) in dependence of the crystal temperature.

Equations (1)

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I SH ( T ) d eff 2 ( T ) I FW 2 L z 2 ( T ) | S ( Δ k x y ) ( T ) | 2 sinc 2 ( Δ k z ( T ) L z ( T ) 2 ) .