Abstract

We study theoretically and numerically the second harmonic generation in a nonlinear crystal with random distribution of ferroelectric domains. We show that the specific features of disordered domain structure greatly affect the emission pattern of the generated harmonics. This phenomena can be used to characterize the degree of disorder in nonlinear photonic structures.

© 2010 Optical Society of America

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  1. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127, 1918–1939 (1962).
    [CrossRef]
  2. P. A. Franken and J. F. Ward, “Optical harmonics and nonlinear phenomena,” Rev. Mod. Phys. 3523–39 (1963).
    [CrossRef]
  3. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched 2nd harmonic-generation - tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
    [CrossRef]
  4. S. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997).
    [CrossRef]
  5. U. K. Sapaev and G. Assanto, “Efficient high-harmonic generation in engineered quasi-phase matching gratings,” Opt. Express 16, 1–6 (2008).
    [CrossRef] [PubMed]
  6. 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]
  7. M. O. Ramirez, D. Jaque, L. Ivleva, and L. E. Bausa, “Evaluation of ytterbium doped strontium barium niobate as a potential tunable laser crystal in the visible,” J. Appl. Phys. 95, 6185–6191 (2004).
    [CrossRef]
  8. V. V. Shvartsman, W. Kleemann, T. Lukasiewicz, and J. Dec, “Nanopolar structure in SrxBa1-xNb2O6 single crystals tuned by Sr/Ba ratio and investigated by piezoelectric force microscopy,” Phys. Rev. B 77, 054105 (2008).
    [CrossRef]
  9. 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, 505–512 (2009).
    [CrossRef]
  10. M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, “Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials,” Nature (London)  432, 374–376 (2004).
    [CrossRef] [PubMed]
  11. M. Horowitz, A. Bekker, and B. Fischer, “Broad-band 2nd-harmonic generation in SrxBa1-xNb2O6 by spread-spectrum phase-matching with controllable domain gratings,” Appl. Phys. Lett. 62, 2619–2621 (1993).
    [CrossRef]
  12. S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, “Second-harmonic generation from needlelike ferroelectric domains in Sr0.6Ba0.4Nb2O6 single crystals,” Appl. Phys. Lett. 73, 768–770 (1998).
    [CrossRef]
  13. J. J. Romero, D. Jaque, J. García Solé, and A. A. Kaminskii, “Simultaneous generation of coherent light in the three fundamental colors by quasicylindrical ferroelectric domains in Sr0.6Ba0.4(NbO3)2,” Appl. Phys. Lett 81, 4106–4108 (2002).
    [CrossRef]
  14. J. J. Romero, C. Aragó, J. A. Gonzalo, D. Jaque, and J. García Solé, “Spectral and thermal properties of quasiphase- matching second-harmonic generation in Nd3+:Sr0.6Ba0.4(NbO3)2 multi-self-frequency-converter nonlinear crystals,” J. Appl. Phys. 93, 3111–3113 (2003).
    [CrossRef]
  15. A. R. Tunyagi, M. Ulex, and K. Betzler, “Noncollinear optical frequency doubling in strontium barium niobate,” Phys. Rev. Lett. 90, 243901 (2003).
    [CrossRef] [PubMed]
  16. R. Fischer, D. N. Neshev, S. M. Saltiel, W. Krolikowski, and Yu. S. Kivshar, “Broadband femtosecond frequency doubling in random media,” Appl. Phys. Lett. 89, 191105 (2006).
    [CrossRef]
  17. P. Molina, M. O. Ramirez, and L. E. Bausa, “Strontium Barium Niobate as a Multifunctional Two-Dimensional Nonlinear Photonic Glass,” Adv. Funct. Mater. 18, 709–715 (2008).
    [CrossRef]
  18. 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 Yu. Kivshar “Third-harmonic generation via broadband cascading in disordered quadratic nonlinear media,” Opt. Express 17, 20117–20123 (2009).
    [CrossRef] [PubMed]
  19. R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Yu. S. Kivshar, “Monitoring ultrashort pulses by the transverse frequency doubling of counterpropagating pulses in random media,” Appl. Phys. Lett. 91, 031104 (2007).
    [CrossRef]
  20. V. Roppo, D. Dumay, J. Trull, C. Cojocaru, S. M. Saltiel, K. Staliunas, R. Vilaseca, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, “Planar second-harmonic generation with noncollinear pumps in disordered media,” Opt. Express 16, 14192–14199 (2008).
    [CrossRef] [PubMed]
  21. S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, and Yu. S. Kivshar, “Spatiotemporal toroidal waves from the transverse second-harmonic generation,” Opt. Lett. 33, 527–529 (2008).
    [CrossRef] [PubMed]
  22. J. Trull, C. Cojocaru, R. Fischer, S. M. Saltiel, K. Staliunas, R. Herrero, R. Vilaseca, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, “Second-harmonic parametric scattering in ferroelectric crystals with disordered nonlinear domain structures,” Opt. Express 15, 15868–15877 (2007).
    [CrossRef] [PubMed]
  23. J. J. Romero, D. Jaque, and J. Garca Sol, “Diffuse multiself-frequency conversion processes in the blue and green by quasicylindrical ferroelectric domains in Nd3 + :Sr0.6Ba0.4(NbO3)2 laser crystal,” Appl. Phys. Lett. 78, 1961–1963 (2001).
    [CrossRef]
  24. Y. Le Grand, D. Rouede, C. Odiu, R. Aubry, and S. Mattauch, “Second-harmonic scattering by domains in RbH2PO4 ferroelectric,” Opt. Commun. 200, 249–260 (2001).
    [CrossRef]
  25. A. L. Aleksandrovskii, O. A. Gliko, I. I. Naumova, and V. I. Pryalkin, “Linear and nonlinear diffraction gratings in lithium niobate single crystals with a periodic domain structure,” Quantum Electron. 26, 641–643 (1996).
    [CrossRef]
  26. Th. Woike, T. Granzow, U. Dörfler, Ch. Poetsch, M. Wohlecke, and R. Pankrath, ”Refractive Indices of Congruently Melting Sr0:61Ba0:39Nb2O6,” Phys. Stat. Solidi A 186, R13–R15 (2001).
    [CrossRef]
  27. Y. Q. Qin, C. Zhang, and Y. Y. Zhu, et al. “Wave-front engineering by Huygens-Fresnel principle for nonlinear optical interactions in domain engineered structures,” Phys. Rev. Lett. 100, 063902 (2008).
    [CrossRef] [PubMed]
  28. T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie “Nonlinear generation and manipulation of Airy beams,” Nature Photonics 3, 395–398 (2009).
    [CrossRef]
  29. G. Dolino, “Effects of domain shapes on second harmonic scattering in Triglycine Sulfate,” Phys. Rev. B 6, 4025–4035 (1972).
    [CrossRef]
  30. E. Yu. 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]
  31. E. Yu. Morozov and A. S. Chirkin, “Stochastic quasi-phase matching in nonlinear-optical crystals with an irregular domain structure,” Sov. J. Quantum Electron. 34, 227–232 (2004).
    [CrossRef]
  32. I. V. Shutov, I. A. Ozheredov, A. V. Shumitski, and A. S. Chirkin, “Second harmonic generation by femtosecond laser pulses in the Laue scheme,” Opt. Spectroscopy 105, 79–84 (2008).
    [CrossRef]
  33. 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]
  34. M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, ”Inhibition of linear absorption in opaque materials using phase-locked harmonic generation,” Phys. Rev. Lett. 101, 113905 (2008).
    [CrossRef] [PubMed]
  35. M. Scalora and M. E. Crenshaw, “A beam propagation method that handles reflections,” Opt. Commun. 108, 191–196 (1994).
    [CrossRef]
  36. E. Soergel, “Visualization of ferroelectric domains in bulk single crystals,” Appl. Phys. B 81, 729–752 (2005).
    [CrossRef]

2009 (3)

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, 505–512 (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 Yu. Kivshar “Third-harmonic generation via broadband cascading in disordered quadratic nonlinear media,” Opt. Express 17, 20117–20123 (2009).
[CrossRef] [PubMed]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie “Nonlinear generation and manipulation of Airy beams,” Nature Photonics 3, 395–398 (2009).
[CrossRef]

2008 (8)

I. V. Shutov, I. A. Ozheredov, A. V. Shumitski, and A. S. Chirkin, “Second harmonic generation by femtosecond laser pulses in the Laue scheme,” Opt. Spectroscopy 105, 79–84 (2008).
[CrossRef]

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, ”Inhibition of linear absorption in opaque materials using phase-locked harmonic generation,” Phys. Rev. Lett. 101, 113905 (2008).
[CrossRef] [PubMed]

Y. Q. Qin, C. Zhang, and Y. Y. Zhu, et al. “Wave-front engineering by Huygens-Fresnel principle for nonlinear optical interactions in domain engineered structures,” Phys. Rev. Lett. 100, 063902 (2008).
[CrossRef] [PubMed]

V. Roppo, D. Dumay, J. Trull, C. Cojocaru, S. M. Saltiel, K. Staliunas, R. Vilaseca, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, “Planar second-harmonic generation with noncollinear pumps in disordered media,” Opt. Express 16, 14192–14199 (2008).
[CrossRef] [PubMed]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, and Yu. S. Kivshar, “Spatiotemporal toroidal waves from the transverse second-harmonic generation,” Opt. Lett. 33, 527–529 (2008).
[CrossRef] [PubMed]

P. Molina, M. O. Ramirez, and L. E. Bausa, “Strontium Barium Niobate as a Multifunctional Two-Dimensional Nonlinear Photonic Glass,” Adv. Funct. Mater. 18, 709–715 (2008).
[CrossRef]

U. K. Sapaev and G. Assanto, “Efficient high-harmonic generation in engineered quasi-phase matching gratings,” Opt. Express 16, 1–6 (2008).
[CrossRef] [PubMed]

V. V. Shvartsman, W. Kleemann, T. Lukasiewicz, and J. Dec, “Nanopolar structure in SrxBa1-xNb2O6 single crystals tuned by Sr/Ba ratio and investigated by piezoelectric force microscopy,” Phys. Rev. B 77, 054105 (2008).
[CrossRef]

2007 (2)

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

R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Yu. S. Kivshar, “Monitoring ultrashort pulses by the transverse frequency doubling of counterpropagating pulses in random media,” Appl. Phys. Lett. 91, 031104 (2007).
[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]

R. Fischer, D. N. Neshev, S. M. Saltiel, W. Krolikowski, and Yu. S. Kivshar, “Broadband femtosecond frequency doubling in random media,” Appl. Phys. Lett. 89, 191105 (2006).
[CrossRef]

2005 (1)

E. Soergel, “Visualization of ferroelectric domains in bulk single crystals,” Appl. Phys. B 81, 729–752 (2005).
[CrossRef]

2004 (3)

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

M. O. Ramirez, D. Jaque, L. Ivleva, and L. E. Bausa, “Evaluation of ytterbium doped strontium barium niobate as a potential tunable laser crystal in the visible,” J. Appl. Phys. 95, 6185–6191 (2004).
[CrossRef]

E. Yu. Morozov and A. S. Chirkin, “Stochastic quasi-phase matching in nonlinear-optical crystals with an irregular domain structure,” Sov. J. Quantum Electron. 34, 227–232 (2004).
[CrossRef]

2003 (2)

J. J. Romero, C. Aragó, J. A. Gonzalo, D. Jaque, and J. García Solé, “Spectral and thermal properties of quasiphase- matching second-harmonic generation in Nd3+:Sr0.6Ba0.4(NbO3)2 multi-self-frequency-converter nonlinear crystals,” J. Appl. Phys. 93, 3111–3113 (2003).
[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]

2002 (2)

J. J. Romero, D. Jaque, J. García Solé, and A. A. Kaminskii, “Simultaneous generation of coherent light in the three fundamental colors by quasicylindrical ferroelectric domains in Sr0.6Ba0.4(NbO3)2,” Appl. Phys. Lett 81, 4106–4108 (2002).
[CrossRef]

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]

2001 (4)

E. Yu. 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]

Th. Woike, T. Granzow, U. Dörfler, Ch. Poetsch, M. Wohlecke, and R. Pankrath, ”Refractive Indices of Congruently Melting Sr0:61Ba0:39Nb2O6,” Phys. Stat. Solidi A 186, R13–R15 (2001).
[CrossRef]

J. J. Romero, D. Jaque, and J. Garca Sol, “Diffuse multiself-frequency conversion processes in the blue and green by quasicylindrical ferroelectric domains in Nd3 + :Sr0.6Ba0.4(NbO3)2 laser crystal,” Appl. Phys. Lett. 78, 1961–1963 (2001).
[CrossRef]

Y. Le Grand, D. Rouede, C. Odiu, R. Aubry, and S. Mattauch, “Second-harmonic scattering by domains in RbH2PO4 ferroelectric,” Opt. Commun. 200, 249–260 (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 Sr0.6Ba0.4Nb2O6 single crystals,” Appl. Phys. Lett. 73, 768–770 (1998).
[CrossRef]

1997 (1)

S. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997).
[CrossRef]

1996 (1)

A. L. Aleksandrovskii, O. A. Gliko, I. I. Naumova, and V. I. Pryalkin, “Linear and nonlinear diffraction gratings in lithium niobate single crystals with a periodic domain structure,” Quantum Electron. 26, 641–643 (1996).
[CrossRef]

1994 (1)

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

1993 (1)

M. Horowitz, A. Bekker, and B. Fischer, “Broad-band 2nd-harmonic generation in SrxBa1-xNb2O6 by spread-spectrum phase-matching with controllable domain gratings,” Appl. Phys. Lett. 62, 2619–2621 (1993).
[CrossRef]

1992 (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched 2nd harmonic-generation - tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

1972 (1)

G. Dolino, “Effects of domain shapes on second harmonic scattering in Triglycine Sulfate,” Phys. Rev. B 6, 4025–4035 (1972).
[CrossRef]

1963 (1)

P. A. Franken and J. F. Ward, “Optical harmonics and nonlinear phenomena,” Rev. Mod. Phys. 3523–39 (1963).
[CrossRef]

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Akozbek, N.

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, ”Inhibition of linear absorption in opaque materials using phase-locked harmonic generation,” Phys. Rev. Lett. 101, 113905 (2008).
[CrossRef] [PubMed]

Aleksandrovskii, A. L.

A. L. Aleksandrovskii, O. A. Gliko, I. I. Naumova, and V. I. Pryalkin, “Linear and nonlinear diffraction gratings in lithium niobate single crystals with a periodic domain structure,” Quantum Electron. 26, 641–643 (1996).
[CrossRef]

Aragó, C.

J. J. Romero, C. Aragó, J. A. Gonzalo, D. Jaque, and J. García Solé, “Spectral and thermal properties of quasiphase- matching second-harmonic generation in Nd3+:Sr0.6Ba0.4(NbO3)2 multi-self-frequency-converter nonlinear crystals,” J. Appl. Phys. 93, 3111–3113 (2003).
[CrossRef]

Arie, A.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie “Nonlinear generation and manipulation of Airy beams,” Nature Photonics 3, 395–398 (2009).
[CrossRef]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Assanto, G.

Aubry, R.

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

Baudrier-Raybaut, M.

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

Bausa, L. E.

P. Molina, M. O. Ramirez, and L. E. Bausa, “Strontium Barium Niobate as a Multifunctional Two-Dimensional Nonlinear Photonic Glass,” Adv. Funct. Mater. 18, 709–715 (2008).
[CrossRef]

M. O. Ramirez, D. Jaque, L. Ivleva, and L. E. Bausa, “Evaluation of ytterbium doped strontium barium niobate as a potential tunable laser crystal in the visible,” J. Appl. Phys. 95, 6185–6191 (2004).
[CrossRef]

Bekker, A.

M. Horowitz, A. Bekker, and B. Fischer, “Broad-band 2nd-harmonic generation in SrxBa1-xNb2O6 by spread-spectrum phase-matching with controllable domain gratings,” Appl. Phys. Lett. 62, 2619–2621 (1993).
[CrossRef]

Betzler, K.

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

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Bloemer, M. J.

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, ”Inhibition of linear absorption in opaque materials using phase-locked harmonic generation,” Phys. Rev. Lett. 101, 113905 (2008).
[CrossRef] [PubMed]

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched 2nd harmonic-generation - tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Centini, M.

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, ”Inhibition of linear absorption in opaque materials using phase-locked harmonic generation,” Phys. Rev. Lett. 101, 113905 (2008).
[CrossRef] [PubMed]

Chirkin, A. S.

I. V. Shutov, I. A. Ozheredov, A. V. Shumitski, and A. S. Chirkin, “Second harmonic generation by femtosecond laser pulses in the Laue scheme,” Opt. Spectroscopy 105, 79–84 (2008).
[CrossRef]

E. Yu. Morozov and A. S. Chirkin, “Stochastic quasi-phase matching in nonlinear-optical crystals with an irregular domain structure,” Sov. J. Quantum Electron. 34, 227–232 (2004).
[CrossRef]

E. Yu. 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.

Crenshaw, M. E.

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

Dec, J.

V. V. Shvartsman, W. Kleemann, T. Lukasiewicz, and J. Dec, “Nanopolar structure in SrxBa1-xNb2O6 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 Sr0.6Ba0.4Nb2O6 single crystals,” Appl. Phys. Lett. 73, 768–770 (1998).
[CrossRef]

Dolino, G.

G. Dolino, “Effects of domain shapes on second harmonic scattering in Triglycine Sulfate,” Phys. Rev. B 6, 4025–4035 (1972).
[CrossRef]

Dörfler, U.

Th. Woike, T. Granzow, U. Dörfler, Ch. Poetsch, M. Wohlecke, and R. Pankrath, ”Refractive Indices of Congruently Melting Sr0:61Ba0:39Nb2O6,” Phys. Stat. Solidi A 186, R13–R15 (2001).
[CrossRef]

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Dumay, D.

Ellenbogen, T.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie “Nonlinear generation and manipulation of Airy beams,” Nature Photonics 3, 395–398 (2009).
[CrossRef]

Fazio, E.

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, ”Inhibition of linear absorption in opaque materials using phase-locked harmonic generation,” Phys. Rev. Lett. 101, 113905 (2008).
[CrossRef] [PubMed]

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 Sr0.6Ba0.4Nb2O6 single crystals,” Appl. Phys. Lett. 73, 768–770 (1998).
[CrossRef]

Fejer, M. M.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched 2nd harmonic-generation - tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Fischer, B.

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R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Yu. S. Kivshar, “Monitoring ultrashort pulses by the transverse frequency doubling of counterpropagating pulses in random media,” Appl. Phys. Lett. 91, 031104 (2007).
[CrossRef]

R. Fischer, D. N. Neshev, S. M. Saltiel, W. Krolikowski, and Yu. S. Kivshar, “Broadband femtosecond frequency doubling in random media,” Appl. Phys. Lett. 89, 191105 (2006).
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J. J. Romero, D. Jaque, J. García Solé, and A. A. Kaminskii, “Simultaneous generation of coherent light in the three fundamental colors by quasicylindrical ferroelectric domains in Sr0.6Ba0.4(NbO3)2,” Appl. Phys. Lett 81, 4106–4108 (2002).
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A. L. Aleksandrovskii, O. A. Gliko, I. I. Naumova, and V. I. Pryalkin, “Linear and nonlinear diffraction gratings in lithium niobate single crystals with a periodic domain structure,” Quantum Electron. 26, 641–643 (1996).
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J. J. Romero, C. Aragó, J. A. Gonzalo, D. Jaque, and J. García Solé, “Spectral and thermal properties of quasiphase- matching second-harmonic generation in Nd3+:Sr0.6Ba0.4(NbO3)2 multi-self-frequency-converter nonlinear crystals,” J. Appl. Phys. 93, 3111–3113 (2003).
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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).
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Th. Woike, T. Granzow, U. Dörfler, Ch. Poetsch, M. Wohlecke, and R. Pankrath, ”Refractive Indices of Congruently Melting Sr0:61Ba0:39Nb2O6,” Phys. Stat. Solidi A 186, R13–R15 (2001).
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M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, ”Inhibition of linear absorption in opaque materials using phase-locked harmonic generation,” Phys. Rev. Lett. 101, 113905 (2008).
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[CrossRef]

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M. Horowitz, A. Bekker, and B. Fischer, “Broad-band 2nd-harmonic generation in SrxBa1-xNb2O6 by spread-spectrum phase-matching with controllable domain gratings,” Appl. Phys. Lett. 62, 2619–2621 (1993).
[CrossRef]

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M. O. Ramirez, D. Jaque, L. Ivleva, and L. E. Bausa, “Evaluation of ytterbium doped strontium barium niobate as a potential tunable laser crystal in the visible,” J. Appl. Phys. 95, 6185–6191 (2004).
[CrossRef]

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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, 505–512 (2009).
[CrossRef]

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M. O. Ramirez, D. Jaque, L. Ivleva, and L. E. Bausa, “Evaluation of ytterbium doped strontium barium niobate as a potential tunable laser crystal in the visible,” J. Appl. Phys. 95, 6185–6191 (2004).
[CrossRef]

J. J. Romero, C. Aragó, J. A. Gonzalo, D. Jaque, and J. García Solé, “Spectral and thermal properties of quasiphase- matching second-harmonic generation in Nd3+:Sr0.6Ba0.4(NbO3)2 multi-self-frequency-converter nonlinear crystals,” J. Appl. Phys. 93, 3111–3113 (2003).
[CrossRef]

J. J. Romero, D. Jaque, J. García Solé, and A. A. Kaminskii, “Simultaneous generation of coherent light in the three fundamental colors by quasicylindrical ferroelectric domains in Sr0.6Ba0.4(NbO3)2,” Appl. Phys. Lett 81, 4106–4108 (2002).
[CrossRef]

J. J. Romero, D. Jaque, and J. Garca Sol, “Diffuse multiself-frequency conversion processes in the blue and green by quasicylindrical ferroelectric domains in Nd3 + :Sr0.6Ba0.4(NbO3)2 laser crystal,” Appl. Phys. Lett. 78, 1961–1963 (2001).
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M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched 2nd harmonic-generation - tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
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Kaminskii, A. A.

J. J. Romero, D. Jaque, J. García Solé, and A. A. Kaminskii, “Simultaneous generation of coherent light in the three fundamental colors by quasicylindrical ferroelectric domains in Sr0.6Ba0.4(NbO3)2,” Appl. Phys. Lett 81, 4106–4108 (2002).
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S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, “Second-harmonic generation from needlelike ferroelectric domains in Sr0.6Ba0.4Nb2O6 single crystals,” Appl. Phys. Lett. 73, 768–770 (1998).
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Kivshar, Yu. S.

Kleemann, W.

V. V. Shvartsman, W. Kleemann, T. Lukasiewicz, and J. Dec, “Nanopolar structure in SrxBa1-xNb2O6 single crystals tuned by Sr/Ba ratio and investigated by piezoelectric force microscopy,” Phys. Rev. B 77, 054105 (2008).
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Krolikowski, W.

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 Yu. Kivshar “Third-harmonic generation via broadband cascading in disordered quadratic nonlinear media,” Opt. Express 17, 20117–20123 (2009).
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S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, and Yu. S. Kivshar, “Spatiotemporal toroidal waves from the transverse second-harmonic generation,” Opt. Lett. 33, 527–529 (2008).
[CrossRef] [PubMed]

V. Roppo, D. Dumay, J. Trull, C. Cojocaru, S. M. Saltiel, K. Staliunas, R. Vilaseca, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, “Planar second-harmonic generation with noncollinear pumps in disordered media,” Opt. Express 16, 14192–14199 (2008).
[CrossRef] [PubMed]

R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Yu. S. Kivshar, “Monitoring ultrashort pulses by the transverse frequency doubling of counterpropagating pulses in random media,” Appl. Phys. Lett. 91, 031104 (2007).
[CrossRef]

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

R. Fischer, D. N. Neshev, S. M. Saltiel, W. Krolikowski, and Yu. S. Kivshar, “Broadband femtosecond frequency doubling in random media,” Appl. Phys. Lett. 89, 191105 (2006).
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M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, “Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials,” Nature (London)  432, 374–376 (2004).
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Y. Le Grand, D. Rouede, C. Odiu, R. Aubry, and S. Mattauch, “Second-harmonic scattering by domains in RbH2PO4 ferroelectric,” Opt. Commun. 200, 249–260 (2001).
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S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, “Second-harmonic generation from needlelike ferroelectric domains in Sr0.6Ba0.4Nb2O6 single crystals,” Appl. Phys. Lett. 73, 768–770 (1998).
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M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, “Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials,” Nature (London)  432, 374–376 (2004).
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V. V. Shvartsman, W. Kleemann, T. Lukasiewicz, and J. Dec, “Nanopolar structure in SrxBa1-xNb2O6 single crystals tuned by Sr/Ba ratio and investigated by piezoelectric force microscopy,” Phys. Rev. B 77, 054105 (2008).
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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, 505–512 (2009).
[CrossRef]

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched 2nd harmonic-generation - tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
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Y. Le Grand, D. Rouede, C. Odiu, R. Aubry, and S. Mattauch, “Second-harmonic scattering by domains in RbH2PO4 ferroelectric,” Opt. Commun. 200, 249–260 (2001).
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E. Yu. Morozov and A. S. Chirkin, “Stochastic quasi-phase matching in nonlinear-optical crystals with an irregular domain structure,” Sov. J. Quantum Electron. 34, 227–232 (2004).
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E. Yu. 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]

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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).
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A. L. Aleksandrovskii, O. A. Gliko, I. I. Naumova, and V. I. Pryalkin, “Linear and nonlinear diffraction gratings in lithium niobate single crystals with a periodic domain structure,” Quantum Electron. 26, 641–643 (1996).
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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 Yu. Kivshar “Third-harmonic generation via broadband cascading in disordered quadratic nonlinear media,” Opt. Express 17, 20117–20123 (2009).
[CrossRef] [PubMed]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, and Yu. S. Kivshar, “Spatiotemporal toroidal waves from the transverse second-harmonic generation,” Opt. Lett. 33, 527–529 (2008).
[CrossRef] [PubMed]

V. Roppo, D. Dumay, J. Trull, C. Cojocaru, S. M. Saltiel, K. Staliunas, R. Vilaseca, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, “Planar second-harmonic generation with noncollinear pumps in disordered media,” Opt. Express 16, 14192–14199 (2008).
[CrossRef] [PubMed]

R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Yu. S. Kivshar, “Monitoring ultrashort pulses by the transverse frequency doubling of counterpropagating pulses in random media,” Appl. Phys. Lett. 91, 031104 (2007).
[CrossRef]

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

R. Fischer, D. N. Neshev, S. M. Saltiel, W. Krolikowski, and Yu. S. Kivshar, “Broadband femtosecond frequency doubling in random media,” Appl. Phys. Lett. 89, 191105 (2006).
[CrossRef]

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

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S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, “Second-harmonic generation from needlelike ferroelectric domains in Sr0.6Ba0.4Nb2O6 single crystals,” Appl. Phys. Lett. 73, 768–770 (1998).
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I. V. Shutov, I. A. Ozheredov, A. V. Shumitski, and A. S. Chirkin, “Second harmonic generation by femtosecond laser pulses in the Laue scheme,” Opt. Spectroscopy 105, 79–84 (2008).
[CrossRef]

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Th. Woike, T. Granzow, U. Dörfler, Ch. Poetsch, M. Wohlecke, and R. Pankrath, ”Refractive Indices of Congruently Melting Sr0:61Ba0:39Nb2O6,” Phys. Stat. Solidi A 186, R13–R15 (2001).
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Th. Woike, T. Granzow, U. Dörfler, Ch. Poetsch, M. Wohlecke, and R. Pankrath, ”Refractive Indices of Congruently Melting Sr0:61Ba0:39Nb2O6,” Phys. Stat. Solidi A 186, R13–R15 (2001).
[CrossRef]

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A. L. Aleksandrovskii, O. A. Gliko, I. I. Naumova, and V. I. Pryalkin, “Linear and nonlinear diffraction gratings in lithium niobate single crystals with a periodic domain structure,” Quantum Electron. 26, 641–643 (1996).
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P. Molina, M. O. Ramirez, and L. E. Bausa, “Strontium Barium Niobate as a Multifunctional Two-Dimensional Nonlinear Photonic Glass,” Adv. Funct. Mater. 18, 709–715 (2008).
[CrossRef]

M. O. Ramirez, D. Jaque, L. Ivleva, and L. E. Bausa, “Evaluation of ytterbium doped strontium barium niobate as a potential tunable laser crystal in the visible,” J. Appl. Phys. 95, 6185–6191 (2004).
[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, 505–512 (2009).
[CrossRef]

Romero, J. J.

J. J. Romero, C. Aragó, J. A. Gonzalo, D. Jaque, and J. García Solé, “Spectral and thermal properties of quasiphase- matching second-harmonic generation in Nd3+:Sr0.6Ba0.4(NbO3)2 multi-self-frequency-converter nonlinear crystals,” J. Appl. Phys. 93, 3111–3113 (2003).
[CrossRef]

J. J. Romero, D. Jaque, J. García Solé, and A. A. Kaminskii, “Simultaneous generation of coherent light in the three fundamental colors by quasicylindrical ferroelectric domains in Sr0.6Ba0.4(NbO3)2,” Appl. Phys. Lett 81, 4106–4108 (2002).
[CrossRef]

J. J. Romero, D. Jaque, and J. Garca Sol, “Diffuse multiself-frequency conversion processes in the blue and green by quasicylindrical ferroelectric domains in Nd3 + :Sr0.6Ba0.4(NbO3)2 laser crystal,” Appl. Phys. Lett. 78, 1961–1963 (2001).
[CrossRef]

Roppo, V.

Rosencher, E.

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

Rouede, D.

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

Saltiel, S. M.

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 Yu. Kivshar “Third-harmonic generation via broadband cascading in disordered quadratic nonlinear media,” Opt. Express 17, 20117–20123 (2009).
[CrossRef] [PubMed]

V. Roppo, D. Dumay, J. Trull, C. Cojocaru, S. M. Saltiel, K. Staliunas, R. Vilaseca, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, “Planar second-harmonic generation with noncollinear pumps in disordered media,” Opt. Express 16, 14192–14199 (2008).
[CrossRef] [PubMed]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, and Yu. S. Kivshar, “Spatiotemporal toroidal waves from the transverse second-harmonic generation,” Opt. Lett. 33, 527–529 (2008).
[CrossRef] [PubMed]

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

R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Yu. S. Kivshar, “Monitoring ultrashort pulses by the transverse frequency doubling of counterpropagating pulses in random media,” Appl. Phys. Lett. 91, 031104 (2007).
[CrossRef]

R. Fischer, D. N. Neshev, S. M. Saltiel, W. Krolikowski, and Yu. S. Kivshar, “Broadband femtosecond frequency doubling in random media,” Appl. Phys. Lett. 89, 191105 (2006).
[CrossRef]

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Scalora, M.

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, ”Inhibition of linear absorption in opaque materials using phase-locked harmonic generation,” Phys. Rev. Lett. 101, 113905 (2008).
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I. V. Shutov, I. A. Ozheredov, A. V. Shumitski, and A. S. Chirkin, “Second harmonic generation by femtosecond laser pulses in the Laue scheme,” Opt. Spectroscopy 105, 79–84 (2008).
[CrossRef]

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I. V. Shutov, I. A. Ozheredov, A. V. Shumitski, and A. S. Chirkin, “Second harmonic generation by femtosecond laser pulses in the Laue scheme,” Opt. Spectroscopy 105, 79–84 (2008).
[CrossRef]

Shvartsman, V. V.

V. V. Shvartsman, W. Kleemann, T. Lukasiewicz, and J. Dec, “Nanopolar structure in SrxBa1-xNb2O6 single crystals tuned by Sr/Ba ratio and investigated by piezoelectric force microscopy,” Phys. Rev. B 77, 054105 (2008).
[CrossRef]

Sibilia, C.

M. Centini, V. Roppo, E. Fazio, F. Pettazzi, C. Sibilia, J. W. Haus, J. V. Foreman, N. Akozbek, M. J. Bloemer, and M. Scalora, ”Inhibition of linear absorption in opaque materials using phase-locked harmonic generation,” Phys. Rev. Lett. 101, 113905 (2008).
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Staliunas, K.

Sukhorukov, A. A.

R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Yu. S. Kivshar, “Monitoring ultrashort pulses by the transverse frequency doubling of counterpropagating pulses in random media,” Appl. Phys. Lett. 91, 031104 (2007).
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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).
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[CrossRef] [PubMed]

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X. Vidal and J. Martorell, “Generation of Light in Media with a Random Distribution of Nonlinear Domains,” Phys. Rev. Lett. 97, 013902 (2006).
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Th. Woike, T. Granzow, U. Dörfler, Ch. Poetsch, M. Wohlecke, and R. Pankrath, ”Refractive Indices of Congruently Melting Sr0:61Ba0:39Nb2O6,” Phys. Stat. Solidi A 186, R13–R15 (2001).
[CrossRef]

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E. Yu. 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).
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Y. Q. Qin, C. Zhang, and Y. Y. Zhu, et al. “Wave-front engineering by Huygens-Fresnel principle for nonlinear optical interactions in domain engineered structures,” Phys. Rev. Lett. 100, 063902 (2008).
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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]

R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Yu. S. Kivshar, “Monitoring ultrashort pulses by the transverse frequency doubling of counterpropagating pulses in random media,” Appl. Phys. Lett. 91, 031104 (2007).
[CrossRef]

J. J. Romero, D. Jaque, and J. Garca Sol, “Diffuse multiself-frequency conversion processes in the blue and green by quasicylindrical ferroelectric domains in Nd3 + :Sr0.6Ba0.4(NbO3)2 laser crystal,” Appl. Phys. Lett. 78, 1961–1963 (2001).
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E. Yu. 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).
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[CrossRef] [PubMed]

Phys. Stat. Solidi A (1)

Th. Woike, T. Granzow, U. Dörfler, Ch. Poetsch, M. Wohlecke, and R. Pankrath, ”Refractive Indices of Congruently Melting Sr0:61Ba0:39Nb2O6,” Phys. Stat. Solidi A 186, R13–R15 (2001).
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Supplementary Material (4)

» Media 1: MOV (106 KB)     
» Media 2: MOV (93 KB)     
» Media 3: MOV (136 KB)     
» Media 4: MOV (178 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

(a) - schematic representation of the second harmonic generation in multi-domain disordered structure in ferroelectric crystal. (b–c) Experimentally recorded various emission patterns in SHG in three different samples of as-grown SBN crystal with random domain distribution. (b) planar (almost 360°) transverse emission. The red arrow indicates the direction of the fundamental beam; (c) examples of SH emission from two different samples of as-grown SBN crystal; top graph: narrow angle forward emission with two distinctive maxima; bottom graph: wide angle forward emission.

Fig. 2.
Fig. 2.

Examples of particular realizations of the random 2D domain pattern. (a) ρ 0 = 0.3μm, σ = 0.05μm, (b) ρ 0 = 0.3μm, σ = 0.1μm, (c) ρ0 = 0.3μm, σ = 0.1μm with agglomerations of the domains. The insets depict histograms of the resulting domain diameters. Bottom row: corresponding spatial Fourier spectrum of the domain patterns. Note that the agglomeration of domains shown in (c) results drastically changes its spatial Fourier spectrum and hence will have a strong impact on SH emission.

Fig. 3.
Fig. 3.

Diagram illustrating few possible scenarios of the phase matching condition for the SH emission in medium with disordered ferroelectric domain structure. Dashed green arrows indicate possible directions of strong emission of SH. (a–b) same disordered domain distribution, different wavelengths of the fundamental wave - λF (λF is shorter in case (b)); (c) random domain distribution with the mean value significantly smaller than in cases (a–b)

Fig. 4.
Fig. 4.

Theoretically predicted angular distribution of the second harmonic emission in the quadratic crystal with random domain distribution [Eq. (1)]. (a) constant average domain diameter ρ 0 = 1μm, (b) constant dispersion σ = 1μm. In all simulations we assumed λF = 1μm. (c) The effect of varying of the wavelength of the fundamental wave on the emission angle of the SH. Here ρ 0 = 1μm and σ = 1μm. In all graphs the dashed line represents phase matching condition with a single reciprocal vector |G⃗mean | = π/ρ 0.

Fig. 5.
Fig. 5.

Numerical simulations - generation of the second harmonic by a femtosecond laser pulse in a disordered structure. A fundamental pulse in initially placed in the air and propagates toward the sample in the right direction. When it reaches the first air/sample interface a portion is backward reflected and the remaining part keep propagating forward. Due to the presence of the nonlinearity a SH pulse is generated and propagates forward. Left column: Spatial intensity distribution of the fundamental (Media 1) (a) and second harmonics (b-d) for three different random samples in three different numerical simulations. Middle column - the structure of the interacting waves in the spatial Fourier space. Note differences in the emission angle. Right column - energy of the fundamental and second harmonics as a function of the time of propagation. The statistical parameters of the domain distribution are: (b) - ρ 0 = 3μm, σ = 0.3μm, λF = 1.064μm, here the sample is bigger to arrange an enough number of domains (Media 2); (c) ρ 0 = 0.9μm, σ = 0.1μm, λF = 1.064μm (Media 3); (d) ρ 0 = 0.3μm, σ = 0.05μm, λF = 0.800μm (Media 4).

Equations (10)

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I ( 2 ω ) I ( ω ) d e f f f ( q , ρ 0 , σ )
f ( q , ρ 0 , σ ) = 4 L q 2 . 1 e q 2 σ 2 1 + e σ 2 q 2 + 2 cos ( q ρ 0 ) e σ 2 q 2 / 2 .
H = x ̂ l = 1 ( H y ( z , y , t ) e il ( kz ωt ) + c . c . )
E = y ̂ l = 1 ( E y ( z , y , t ) e il ( kz ωt ) + c . c . ) + z ̂ l = 1 ( E z ( z , y , t ) e il ( kz ωt ) + c . c . )
H x τ = l ( H x + E z sin θ i + E y cos θ i ) E z y ˜ + E x ξ
E y τ = l ( E y + H x cos θ i ) 4 π ( J y i β l P y ) + 4 β l P y , NL P y , NL τ + H x ξ
E z τ = l ( E z + H x sin θ i ) 4 π ( J z i β l P z ) + 4 β l P z , NL P z , NL τ H x y ˜
J y τ = ( 2 i β l γ ) J y + ( β l 2 + β l β r 2 ) P y + π ω p 2 ω 0 2 E y
J z τ = ( 2 i β l γ ) J z + ( β l 2 + β l β r 2 ) P z + π ω p 2 ω 0 2 E z
J y = P y τ , J z = P z τ

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