We show that the weak second harmonic light generated from a random distribution of nonlinear domains of transparent Strontium Barium Niobate crystals can display a particularly intense generation in the forward direction. By using a theoretical model able to analyze the optical response of arbitrary distributions of three-dimensional nonlinear volumes of any shape, we found that the physical origin of this observation can be explained in terms of the scattering of light by a single nonlinear domain.

© 2010 Optical Society of America

1. R. C. Miller, “Optical harmonic generation in single crystal BaTiO3,” Phys. Rev. 134, A1313–A1319 (1964). [CrossRef]
2. C. F. Dewey, Jr., and L. O. Hocker, “Enhanced nonlinear optical effects in rotationally twinned crystals,” Appl. Phys. Lett. 26, 442–444 (1975). [CrossRef]
3. M. Baudrier-Raybaut, R. Hadar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, “Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials,” Nature 432, 374–376 (2004). [CrossRef] [PubMed]
4. 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]
5. S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, “Second-harmonic generation from needlelike ferroelectric domains in Sr0.6Ba0.4Nd2O6 single crystals,” Appl. Phys. Lett. 73, 768–770 (1998). [CrossRef]
6. R. Fischer, S. M. Saltiel, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, “Broadband femtosecond frequency doubling in random media,” Appl. Phys. Lett. 89, 191105 (2006). [CrossRef]
7. 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, 15868–15877 (2007). [CrossRef] [PubMed]
8. See for instance, A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE Press, New York, 1997).
9. P. D. Maker, R. W. Terhune, M. Nisenhoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21–22 (1962). [CrossRef]
10. J.-X. Cheng, and X. S. Xie, “Green’s function formulation for third-harmonic generation microscopy,” J. Opt. Soc. Am. B 19, 1604–1610 (2002). [CrossRef]
11. E. Yew, and C. Sheppard, “Effects of axial field components on second harmonic generation microscopy,” Opt. Express 14, 1167–1174 (2006). [CrossRef] [PubMed]
12. See for instance, L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge Univ. Press, Cambridge, 2006), pp. 25–30.
13. R. W. Boyd, Nonlinear Optics, 2nd Ed. (Academic, San Diego, 2003), pp. 37–38.
14. D. L. Andrews, P. Allcock, and A. A. Demidov, “Theory of second harmonic generation in randomly oriented species,” Chem. Phys. 190, 1–9 (1995). [CrossRef]
15. S. Brasselet, V. Le Floch, F. Treussart, J.-F. Roch, J. Zyss, E. Botzung-Appert, and A. Ibanez, “In situ diagnostics of the crystalline nature of single organic nanocrystals by nonlinear microscopy,” Phys. Rev. Lett. 92, 207401 (2004). [CrossRef] [PubMed]

Appl. Phys. Lett.

• S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, “Second-harmonic generation from needlelike ferroelectric domains in Sr0.6Ba0.4Nd2O6 single crystals,” Appl. Phys. Lett. 73, 768–770 (1998). [CrossRef]
• R. Fischer, S. M. Saltiel, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, “Broadband femtosecond frequency doubling in random media,” Appl. Phys. Lett. 89, 191105 (2006). [CrossRef]
• C. F. Dewey, Jr., and L. O. Hocker, “Enhanced nonlinear optical effects in rotationally twinned crystals,” Appl. Phys. Lett. 26, 442–444 (1975). [CrossRef]

Chem. Phys.

• D. L. Andrews, P. Allcock, and A. A. Demidov, “Theory of second harmonic generation in randomly oriented species,” Chem. Phys. 190, 1–9 (1995). [CrossRef]

J. Opt. Soc. Am. B

• J.-X. Cheng, and X. S. Xie, “Green’s function formulation for third-harmonic generation microscopy,” J. Opt. Soc. Am. B 19, 1604–1610 (2002). [CrossRef]

Nature

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

Opt. Express

• 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, 15868–15877 (2007). [CrossRef] [PubMed]
• E. Yew, and C. Sheppard, “Effects of axial field components on second harmonic generation microscopy,” Opt. Express 14, 1167–1174 (2006). [CrossRef] [PubMed]

Phys. Rev.

• R. C. Miller, “Optical harmonic generation in single crystal BaTiO3,” Phys. Rev. 134, A1313–A1319 (1964). [CrossRef]

Phys. Rev. Lett.

• P. D. Maker, R. W. Terhune, M. Nisenhoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21–22 (1962). [CrossRef]
• 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]
• S. Brasselet, V. Le Floch, F. Treussart, J.-F. Roch, J. Zyss, E. Botzung-Appert, and A. Ibanez, “In situ diagnostics of the crystalline nature of single organic nanocrystals by nonlinear microscopy,” Phys. Rev. Lett. 92, 207401 (2004). [CrossRef] [PubMed]

Other

• See for instance, L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge Univ. Press, Cambridge, 2006), pp. 25–30.
• R. W. Boyd, Nonlinear Optics, 2nd Ed. (Academic, San Diego, 2003), pp. 37–38.
• See for instance, A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE Press, New York, 1997).

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