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Comparative analysis of ferroelectric domain statistics via nonlinear diffraction in random nonlinear materials

B. Wang, K. Switkowski, C. Cojocaru, V. Roppo, Y. Sheng, M. Scalora, J. Kisielewski, D. Pawlak, R. Vilaseca, H. Akhouayri, W. Krolikowski, and J. Trull

Open Access Open Access

Abstract

We present an indirect, non-destructive optical method for domain statistic characterization in disordered nonlinear crystals having homogeneous refractive index and spatially random distribution of ferroelectric domains. This method relies on the analysis of the wave-dependent spatial distribution of the second harmonic, in the plane perpendicular to the optical axis in combination with numerical simulations. We apply this technique to the characterization of two different media, Calcium Barium Niobate and Strontium Barium Niobate, with drastically different statistical distributions of ferroelectric domains.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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Corrections

6 February 2018: A typographical correction was made to the author listing.

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References

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  • Publication
  1. I. Freund, “Nonlinear Diffraction,” Phys. Rev. Lett. 21(19), 1404–1406 (1968).
    [Crossref]
  2. G. Dolino, J. Lajzerowicz, and M. Vallade, “Second-harmonic Light Scattering by Domains in Ferroelectric Triglycine Sulfate,” Phys. Rev. B 2(6), 2194–2200 (1976).
    [Crossref]
  3. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in nonlinear dielectrics,” Phys. Rev. A 127(6), 1918–1939 (1962).
    [Crossref]
  4. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-Phase-matched Second harmonic Generation: Tuning and Tolerances,” IEEE Journal Quant. Electron. 28(11), 2631–2654 (1992).
  5. V. Berger, “Nonlinear Photonic Crystals,” Phys. Rev. Lett. 81(19), 4136–4139 (1998).
    [Crossref]
  6. M. H. Chou, K. R. Parameswaran, M. M. Fejer, and I. Brener, “Multiple-channel wavelength conversion by use of engineered quasi-phase-matching structures in LiNbO3 waveguides,” Opt. Lett. 24(16), 1157–1159 (1999).
    [Crossref] [PubMed]
  7. N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally Poled Lithium Niobate: A Two-Dimensional Nonlinear Photonic Crystal,” Phys. Rev. Lett. 84(19), 4345–4348 (2000).
    [Crossref] [PubMed]
  8. Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, “Broadband efficient second harmonic generation in media with short-range order,” Appl. Phys. Lett. 91, 011104 (2007).
  9. R. C. Miller, “Optical harmonic generation in single crystal BaTiO3,” Phys. Rev. A 134(5), A313–A1319 (1998).
  10. R. V. Gainutdinov, T. R. Volk, O. A. Lysova, I. I. Razgonov, A. L. Tolstikhina, and L. I. Ivleva, “Recording of domains and regular domain patterns in strontium-barium-niobate crystals in the field of atomic force microscope,” Appl. Phys. B 95(3), 505–512 (2009).
    [Crossref]
  11. 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(6), 768–770 (1998).
    [Crossref]
  12. A.R. Tunyagi, M. Ulex, and K. Betzler, “Noncollinear Optical frequency Doubling in Strontium Barium Niobate,” Phys. Rev. Lett. 90(24), 243901 (2003).
  13. J. Trull, I. Sola, B. Wang, A. Parra, W. Krolikowski, Y. Sheng, R. Vilaseca, and C. Cojocaru, “Ultrashort pulse chirp measurement via transverse second-harmonic generation in strontium barium niobate crystal,” Appl. Phys. Lett. 106(22), 221108 (2015).
    [Crossref]
  14. A. S. Aleksandrovsky, A. M. Vyunishev, A. I. Zaitsev, A. A. Ikonnikov, and G. I. Pospelov, “Ultrashort pulses characterization by nonlinear diffraction from virtual beam,” Appl. Phys. Lett. 98(6), 061104 (2011).
    [Crossref]
  15. B. Wang, C. Cojocaru, W. Krolikowski, Y. Sheng, and J. Trull, “Transverse single-shot cross-correlation scheme for laser pulse temporal measurement via planar second harmonic generation,” Opt. Express 24(19), 22210–22218 (2016).
    [Crossref] [PubMed]
  16. 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(22), 20117–20123 (2009).
    [Crossref] [PubMed]
  17. Y. Sheng, A. Best, H. J. Butt, W. Krolikowski, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualization by Cerenkov-type second harmonic generation,” Opt. Express 18(16), 16539–16545 (2010).
    [Crossref] [PubMed]
  18. Y. Le Grand, D. Rouede, C. Odin, R. Aubry, and S. Mattauch, “Second-harmonic scattering by domains in RbH2PO4 ferroelectric,” Opt. Commun. 200(1-6), 249–260 (2001).
    [Crossref]
  19. V. Roppo, W. Wang, K. Kalinowski, Y. Kong, C. Cojocaru, J. Trull, R. Vilaseca, M. Scalora, W. Krolikowski, and Y. Kivshar, “The role of ferroelectric domain structure in second harmonic generation in random quadratic media,” Opt. Express 18(5), 4012–4022 (2010).
    [Crossref] [PubMed]
  20. M. Ayoub, J. Imbrock, and C. Denz, “Ferroelectric domain diagnostics near the phase transition by Čerenkov second-harmonic generation,” Opt. Mater. Express 7(9), 3448 (2017).
    [Crossref]
  21. M. Ayoub, J. Imbrock, and C. Denz, “Second harmonic generation in multi-domain χ(2) media: from disorder to order,” Opt. Express 19(12), 11340 (2011).
    [Crossref] [PubMed]
  22. Th. Woike, T. Granzow, U. Dörfler, Ch. Poetsch, M. Wöhlecke, and R. Pankrath, “Refractive indices in congruently melting Sr0.61Ba0.39Nb2O6,” Phys. Status Solidi 186, R13–R15 (2001).
    [Crossref]
  23. M. Eßer, M. Burianek, P. Held, J. Stade, S. Bulut, C. Wickleder, and M. Mühlberg, “Optical characterization and crystal structure of the novel bronze type CaxBa1-xNb2O6 (x = 0.28; CBN-28),” Cryst. Res. Technol. 38(6), 457–464 (2003).
    [Crossref]
  24. J. Trull, C. Cojocaru, R. Fischer, S. M. Saltiel, K. Staliunas, R. Herrero, R. Vilaseca, D. N Neshev, W. Krolikowski, and Y. S. Kivshar, “Second-harmonic parametric scattering in ferroelectric crystals with disordered nonlinear domain structures,” Opt. Express 15(24), 15868–15877 (2007).
    [Crossref] [PubMed]
  25. E. Soergel, “Visualization of ferroelectric domains in bulk single crystals,” Appl. Phys. B 81(6), 729–751 (2005).
    [Crossref]
  26. M. Scalora and M. E. Crenshaw, “A beam propagation method that handles reflections,” Opt. Commun. 108(4-6), 191–196 (1994).
    [Crossref]

2017 (1)

2016 (1)

2015 (1)

J. Trull, I. Sola, B. Wang, A. Parra, W. Krolikowski, Y. Sheng, R. Vilaseca, and C. Cojocaru, “Ultrashort pulse chirp measurement via transverse second-harmonic generation in strontium barium niobate crystal,” Appl. Phys. Lett. 106(22), 221108 (2015).
[Crossref]

2011 (2)

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

M. Ayoub, J. Imbrock, and C. Denz, “Second harmonic generation in multi-domain χ(2) media: from disorder to order,” Opt. Express 19(12), 11340 (2011).
[Crossref] [PubMed]

2010 (2)

2009 (2)

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(22), 20117–20123 (2009).
[Crossref] [PubMed]

R. V. Gainutdinov, T. R. Volk, O. A. Lysova, I. I. Razgonov, A. L. Tolstikhina, and L. I. Ivleva, “Recording of domains and regular domain patterns in strontium-barium-niobate crystals in the field of atomic force microscope,” Appl. Phys. B 95(3), 505–512 (2009).
[Crossref]

2007 (2)

2005 (1)

E. Soergel, “Visualization of ferroelectric domains in bulk single crystals,” Appl. Phys. B 81(6), 729–751 (2005).
[Crossref]

2003 (2)

M. Eßer, M. Burianek, P. Held, J. Stade, S. Bulut, C. Wickleder, and M. Mühlberg, “Optical characterization and crystal structure of the novel bronze type CaxBa1-xNb2O6 (x = 0.28; CBN-28),” Cryst. Res. Technol. 38(6), 457–464 (2003).
[Crossref]

A.R. Tunyagi, M. Ulex, and K. Betzler, “Noncollinear Optical frequency Doubling in Strontium Barium Niobate,” Phys. Rev. Lett. 90(24), 243901 (2003).

2001 (2)

Y. Le Grand, D. Rouede, C. Odin, R. Aubry, and S. Mattauch, “Second-harmonic scattering by domains in RbH2PO4 ferroelectric,” Opt. Commun. 200(1-6), 249–260 (2001).
[Crossref]

Th. Woike, T. Granzow, U. Dörfler, Ch. Poetsch, M. Wöhlecke, and R. Pankrath, “Refractive indices in congruently melting Sr0.61Ba0.39Nb2O6,” Phys. Status Solidi 186, R13–R15 (2001).
[Crossref]

2000 (1)

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally Poled Lithium Niobate: A Two-Dimensional Nonlinear Photonic Crystal,” Phys. Rev. Lett. 84(19), 4345–4348 (2000).
[Crossref] [PubMed]

1999 (1)

1998 (3)

V. Berger, “Nonlinear Photonic Crystals,” Phys. Rev. Lett. 81(19), 4136–4139 (1998).
[Crossref]

R. C. Miller, “Optical harmonic generation in single crystal BaTiO3,” Phys. Rev. A 134(5), A313–A1319 (1998).

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(6), 768–770 (1998).
[Crossref]

1994 (1)

M. Scalora and M. E. Crenshaw, “A beam propagation method that handles reflections,” Opt. Commun. 108(4-6), 191–196 (1994).
[Crossref]

1992 (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-Phase-matched Second harmonic Generation: Tuning and Tolerances,” IEEE Journal Quant. Electron. 28(11), 2631–2654 (1992).

1976 (1)

G. Dolino, J. Lajzerowicz, and M. Vallade, “Second-harmonic Light Scattering by Domains in Ferroelectric Triglycine Sulfate,” Phys. Rev. B 2(6), 2194–2200 (1976).
[Crossref]

1968 (1)

I. Freund, “Nonlinear Diffraction,” Phys. Rev. Lett. 21(19), 1404–1406 (1968).
[Crossref]

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in nonlinear dielectrics,” Phys. Rev. A 127(6), 1918–1939 (1962).
[Crossref]

Aleksandrovsky, A. S.

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

Arie, A.

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in nonlinear dielectrics,” Phys. Rev. A 127(6), 1918–1939 (1962).
[Crossref]

Aubry, R.

Y. Le Grand, D. Rouede, C. Odin, R. Aubry, and S. Mattauch, “Second-harmonic scattering by domains in RbH2PO4 ferroelectric,” Opt. Commun. 200(1-6), 249–260 (2001).
[Crossref]

Ayoub, M.

Berger, V.

V. Berger, “Nonlinear Photonic Crystals,” Phys. Rev. Lett. 81(19), 4136–4139 (1998).
[Crossref]

Best, A.

Betzler, K.

A.R. Tunyagi, M. Ulex, and K. Betzler, “Noncollinear Optical frequency Doubling in Strontium Barium Niobate,” Phys. Rev. Lett. 90(24), 243901 (2003).

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in nonlinear dielectrics,” Phys. Rev. A 127(6), 1918–1939 (1962).
[Crossref]

Brener, I.

Broderick, N. G. R.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally Poled Lithium Niobate: A Two-Dimensional Nonlinear Photonic Crystal,” Phys. Rev. Lett. 84(19), 4345–4348 (2000).
[Crossref] [PubMed]

Bulut, S.

M. Eßer, M. Burianek, P. Held, J. Stade, S. Bulut, C. Wickleder, and M. Mühlberg, “Optical characterization and crystal structure of the novel bronze type CaxBa1-xNb2O6 (x = 0.28; CBN-28),” Cryst. Res. Technol. 38(6), 457–464 (2003).
[Crossref]

Burianek, M.

M. Eßer, M. Burianek, P. Held, J. Stade, S. Bulut, C. Wickleder, and M. Mühlberg, “Optical characterization and crystal structure of the novel bronze type CaxBa1-xNb2O6 (x = 0.28; CBN-28),” Cryst. Res. Technol. 38(6), 457–464 (2003).
[Crossref]

Butt, H. J.

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-Phase-matched Second harmonic Generation: Tuning and Tolerances,” IEEE Journal Quant. Electron. 28(11), 2631–2654 (1992).

Cheng, B.

Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, “Broadband efficient second harmonic generation in media with short-range order,” Appl. Phys. Lett. 91, 011104 (2007).

Chou, M. H.

Cojocaru, C.

Crenshaw, M. E.

M. Scalora and M. E. Crenshaw, “A beam propagation method that handles reflections,” Opt. Commun. 108(4-6), 191–196 (1994).
[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(6), 768–770 (1998).
[Crossref]

Denz, C.

Dolino, G.

G. Dolino, J. Lajzerowicz, and M. Vallade, “Second-harmonic Light Scattering by Domains in Ferroelectric Triglycine Sulfate,” Phys. Rev. B 2(6), 2194–2200 (1976).
[Crossref]

Dörfler, U.

Th. Woike, T. Granzow, U. Dörfler, Ch. Poetsch, M. Wöhlecke, and R. Pankrath, “Refractive indices in congruently melting Sr0.61Ba0.39Nb2O6,” Phys. Status Solidi 186, R13–R15 (2001).
[Crossref]

Dou, J.

Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, “Broadband efficient second harmonic generation in media with short-range order,” Appl. Phys. Lett. 91, 011104 (2007).

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in nonlinear dielectrics,” Phys. Rev. A 127(6), 1918–1939 (1962).
[Crossref]

Eßer, M.

M. Eßer, M. Burianek, P. Held, J. Stade, S. Bulut, C. Wickleder, and M. Mühlberg, “Optical characterization and crystal structure of the novel bronze type CaxBa1-xNb2O6 (x = 0.28; CBN-28),” Cryst. Res. Technol. 38(6), 457–464 (2003).
[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(6), 768–770 (1998).
[Crossref]

Fejer, M. M.

M. H. Chou, K. R. Parameswaran, M. M. Fejer, and I. Brener, “Multiple-channel wavelength conversion by use of engineered quasi-phase-matching structures in LiNbO3 waveguides,” Opt. Lett. 24(16), 1157–1159 (1999).
[Crossref] [PubMed]

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-Phase-matched Second harmonic Generation: Tuning and Tolerances,” IEEE Journal Quant. Electron. 28(11), 2631–2654 (1992).

Fischer, R.

Freund, I.

I. Freund, “Nonlinear Diffraction,” Phys. Rev. Lett. 21(19), 1404–1406 (1968).
[Crossref]

Gainutdinov, R. V.

R. V. Gainutdinov, T. R. Volk, O. A. Lysova, I. I. Razgonov, A. L. Tolstikhina, and L. I. Ivleva, “Recording of domains and regular domain patterns in strontium-barium-niobate crystals in the field of atomic force microscope,” Appl. Phys. B 95(3), 505–512 (2009).
[Crossref]

Granzow, T.

Th. Woike, T. Granzow, U. Dörfler, Ch. Poetsch, M. Wöhlecke, and R. Pankrath, “Refractive indices in congruently melting Sr0.61Ba0.39Nb2O6,” Phys. Status Solidi 186, R13–R15 (2001).
[Crossref]

Hanna, D. C.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally Poled Lithium Niobate: A Two-Dimensional Nonlinear Photonic Crystal,” Phys. Rev. Lett. 84(19), 4345–4348 (2000).
[Crossref] [PubMed]

Held, P.

M. Eßer, M. Burianek, P. Held, J. Stade, S. Bulut, C. Wickleder, and M. Mühlberg, “Optical characterization and crystal structure of the novel bronze type CaxBa1-xNb2O6 (x = 0.28; CBN-28),” Cryst. Res. Technol. 38(6), 457–464 (2003).
[Crossref]

Herrero, R.

Ikonnikov, A. A.

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

Imbrock, J.

Ivleva, L. I.

R. V. Gainutdinov, T. R. Volk, O. A. Lysova, I. I. Razgonov, A. L. Tolstikhina, and L. I. Ivleva, “Recording of domains and regular domain patterns in strontium-barium-niobate crystals in the field of atomic force microscope,” Appl. Phys. B 95(3), 505–512 (2009).
[Crossref]

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-Phase-matched Second harmonic Generation: Tuning and Tolerances,” IEEE Journal Quant. Electron. 28(11), 2631–2654 (1992).

Kalinowski, K.

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(6), 768–770 (1998).
[Crossref]

Kivshar, Y.

Kivshar, Y. S.

Kong, Y.

Koynov, K.

Krolikowski, W.

B. Wang, C. Cojocaru, W. Krolikowski, Y. Sheng, and J. Trull, “Transverse single-shot cross-correlation scheme for laser pulse temporal measurement via planar second harmonic generation,” Opt. Express 24(19), 22210–22218 (2016).
[Crossref] [PubMed]

J. Trull, I. Sola, B. Wang, A. Parra, W. Krolikowski, Y. Sheng, R. Vilaseca, and C. Cojocaru, “Ultrashort pulse chirp measurement via transverse second-harmonic generation in strontium barium niobate crystal,” Appl. Phys. Lett. 106(22), 221108 (2015).
[Crossref]

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

V. Roppo, W. Wang, K. Kalinowski, Y. Kong, C. Cojocaru, J. Trull, R. Vilaseca, M. Scalora, W. Krolikowski, and Y. Kivshar, “The role of ferroelectric domain structure in second harmonic generation in random quadratic media,” Opt. Express 18(5), 4012–4022 (2010).
[Crossref] [PubMed]

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(22), 20117–20123 (2009).
[Crossref] [PubMed]

J. Trull, C. Cojocaru, R. Fischer, S. M. Saltiel, K. Staliunas, R. Herrero, R. Vilaseca, D. N Neshev, W. Krolikowski, and Y. S. Kivshar, “Second-harmonic parametric scattering in ferroelectric crystals with disordered nonlinear domain structures,” Opt. Express 15(24), 15868–15877 (2007).
[Crossref] [PubMed]

Lajzerowicz, J.

G. Dolino, J. Lajzerowicz, and M. Vallade, “Second-harmonic Light Scattering by Domains in Ferroelectric Triglycine Sulfate,” Phys. Rev. B 2(6), 2194–2200 (1976).
[Crossref]

Le Grand, Y.

Y. Le Grand, D. Rouede, C. Odin, R. Aubry, and S. Mattauch, “Second-harmonic scattering by domains in RbH2PO4 ferroelectric,” Opt. Commun. 200(1-6), 249–260 (2001).
[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(6), 768–770 (1998).
[Crossref]

Lysova, O. A.

R. V. Gainutdinov, T. R. Volk, O. A. Lysova, I. I. Razgonov, A. L. Tolstikhina, and L. I. Ivleva, “Recording of domains and regular domain patterns in strontium-barium-niobate crystals in the field of atomic force microscope,” Appl. Phys. B 95(3), 505–512 (2009).
[Crossref]

Ma, B.

Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, “Broadband efficient second harmonic generation in media with short-range order,” Appl. Phys. Lett. 91, 011104 (2007).

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-Phase-matched Second harmonic Generation: Tuning and Tolerances,” IEEE Journal Quant. Electron. 28(11), 2631–2654 (1992).

Mattauch, S.

Y. Le Grand, D. Rouede, C. Odin, R. Aubry, and S. Mattauch, “Second-harmonic scattering by domains in RbH2PO4 ferroelectric,” Opt. Commun. 200(1-6), 249–260 (2001).
[Crossref]

Miller, R. C.

R. C. Miller, “Optical harmonic generation in single crystal BaTiO3,” Phys. Rev. A 134(5), A313–A1319 (1998).

Mühlberg, M.

M. Eßer, M. Burianek, P. Held, J. Stade, S. Bulut, C. Wickleder, and M. Mühlberg, “Optical characterization and crystal structure of the novel bronze type CaxBa1-xNb2O6 (x = 0.28; CBN-28),” Cryst. Res. Technol. 38(6), 457–464 (2003).
[Crossref]

N Neshev, D.

Neshev, D. N.

Odin, C.

Y. Le Grand, D. Rouede, C. Odin, R. Aubry, and S. Mattauch, “Second-harmonic scattering by domains in RbH2PO4 ferroelectric,” Opt. Commun. 200(1-6), 249–260 (2001).
[Crossref]

Offerhaus, H. L.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally Poled Lithium Niobate: A Two-Dimensional Nonlinear Photonic Crystal,” Phys. Rev. Lett. 84(19), 4345–4348 (2000).
[Crossref] [PubMed]

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(6), 768–770 (1998).
[Crossref]

Pankrath, R.

Th. Woike, T. Granzow, U. Dörfler, Ch. Poetsch, M. Wöhlecke, and R. Pankrath, “Refractive indices in congruently melting Sr0.61Ba0.39Nb2O6,” Phys. Status Solidi 186, R13–R15 (2001).
[Crossref]

Parameswaran, K. R.

Parra, A.

J. Trull, I. Sola, B. Wang, A. Parra, W. Krolikowski, Y. Sheng, R. Vilaseca, and C. Cojocaru, “Ultrashort pulse chirp measurement via transverse second-harmonic generation in strontium barium niobate crystal,” Appl. Phys. Lett. 106(22), 221108 (2015).
[Crossref]

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in nonlinear dielectrics,” Phys. Rev. A 127(6), 1918–1939 (1962).
[Crossref]

Poetsch, Ch.

Th. Woike, T. Granzow, U. Dörfler, Ch. Poetsch, M. Wöhlecke, and R. Pankrath, “Refractive indices in congruently melting Sr0.61Ba0.39Nb2O6,” Phys. Status Solidi 186, R13–R15 (2001).
[Crossref]

Pospelov, G. I.

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

Razgonov, I. I.

R. V. Gainutdinov, T. R. Volk, O. A. Lysova, I. I. Razgonov, A. L. Tolstikhina, and L. I. Ivleva, “Recording of domains and regular domain patterns in strontium-barium-niobate crystals in the field of atomic force microscope,” Appl. Phys. B 95(3), 505–512 (2009).
[Crossref]

Richardson, D. J.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally Poled Lithium Niobate: A Two-Dimensional Nonlinear Photonic Crystal,” Phys. Rev. Lett. 84(19), 4345–4348 (2000).
[Crossref] [PubMed]

Roppo, V.

Ross, G. W.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally Poled Lithium Niobate: A Two-Dimensional Nonlinear Photonic Crystal,” Phys. Rev. Lett. 84(19), 4345–4348 (2000).
[Crossref] [PubMed]

Rouede, D.

Y. Le Grand, D. Rouede, C. Odin, R. Aubry, and S. Mattauch, “Second-harmonic scattering by domains in RbH2PO4 ferroelectric,” Opt. Commun. 200(1-6), 249–260 (2001).
[Crossref]

Saltiel, S. M.

Scalora, M.

Sheng, Y.

B. Wang, C. Cojocaru, W. Krolikowski, Y. Sheng, and J. Trull, “Transverse single-shot cross-correlation scheme for laser pulse temporal measurement via planar second harmonic generation,” Opt. Express 24(19), 22210–22218 (2016).
[Crossref] [PubMed]

J. Trull, I. Sola, B. Wang, A. Parra, W. Krolikowski, Y. Sheng, R. Vilaseca, and C. Cojocaru, “Ultrashort pulse chirp measurement via transverse second-harmonic generation in strontium barium niobate crystal,” Appl. Phys. Lett. 106(22), 221108 (2015).
[Crossref]

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

Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, “Broadband efficient second harmonic generation in media with short-range order,” Appl. Phys. Lett. 91, 011104 (2007).

Soergel, E.

E. Soergel, “Visualization of ferroelectric domains in bulk single crystals,” Appl. Phys. B 81(6), 729–751 (2005).
[Crossref]

Sola, I.

J. Trull, I. Sola, B. Wang, A. Parra, W. Krolikowski, Y. Sheng, R. Vilaseca, and C. Cojocaru, “Ultrashort pulse chirp measurement via transverse second-harmonic generation in strontium barium niobate crystal,” Appl. Phys. Lett. 106(22), 221108 (2015).
[Crossref]

Stade, J.

M. Eßer, M. Burianek, P. Held, J. Stade, S. Bulut, C. Wickleder, and M. Mühlberg, “Optical characterization and crystal structure of the novel bronze type CaxBa1-xNb2O6 (x = 0.28; CBN-28),” Cryst. Res. Technol. 38(6), 457–464 (2003).
[Crossref]

Staliunas, K.

Tolstikhina, A. L.

R. V. Gainutdinov, T. R. Volk, O. A. Lysova, I. I. Razgonov, A. L. Tolstikhina, and L. I. Ivleva, “Recording of domains and regular domain patterns in strontium-barium-niobate crystals in the field of atomic force microscope,” Appl. Phys. B 95(3), 505–512 (2009).
[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(24), 243901 (2003).

Ulex, M.

A.R. Tunyagi, M. Ulex, and K. Betzler, “Noncollinear Optical frequency Doubling in Strontium Barium Niobate,” Phys. Rev. Lett. 90(24), 243901 (2003).

Vallade, M.

G. Dolino, J. Lajzerowicz, and M. Vallade, “Second-harmonic Light Scattering by Domains in Ferroelectric Triglycine Sulfate,” Phys. Rev. B 2(6), 2194–2200 (1976).
[Crossref]

Vilaseca, R.

Volk, T. R.

R. V. Gainutdinov, T. R. Volk, O. A. Lysova, I. I. Razgonov, A. L. Tolstikhina, and L. I. Ivleva, “Recording of domains and regular domain patterns in strontium-barium-niobate crystals in the field of atomic force microscope,” Appl. Phys. B 95(3), 505–512 (2009).
[Crossref]

Vyunishev, A. M.

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

Wang, B.

B. Wang, C. Cojocaru, W. Krolikowski, Y. Sheng, and J. Trull, “Transverse single-shot cross-correlation scheme for laser pulse temporal measurement via planar second harmonic generation,” Opt. Express 24(19), 22210–22218 (2016).
[Crossref] [PubMed]

J. Trull, I. Sola, B. Wang, A. Parra, W. Krolikowski, Y. Sheng, R. Vilaseca, and C. Cojocaru, “Ultrashort pulse chirp measurement via transverse second-harmonic generation in strontium barium niobate crystal,” Appl. Phys. Lett. 106(22), 221108 (2015).
[Crossref]

Wang, W.

Wickleder, C.

M. Eßer, M. Burianek, P. Held, J. Stade, S. Bulut, C. Wickleder, and M. Mühlberg, “Optical characterization and crystal structure of the novel bronze type CaxBa1-xNb2O6 (x = 0.28; CBN-28),” Cryst. Res. Technol. 38(6), 457–464 (2003).
[Crossref]

Wöhlecke, M.

Th. Woike, T. Granzow, U. Dörfler, Ch. Poetsch, M. Wöhlecke, and R. Pankrath, “Refractive indices in congruently melting Sr0.61Ba0.39Nb2O6,” Phys. Status Solidi 186, R13–R15 (2001).
[Crossref]

Woike, Th.

Th. Woike, T. Granzow, U. Dörfler, Ch. Poetsch, M. Wöhlecke, and R. Pankrath, “Refractive indices in congruently melting Sr0.61Ba0.39Nb2O6,” Phys. Status Solidi 186, R13–R15 (2001).
[Crossref]

Zaitsev, A. I.

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

Zhang, D.

Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, “Broadband efficient second harmonic generation in media with short-range order,” Appl. Phys. Lett. 91, 011104 (2007).

Appl. Phys. B (2)

R. V. Gainutdinov, T. R. Volk, O. A. Lysova, I. I. Razgonov, A. L. Tolstikhina, and L. I. Ivleva, “Recording of domains and regular domain patterns in strontium-barium-niobate crystals in the field of atomic force microscope,” Appl. Phys. B 95(3), 505–512 (2009).
[Crossref]

E. Soergel, “Visualization of ferroelectric domains in bulk single crystals,” Appl. Phys. B 81(6), 729–751 (2005).
[Crossref]

Appl. Phys. Lett. (4)

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(6), 768–770 (1998).
[Crossref]

J. Trull, I. Sola, B. Wang, A. Parra, W. Krolikowski, Y. Sheng, R. Vilaseca, and C. Cojocaru, “Ultrashort pulse chirp measurement via transverse second-harmonic generation in strontium barium niobate crystal,” Appl. Phys. Lett. 106(22), 221108 (2015).
[Crossref]

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

Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, “Broadband efficient second harmonic generation in media with short-range order,” Appl. Phys. Lett. 91, 011104 (2007).

Cryst. Res. Technol. (1)

M. Eßer, M. Burianek, P. Held, J. Stade, S. Bulut, C. Wickleder, and M. Mühlberg, “Optical characterization and crystal structure of the novel bronze type CaxBa1-xNb2O6 (x = 0.28; CBN-28),” Cryst. Res. Technol. 38(6), 457–464 (2003).
[Crossref]

IEEE Journal Quant. Electron. (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-Phase-matched Second harmonic Generation: Tuning and Tolerances,” IEEE Journal Quant. Electron. 28(11), 2631–2654 (1992).

Opt. Commun. (2)

Y. Le Grand, D. Rouede, C. Odin, R. Aubry, and S. Mattauch, “Second-harmonic scattering by domains in RbH2PO4 ferroelectric,” Opt. Commun. 200(1-6), 249–260 (2001).
[Crossref]

M. Scalora and M. E. Crenshaw, “A beam propagation method that handles reflections,” Opt. Commun. 108(4-6), 191–196 (1994).
[Crossref]

Opt. Express (6)

J. Trull, C. Cojocaru, R. Fischer, S. M. Saltiel, K. Staliunas, R. Herrero, R. Vilaseca, D. N Neshev, W. Krolikowski, and Y. S. Kivshar, “Second-harmonic parametric scattering in ferroelectric crystals with disordered nonlinear domain structures,” Opt. Express 15(24), 15868–15877 (2007).
[Crossref] [PubMed]

M. Ayoub, J. Imbrock, and C. Denz, “Second harmonic generation in multi-domain χ(2) media: from disorder to order,” Opt. Express 19(12), 11340 (2011).
[Crossref] [PubMed]

V. Roppo, W. Wang, K. Kalinowski, Y. Kong, C. Cojocaru, J. Trull, R. Vilaseca, M. Scalora, W. Krolikowski, and Y. Kivshar, “The role of ferroelectric domain structure in second harmonic generation in random quadratic media,” Opt. Express 18(5), 4012–4022 (2010).
[Crossref] [PubMed]

B. Wang, C. Cojocaru, W. Krolikowski, Y. Sheng, and J. Trull, “Transverse single-shot cross-correlation scheme for laser pulse temporal measurement via planar second harmonic generation,” Opt. Express 24(19), 22210–22218 (2016).
[Crossref] [PubMed]

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(22), 20117–20123 (2009).
[Crossref] [PubMed]

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

Opt. Lett. (1)

Opt. Mater. Express (1)

Phys. Rev. A (2)

R. C. Miller, “Optical harmonic generation in single crystal BaTiO3,” Phys. Rev. A 134(5), A313–A1319 (1998).

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in nonlinear dielectrics,” Phys. Rev. A 127(6), 1918–1939 (1962).
[Crossref]

Phys. Rev. B (1)

G. Dolino, J. Lajzerowicz, and M. Vallade, “Second-harmonic Light Scattering by Domains in Ferroelectric Triglycine Sulfate,” Phys. Rev. B 2(6), 2194–2200 (1976).
[Crossref]

Phys. Rev. Lett. (4)

I. Freund, “Nonlinear Diffraction,” Phys. Rev. Lett. 21(19), 1404–1406 (1968).
[Crossref]

V. Berger, “Nonlinear Photonic Crystals,” Phys. Rev. Lett. 81(19), 4136–4139 (1998).
[Crossref]

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally Poled Lithium Niobate: A Two-Dimensional Nonlinear Photonic Crystal,” Phys. Rev. Lett. 84(19), 4345–4348 (2000).
[Crossref] [PubMed]

A.R. Tunyagi, M. Ulex, and K. Betzler, “Noncollinear Optical frequency Doubling in Strontium Barium Niobate,” Phys. Rev. Lett. 90(24), 243901 (2003).

Phys. Status Solidi (1)

Th. Woike, T. Granzow, U. Dörfler, Ch. Poetsch, M. Wöhlecke, and R. Pankrath, “Refractive indices in congruently melting Sr0.61Ba0.39Nb2O6,” Phys. Status Solidi 186, R13–R15 (2001).
[Crossref]

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Figures (14)
Fig. 1
Fig. 1 (a) Schematic plot of planar SHG from an as-grown ferroelectric crystal with a random distribution of domains with inverted sign of the quadratic nonlinearity. (b) Phase-mismatch compensation diagram via the use of RLV of modulus G (z corresponds to the optical axis)

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Fig. 2
Fig. 2 (a) SH emission over a plane perpendicular to the optical axis for a structure made with normal distribution of domains with a mean value ρo = 0.9μm and standard deviation σ = 0.3μm as a function of the incident fundamental wavelength. The 0° direction corresponds to emission in the forward direction of the incident beam. (b) The angle of maximum SH emission as a function of wavelength.

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Fig. 3
Fig. 3 Modulus of G needed to compensate the phase mismatch at a given wavelength and emission angle within the plane transverse to the optical axis for SBN crystals.

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Fig. 4
Fig. 4 Experimentally measurement of the SH emission pattern from sample 1 (CBN) and sample 2 (SBN) for two different fundamental wavelengths: 800 nm (blue line; circles) and 1064 nm (green line; triangles). Below each figure we show a picture of the SH pattern at 400 nm for each sample, recorded with a CCD camera placed behind the crystal.

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Fig. 5
Fig. 5 Schematic representation of the experimental setup. HW - half-wave plate, P - polarizer, F - IR blocking filter, S - diffusive screen.

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Fig. 6
Fig. 6 Experimental results for CBN sample. Normalized SH intensity as a function of the emission angle

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Fig. 7
Fig. 7 Overview of experimental results for oo-e and ee-e interactions in the CBN sample. The map of colors shows the modulus of G needed to compensate the phase mismatch at a given wavelength and emission angle (see Fig. 3). Circles represent the maximum SH angle and the bars the angular width of the SH emission, for all different wavelengths used in the experiment.

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Fig. 8
Fig. 8 Experimentally measured angular SH intensity distribution for sample 2 (SBN61). The data was normalized for clarity of presentation.

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Fig. 9
Fig. 9 Overview of experimental results for SBN sample for oo-e and ee-e interactions. The map of colors shows the modulus of G needed to compensate the phase mismatch at a given wavelength and emission angle (see Fig. 3). Circles represent the maximum SH angle and the bars show the angular width of the SH emission, for all different wavelength used in the experiment.

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Fig. 10
Fig. 10 SHG microscopy images corresponding to: (a) as grown CBN crystal (sample 1); (b) artificially poled SABN crystal (sample 2). Note that the scale is different in the two pictures.

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Fig. 11
Fig. 11 (a) 2D domain pattern simulation in real space for the as grown CBN crystal (sample 1); (b) the corresponding Fourier spectrum in the reciprocal space for sample 1; (c) 2D domain pattern simulation in real space for the artificial poled SBN crystal (sample 2) and (d) the corresponding Fourier spectrum in the reciprocal space for sample 2.

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Fig. 12
Fig. 12 (a) Far field SH angular pattern as a function of propagating distance. (b) Far field intensity distribution after x = 70 μm propagation distance within the crystal.

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Fig. 13
Fig. 13 Comparison between the experimental results for as-grown CBN crystal (top) and numerical simulations (bottom) at different wavelengths for the domain distribution shown in Fig. 11(a)

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Fig. 14
Fig. 14 Comparison between the experimental results for SBN crystal, sample 2 (top) and the numerical simulations (bottom) at different wavelengths for the domain distribution shown in Fig. 11(c)

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Equations (2)

Equations on this page are rendered with MathJax. Learn more.

G ( λ , θ ) = k 2 ω 2 + ( 2 k ω ) 2 − 2 k 2 ω ( 2 k ω ) cos ( sin − 1 ( sin θ / n 2 ω ) )
I ( 2 ω ) ∝ I ( ω ) d e f f k ω 2 n ω 4 · n 2 ω · 4 L G 2 · 1 − e − G 2 σ 2 1 + e − G 2 σ 2 + 2 cos ( G ρ o ) e − G 2 σ 2 / 2 .

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