Abstract

We study parametric frequency conversion in quadratic nonlinear media with disordered ferroelectric domains. We demonstrate that disorder allows realizing broadband third-harmonic generation via cascading of two second-order quasi-phase matched nonlinear processes. We analyze both spatial and polarization properties of the emitted radiation and find the results in agreement with our theoretical predictions.

© 2009 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. M. Lu and X. F. Chen, “Multiple quasi-phase matching in engineered domain-inverted optical superlattice,” J. Nonlininear Opt. Phys. Mater. 16, 185–198 (2007).
    [Crossref]
  7. 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, 2619–2654 (1993).
    [Crossref]
  8. S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, “Second-harmonic generation from needle-like ferroelectric domains in Sr0.6Ba0.4Nb2O6 single crystals,” Appl. Phys. Lett. 73, 768–770 (1998).
    [Crossref]
  9. 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]
  10. 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]
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    [Crossref]
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    [Crossref]
  13. M. O. Ramirez, J. J. Romero, P. Molina, and L. E. Bausa, “Near infrared and visible tunability from a diode pumped Nd3+ activated strontium barium niobate laser crystal,” Appl. Phys. B 81, 827–830 (2005).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  21. N. Fujioka, S. Ashihara, H. Ono, T. Shimura, and K. Kuroda, “Cascaded third-harmonic generation of ultrashort optical pulses in two-dimensional quasi-phase-matching gratings,” J. Opt. Soc. Am. B 24, 2394–2405 (2007).
    [Crossref]
  22. Y. Sheng, S. M. Saltiel, and K. Koynov, “Cascaded third-harmonic generation in single short-range-ordered nonlinear photonic crystal,” Opt. Lett. 34, 656–658 (2009).
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  23. 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]

2009 (1)

2008 (3)

2007 (4)

M. Lu and X. F. Chen, “Multiple quasi-phase matching in engineered domain-inverted optical superlattice,” J. Nonlininear Opt. Phys. Mater. 16, 185–198 (2007).
[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]

N. Fujioka, S. Ashihara, H. Ono, T. Shimura, and K. Kuroda, “Cascaded third-harmonic generation of ultrashort optical pulses in two-dimensional quasi-phase-matching gratings,” J. Opt. Soc. Am. B 24, 2394–2405 (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]

2006 (1)

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 (2)

S. M. Saltiel, A. A. Sukhorukov, and Y. S. Kivshar, “Multistep parametric processes in nonlinear optics,” Prog. Opt. 47, 1–73 (2005).
[Crossref]

M. O. Ramirez, J. J. Romero, P. Molina, and L. E. Bausa, “Near infrared and visible tunability from a diode pumped Nd3+ activated strontium barium niobate laser crystal,” Appl. Phys. B 81, 827–830 (2005).
[Crossref]

2004 (1)

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]

2003 (2)

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

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]

2002 (1)

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]

2001 (1)

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 needle-like ferroelectric domains in Sr0.6Ba0.4Nb2O6 single crystals,” Appl. Phys. Lett. 73, 768–770 (1998).
[Crossref]

1997 (2)

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, 2619–2654 (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]

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]

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]

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]

Ashihara, S.

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]

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, J. J. Romero, P. Molina, and L. E. Bausa, “Near infrared and visible tunability from a diode pumped Nd3+ activated strontium barium niobate laser crystal,” Appl. Phys. B 81, 827–830 (2005).
[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, 2619–2654 (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]

Bosenberg, W. R.

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]

Chen, X. F.

M. Lu and X. F. Chen, “Multiple quasi-phase matching in engineered domain-inverted optical superlattice,” J. Nonlininear Opt. Phys. Mater. 16, 185–198 (2007).
[Crossref]

Cojocaru, C.

DeMattei, R. C.

S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, “Second-harmonic generation from needle-like ferroelectric domains in Sr0.6Ba0.4Nb2O6 single crystals,” Appl. Phys. Lett. 73, 768–770 (1998).
[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.

Feigelson, R. S.

S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, “Second-harmonic generation from needle-like 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.

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, 2619–2654 (1993).
[Crossref]

Fischer, R.

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]

Franken, P. A.

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

Fujioka, N.

García Solé, 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]

Gonzalo, J. A.

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]

Haidar, R.

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]

Herrero, R.

Hollberg, L.

Horowitz, M.

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, 2619–2654 (1993).
[Crossref]

Jaque, D.

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]

Jundt, D. H.

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]

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).
[Crossref]

Kawai, S.

S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, “Second-harmonic generation from needle-like ferroelectric domains in Sr0.6Ba0.4Nb2O6 single crystals,” Appl. Phys. Lett. 73, 768–770 (1998).
[Crossref]

Kivshar, Y. S.

S. M. Saltiel, A. A. Sukhorukov, and Y. S. Kivshar, “Multistep parametric processes in nonlinear optics,” Prog. Opt. 47, 1–73 (2005).
[Crossref]

Kivshar, Yu. S.

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]

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]

Koynov, K.

Krolikowski, W.

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]

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]

Kupecek, Ph.

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]

Kuroda, K.

Le Grand, Y.

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]

Lee, H. S.

S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, “Second-harmonic generation from needle-like ferroelectric domains in Sr0.6Ba0.4Nb2O6 single crystals,” Appl. Phys. Lett. 73, 768–770 (1998).
[Crossref]

Lemasson, Ph.

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]

Levenson, M. D.

Lu, M.

M. Lu and X. F. Chen, “Multiple quasi-phase matching in engineered domain-inverted optical superlattice,” J. Nonlininear Opt. Phys. Mater. 16, 185–198 (2007).
[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)
[Crossref]

Mattauch, S.

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]

Ming, N. B.

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]

Molina, P.

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, J. J. Romero, P. Molina, and L. E. Bausa, “Near infrared and visible tunability from a diode pumped Nd3+ activated strontium barium niobate laser crystal,” Appl. Phys. B 81, 827–830 (2005).
[Crossref]

Neshev, D. N.

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]

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]

Odiu, C.

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]

Ogawa, T.

S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, “Second-harmonic generation from needle-like ferroelectric domains in Sr0.6Ba0.4Nb2O6 single crystals,” Appl. Phys. Lett. 73, 768–770 (1998).
[Crossref]

Ono, H.

Pershan, P. S.

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]

Pfister, O.

Ramirez, M. O.

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, J. J. Romero, P. Molina, and L. E. Bausa, “Near infrared and visible tunability from a diode pumped Nd3+ activated strontium barium niobate laser crystal,” Appl. Phys. B 81, 827–830 (2005).
[Crossref]

Romero, J. J.

M. O. Ramirez, J. J. Romero, P. Molina, and L. E. Bausa, “Near infrared and visible tunability from a diode pumped Nd3+ activated strontium barium niobate laser crystal,” Appl. Phys. B 81, 827–830 (2005).
[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]

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]

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]

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Y. Sheng, S. M. Saltiel, and K. Koynov, “Cascaded third-harmonic generation in single short-range-ordered nonlinear photonic crystal,” Opt. Lett. 34, 656–658 (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]

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]

S. M. Saltiel, A. A. Sukhorukov, and Y. S. Kivshar, “Multistep parametric processes in nonlinear optics,” Prog. Opt. 47, 1–73 (2005).
[Crossref]

Sapaev, U. K.

Sheng, Y.

Shimura, T.

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).
[Crossref]

S. M. Saltiel, A. A. Sukhorukov, and Y. S. Kivshar, “Multistep parametric processes in nonlinear optics,” Prog. Opt. 47, 1–73 (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]

VanBaak, D. A.

Vilaseca, R.

Ward, J. F.

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

Wells, J. S.

Zhu, S.

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]

Zhu, Y. Y.

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]

Zink, L.

Adv. Funct. Mater. (1)

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]

Appl. Phys. B (1)

M. O. Ramirez, J. J. Romero, P. Molina, and L. E. Bausa, “Near infrared and visible tunability from a diode pumped Nd3+ activated strontium barium niobate laser crystal,” Appl. Phys. B 81, 827–830 (2005).
[Crossref]

Appl. Phys. Lett (1)

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]

Appl. Phys. Lett. (4)

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]

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]

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, 2619–2654 (1993).
[Crossref]

S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, “Second-harmonic generation from needle-like ferroelectric domains in Sr0.6Ba0.4Nb2O6 single crystals,” Appl. Phys. Lett. 73, 768–770 (1998).
[Crossref]

IEEE J. Quantum Electron. (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]

J. Appl. Phys. (1)

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. Nonlininear Opt. Phys. Mater. (1)

M. Lu and X. F. Chen, “Multiple quasi-phase matching in engineered domain-inverted optical superlattice,” J. Nonlininear Opt. Phys. Mater. 16, 185–198 (2007).
[Crossref]

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

Nature (London) (1)

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]

Opt. Commun. (1)

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]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. (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]

Phys. Rev. Lett. (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]

Prog. Opt. (1)

S. M. Saltiel, A. A. Sukhorukov, and Y. S. Kivshar, “Multistep parametric processes in nonlinear optics,” Prog. Opt. 47, 1–73 (2005).
[Crossref]

Rev. Mod. Phys. (1)

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

Science (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]

Supplementary Material (1)

» Media 1: MOV (3382 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

(a) Schematic of the experimental setup. The multi-domain structure of the SBN sample is schematically shown. L — lens, WP — half wave-plate, BPF — band pass filter, P — polarizer. (b) Power of the third harmonics vs. the input power of the fundamental beam (measured with Ophir Laser Power Head PD300-UV, accuracy ±3%). Solid line represents a cubic fit. (c) Experimentally recorded transverse intensity distribution of the second (top) and third (bottom) harmonics.

Fig. 2.
Fig. 2.

Diagram of the phase matching for cascaded third harmonic generation in random SBN crystal. Reciprocal vectors G m1 and G m2 phase match the seconds and third harmonics generation, respectively. Note the broadening of the emission angle for the THG.

Fig. 3.
Fig. 3.

The power of the ordinary (blue) and extraordinary (red) components of the second (a) and third (b) harmonic as a function of the input polarization angle of the fundamental beam. 0° corresponds to the extraordinary fundamental wave. Points - experimental data; lines - theoretical fit — Eqs.(12).

Fig. 4.
Fig. 4.

Numerically results (Media 1). Generation of the second and third harmonics by a femtosecond laser pulse in a disordered structure. Left column: Spatial intensity distribution of the fundamental, second, and third harmonics (from the top to bottom). Middle column- the transverse structure of the interacting waves in the Fourier space. Note the much broader emission angle for the third harmonics. Right column - energy of the fundamental, second, and third harmonics as a function of the time of propagation of the fundamental pulse in the SBN crystal.

Equations (2)

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I(2ω)(e) I(ω)2 (cos4α+R1sin4α),I(2ω)(o)=0,
I(3ω)(e)I(ω)3(cos6α+R2sin4αcos2α),I(3ω)(o)I(ω)3(sin6α+R3sin2αcos4α),

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