Abstract

We describe second-harmonic generation (SHG) in ZnO(0002) wurtzite structures with [11¯00]/(1102) twin boundaries using the simplified bond hyperpolarizability model (SBHM). We show explicitly how the reflective second-harmonic generation (RSHG) intensity profile for the s-incoming fundamental and s-outgoing SHG polarized light arise via superposition of the SHG dipole fields. The nonlinear fields originate from anharmonic motions of electric charges along each bond. The total dipole fields from within the ZnO bulk sum up to zero but produce a constructive SHG radiation from the unreduced surface and twin boundary. In addition, we compare the third-order susceptibility tensor obtained from group theory and the SBHM and calculate the values for the nonzero components. We found that the off-resonance RSHG intensity data in diatomic wurtzite structures even with the presence of twin boundaries can be modeled using only three independent fitting parameters, namely, the effective bulk, reduced surface, and twin boundary SHG hyperpolarizability. The results show that the SBHM can be used to investigate impurities and surface defects in ZnO as well as their contribution to nonlinear radiation with potential application to frequency conversion in nanoscale optical circuitry.

© 2019 Optical Society of America

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References

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    [Crossref]
  6. P. Ewald, “Theory of dispersion, reflection, and refraction,” Ann. Phys. 354, 1–38 (1916).
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  7. C. W. Oseen, “The interaction between two electric dipoles and the rotation of the polarization plane in crystals and liquids,” Ann. Phys. 353, 1–56 (1915).
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    [Crossref]
  9. J. A. Litwin, J. E. Sipe, and H. M. van Driel, “Picosecond and nanosecond laser-induced second-harmonic generation from centrosymmetric semiconductors,” Phys. Rev. B 31, 5543–5546 (1984).
    [Crossref]
  10. J. E. Sipe, D. J. Moss, and H. M. van Driel, “Phenomenological theory of optical second- and third-harmonic generation from cubic centrosymmetric crystals,” Phys. Rev. B 35, 1129–1141 (1987).
    [Crossref]
  11. V. Mizrahi and J. E. Sipe, “Phenomenological treatment of surface second-harmonic generation,” J. Opt. Soc. Am. B 5, 660–667 (1988).
    [Crossref]
  12. H. J. Peng, E. J. Adles, J.-F. Wang, and D. E. Aspnes, “Relative bulk and interface contributions to optical second-harmonic generation in silicon,” Phys. Rev. B 72, 205203 (2005).
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  13. E. J. Adles and D. E. Aspnes, “Application of the anisotropic bond model to second-harmonic generation from amorphous media,” Phys. Rev. B 77, 165102 (2008).
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    [Crossref]
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    [Crossref]
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    [Crossref]
  17. H. Hardhienata, “How nonlinear optics can be simplified to study molecular deposition and surface vicinality of a Si(001) interface,” IOP Conf. Series: Earth Environ. Sci. 31, 012017 (2016).
    [Crossref]
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    [Crossref]
  19. E. S. Jatirian-Foltides, J. J. Escobedo-Alatorre, P. A. Márquez-Aguilar, H. Hardhienata, K. Hingerl, and A. Alejo-Molinaa, “About the calculation of the second-order susceptibility tensorial elements for crystals using group theory,” Rev. Mex. Fis. E 62, 5–13 (2016).
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    [Crossref]
  21. H. Hardhienata, A. Alejo-Molina, C. Reitböck, A. Prylepa, D. Stifter, and K. Hingerl, “Bulk dipolar contribution to second-harmonic generation in zincblende,” J. Opt. Soc. Am. B 33, 195–201 (2016).
    [Crossref]
  22. B. S. Mendoza and W. L. Mochán, “Local field effect in the second harmonic generation spectra of Si surfaces,” Phys. Rev. B 53, R10473 (1996).
    [Crossref]
  23. A. Alejo-Molina, “The role of Kleinman symmetry in the simplified bond hyperpolarizability model,” IOP Conf. Series: Earth Environ. Sci. 31, 012020 (2016).
    [Crossref]
  24. V. Mizrahi and J. E. Sipe, “Phenomenological treatment of surface second-harmonic generation,” J. Opt. Soc. Am. B 5, 233402 (1988).
    [Crossref]
  25. B. S. Mendoza and W. L. Mochán, “Exactly solvable model of surface second harmonic generation,” Phys. Rev. B 53, 4999–5006 (1996).
    [Crossref]
  26. K. Y. Lo, Y. J. Huang, Z. C. Feng, W. E. Fenwick, M. Pan, and I. T. Ferguson, “Reflective second harmonic generation from ZnO thin films: a study on the Zn-O bonding,” Appl. Phys. Lett. 90, 161904 (2007).
    [Crossref]
  27. K. Y. Lo, S. Lo, Y. C. Feng, T. Tite, J. Y. Huang, Y. J. Huang, R. Chang, and S. Chu, “Optical second harmonic generation from the twin boundary of ZnO thin films grown on silicon,” Appl. Phys. Lett 92, 091909 (2008).
    [Crossref]
  28. M. C. Laciprente and M. Centrin, “Second harmonic generation from ZnO films and nanostructures,” Appl. Phys. Rev. 2, 031302 (2015).
    [Crossref]
  29. J. C. Johnson, H. Yan, R. D. Schaller, P. B. Petersen, P. Yang, and R. J. Saykally, “Near-field imaging of nonlinear optical mixing in single zinc oxide nanowires,” Nano Lett. 2, 279–283 (2002).
    [Crossref]
  30. Y. Ogata, A. Vorobyev, and C. Guo, “Optical third harmonic generation using nickel nanostructure-covered microcube structures,” Materials 11, 501 (2018).
    [Crossref]
  31. G. Grinblat, M. Rahmani, E. Cortes, M. Caldarola, D. Comedi, S. A. Maier, and A. V. Bragas, “High-efficiency second harmonic generation from a single hybrid ZnO nanowire/Au plasmonic nano-oligomer,” Nano Lett. 14, 6660–6665 (2014).
    [Crossref]
  32. H. Linnenbank, Y. Grynko, J. Foerstner, and S. Linden, “Second harmonic generation spectroscopy on hybrid plasmonic/dielectric nanoantennas,” Light: Sci. Appl. 5, e16013 (2016).
    [Crossref]
  33. F. B. Afruz, M. J. Tafreshi, M. R. Mohammadizadeh, and M. Fazli, “Structural and electronic properties of hydrogen doped wurtzite ZnO,” Comput. Mater. Sci. 143, 232–239 (2018).
    [Crossref]
  34. J. Kwon and M. C. Downer, “Second harmonic and reflectance anisotropy spectroscopy of vicinal Si(001)/SiO2 interfaces: experiment and simplified microscope model,” Phys. Rev. B 73, 195330 (2006).
    [Crossref]
  35. K.-D. Bauer and K. Hingerl, “Bulk quadrupole contribution to second harmonic generation from classical oscillator model in silicon,” Opt. Express 25, 26567–26580 (2017).
    [Crossref]
  36. Y. Ogata, “Optical second harmonic generation from nanostructure-covered micro-cubes on nickel,” Opt. Mater. Express 6, 1520–1529 (2016).
    [Crossref]
  37. A. A. Maradudin and D. L. Mills, “Scattering and absorption of electromagnetic radiation by a semi-infinite medium in the presence of surface roughness,” Phys. Rev. B 11, 1392–1415 (1975).
    [Crossref]
  38. Y. Ogata, N. Anh Tuan, Y. Miyauchi, and G. Mizutani, “Optical second harmonic generation from Pt nanowires with boomerang-like cross-sectional shapes,” J. Appl. Phys. 110, 044301 (2011).
    [Crossref]
  39. Y. Ogata and C. Guo, “Nonlinear optics on nano/micro-hierarchical structures on metals: focus on symmetric and plasmonic effects,” Nano Rev. Exp. 8, 1339545 (2017).
    [Crossref]
  40. Y. Yan, M. M. Al-Jassim, M. F. Chisholm, L. A. Boatner, S. J. Pennycook, and M. Oxley, “[11¯00]/(1102) twin boundaries in wurtzite ZnO and group-III-nitrides,” Phys. Rev. B 71, 041309(R) (2005).
    [Crossref]
  41. B. S. Mendoza, J. Wei, and M. C. Downer, “Blue-shift of E2 critical point resonance in optical second-harmonic spectrum of Si nanocrystals,” Phys. Status Solidi B 249, 1166–1172 (2012).
    [Crossref]
  42. C. Mrabet, A. Mahdhib, M. Boukhachema, M. Amlouka, and T. Manoubia, “Effects of surface oxygen vacancies content on wettability of zinc oxide nanorods doped with lanthanum,” J. Alloys Compd. 688, 122–132 (2016).
    [Crossref]
  43. H. Hardhienata, T. I. Sumaryada, B. Pesendorfer, and H. Alatas, “Bond model of second and third harmonic generation in body and face centered crystal structures,” Adv. Mater. Sci. Eng. 2018, 7153247 (2018).
    [Crossref]

2018 (3)

Y. Ogata, A. Vorobyev, and C. Guo, “Optical third harmonic generation using nickel nanostructure-covered microcube structures,” Materials 11, 501 (2018).
[Crossref]

F. B. Afruz, M. J. Tafreshi, M. R. Mohammadizadeh, and M. Fazli, “Structural and electronic properties of hydrogen doped wurtzite ZnO,” Comput. Mater. Sci. 143, 232–239 (2018).
[Crossref]

H. Hardhienata, T. I. Sumaryada, B. Pesendorfer, and H. Alatas, “Bond model of second and third harmonic generation in body and face centered crystal structures,” Adv. Mater. Sci. Eng. 2018, 7153247 (2018).
[Crossref]

2017 (2)

Y. Ogata and C. Guo, “Nonlinear optics on nano/micro-hierarchical structures on metals: focus on symmetric and plasmonic effects,” Nano Rev. Exp. 8, 1339545 (2017).
[Crossref]

K.-D. Bauer and K. Hingerl, “Bulk quadrupole contribution to second harmonic generation from classical oscillator model in silicon,” Opt. Express 25, 26567–26580 (2017).
[Crossref]

2016 (8)

Y. Ogata, “Optical second harmonic generation from nanostructure-covered micro-cubes on nickel,” Opt. Mater. Express 6, 1520–1529 (2016).
[Crossref]

H. Hardhienata, A. Alejo-Molina, C. Reitböck, A. Prylepa, D. Stifter, and K. Hingerl, “Bulk dipolar contribution to second-harmonic generation in zincblende,” J. Opt. Soc. Am. B 33, 195–201 (2016).
[Crossref]

A. Alejo-Molina, “The role of Kleinman symmetry in the simplified bond hyperpolarizability model,” IOP Conf. Series: Earth Environ. Sci. 31, 012020 (2016).
[Crossref]

C. Reitböck, D. Stifter, A. Alejo-Molina, K. Hingerl, and H. Hardhienata, “Bulk quadrupole and interface dipole contribution for second harmonic generation in Si(111),” J. Opt. 18, 035501 (2016).
[Crossref]

H. Hardhienata, “How nonlinear optics can be simplified to study molecular deposition and surface vicinality of a Si(001) interface,” IOP Conf. Series: Earth Environ. Sci. 31, 012017 (2016).
[Crossref]

E. S. Jatirian-Foltides, J. J. Escobedo-Alatorre, P. A. Márquez-Aguilar, H. Hardhienata, K. Hingerl, and A. Alejo-Molinaa, “About the calculation of the second-order susceptibility tensorial elements for crystals using group theory,” Rev. Mex. Fis. E 62, 5–13 (2016).

H. Linnenbank, Y. Grynko, J. Foerstner, and S. Linden, “Second harmonic generation spectroscopy on hybrid plasmonic/dielectric nanoantennas,” Light: Sci. Appl. 5, e16013 (2016).
[Crossref]

C. Mrabet, A. Mahdhib, M. Boukhachema, M. Amlouka, and T. Manoubia, “Effects of surface oxygen vacancies content on wettability of zinc oxide nanorods doped with lanthanum,” J. Alloys Compd. 688, 122–132 (2016).
[Crossref]

2015 (2)

2014 (2)

G. Grinblat, M. Rahmani, E. Cortes, M. Caldarola, D. Comedi, S. A. Maier, and A. V. Bragas, “High-efficiency second harmonic generation from a single hybrid ZnO nanowire/Au plasmonic nano-oligomer,” Nano Lett. 14, 6660–6665 (2014).
[Crossref]

A. Alejo-Molina, H. Hardhienata, and K. Hingerl, “Simplified bond hyperpolarizability model of second harmonic generation, group theory, and Neumann’s principle,” J. Opt. Soc. Am. B 31, 526–533 (2014).
[Crossref]

2013 (1)

H. Hardhienata, A. Prylepa, D. Stifter, and K. Hingerl, “Simplified bond-hyperpolarizability model of second-harmonic-generation in Si(111): theory and experiment,” J. Phys. 423, 012046 (2013).
[Crossref]

2012 (1)

B. S. Mendoza, J. Wei, and M. C. Downer, “Blue-shift of E2 critical point resonance in optical second-harmonic spectrum of Si nanocrystals,” Phys. Status Solidi B 249, 1166–1172 (2012).
[Crossref]

2011 (1)

Y. Ogata, N. Anh Tuan, Y. Miyauchi, and G. Mizutani, “Optical second harmonic generation from Pt nanowires with boomerang-like cross-sectional shapes,” J. Appl. Phys. 110, 044301 (2011).
[Crossref]

2008 (2)

K. Y. Lo, S. Lo, Y. C. Feng, T. Tite, J. Y. Huang, Y. J. Huang, R. Chang, and S. Chu, “Optical second harmonic generation from the twin boundary of ZnO thin films grown on silicon,” Appl. Phys. Lett 92, 091909 (2008).
[Crossref]

E. J. Adles and D. E. Aspnes, “Application of the anisotropic bond model to second-harmonic generation from amorphous media,” Phys. Rev. B 77, 165102 (2008).
[Crossref]

2007 (2)

J. F. McGilp, “Using steps at the Si, SiO2 interface to test simple bond models of the optical second-harmonic response,” J. Phys. Condens. Matter 19, 016006 (2007).
[Crossref]

K. Y. Lo, Y. J. Huang, Z. C. Feng, W. E. Fenwick, M. Pan, and I. T. Ferguson, “Reflective second harmonic generation from ZnO thin films: a study on the Zn-O bonding,” Appl. Phys. Lett. 90, 161904 (2007).
[Crossref]

2006 (1)

J. Kwon and M. C. Downer, “Second harmonic and reflectance anisotropy spectroscopy of vicinal Si(001)/SiO2 interfaces: experiment and simplified microscope model,” Phys. Rev. B 73, 195330 (2006).
[Crossref]

2005 (2)

H. J. Peng, E. J. Adles, J.-F. Wang, and D. E. Aspnes, “Relative bulk and interface contributions to optical second-harmonic generation in silicon,” Phys. Rev. B 72, 205203 (2005).
[Crossref]

Y. Yan, M. M. Al-Jassim, M. F. Chisholm, L. A. Boatner, S. J. Pennycook, and M. Oxley, “[11¯00]/(1102) twin boundaries in wurtzite ZnO and group-III-nitrides,” Phys. Rev. B 71, 041309(R) (2005).
[Crossref]

2002 (2)

G. D. Powell, J.-F. Wang, and D. E. Aspnes, “Simplified bond-hyperpolarizability model of second harmonic generation,” Phys. Rev. B 65, 205320 (2002).
[Crossref]

J. C. Johnson, H. Yan, R. D. Schaller, P. B. Petersen, P. Yang, and R. J. Saykally, “Near-field imaging of nonlinear optical mixing in single zinc oxide nanowires,” Nano Lett. 2, 279–283 (2002).
[Crossref]

1996 (2)

B. S. Mendoza and W. L. Mochán, “Exactly solvable model of surface second harmonic generation,” Phys. Rev. B 53, 4999–5006 (1996).
[Crossref]

B. S. Mendoza and W. L. Mochán, “Local field effect in the second harmonic generation spectra of Si surfaces,” Phys. Rev. B 53, R10473 (1996).
[Crossref]

1994 (1)

1988 (2)

V. Mizrahi and J. E. Sipe, “Phenomenological treatment of surface second-harmonic generation,” J. Opt. Soc. Am. B 5, 660–667 (1988).
[Crossref]

V. Mizrahi and J. E. Sipe, “Phenomenological treatment of surface second-harmonic generation,” J. Opt. Soc. Am. B 5, 233402 (1988).
[Crossref]

1987 (1)

J. E. Sipe, D. J. Moss, and H. M. van Driel, “Phenomenological theory of optical second- and third-harmonic generation from cubic centrosymmetric crystals,” Phys. Rev. B 35, 1129–1141 (1987).
[Crossref]

1984 (1)

J. A. Litwin, J. E. Sipe, and H. M. van Driel, “Picosecond and nanosecond laser-induced second-harmonic generation from centrosymmetric semiconductors,” Phys. Rev. B 31, 5543–5546 (1984).
[Crossref]

1975 (1)

A. A. Maradudin and D. L. Mills, “Scattering and absorption of electromagnetic radiation by a semi-infinite medium in the presence of surface roughness,” Phys. Rev. B 11, 1392–1415 (1975).
[Crossref]

1968 (1)

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev. 174, 813–822 (1968).
[Crossref]

1961 (1)

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
[Crossref]

1916 (1)

P. Ewald, “Theory of dispersion, reflection, and refraction,” Ann. Phys. 354, 1–38 (1916).
[Crossref]

1915 (1)

C. W. Oseen, “The interaction between two electric dipoles and the rotation of the polarization plane in crystals and liquids,” Ann. Phys. 353, 1–56 (1915).
[Crossref]

Adles, E. J.

E. J. Adles and D. E. Aspnes, “Application of the anisotropic bond model to second-harmonic generation from amorphous media,” Phys. Rev. B 77, 165102 (2008).
[Crossref]

H. J. Peng, E. J. Adles, J.-F. Wang, and D. E. Aspnes, “Relative bulk and interface contributions to optical second-harmonic generation in silicon,” Phys. Rev. B 72, 205203 (2005).
[Crossref]

Afruz, F. B.

F. B. Afruz, M. J. Tafreshi, M. R. Mohammadizadeh, and M. Fazli, “Structural and electronic properties of hydrogen doped wurtzite ZnO,” Comput. Mater. Sci. 143, 232–239 (2018).
[Crossref]

Alatas, H.

H. Hardhienata, T. I. Sumaryada, B. Pesendorfer, and H. Alatas, “Bond model of second and third harmonic generation in body and face centered crystal structures,” Adv. Mater. Sci. Eng. 2018, 7153247 (2018).
[Crossref]

Alejo-Molina, A.

Alejo-Molinaa, A.

E. S. Jatirian-Foltides, J. J. Escobedo-Alatorre, P. A. Márquez-Aguilar, H. Hardhienata, K. Hingerl, and A. Alejo-Molinaa, “About the calculation of the second-order susceptibility tensorial elements for crystals using group theory,” Rev. Mex. Fis. E 62, 5–13 (2016).

Al-Jassim, M. M.

Y. Yan, M. M. Al-Jassim, M. F. Chisholm, L. A. Boatner, S. J. Pennycook, and M. Oxley, “[11¯00]/(1102) twin boundaries in wurtzite ZnO and group-III-nitrides,” Phys. Rev. B 71, 041309(R) (2005).
[Crossref]

Amlouka, M.

C. Mrabet, A. Mahdhib, M. Boukhachema, M. Amlouka, and T. Manoubia, “Effects of surface oxygen vacancies content on wettability of zinc oxide nanorods doped with lanthanum,” J. Alloys Compd. 688, 122–132 (2016).
[Crossref]

Anh Tuan, N.

Y. Ogata, N. Anh Tuan, Y. Miyauchi, and G. Mizutani, “Optical second harmonic generation from Pt nanowires with boomerang-like cross-sectional shapes,” J. Appl. Phys. 110, 044301 (2011).
[Crossref]

Aspnes, D. E.

E. J. Adles and D. E. Aspnes, “Application of the anisotropic bond model to second-harmonic generation from amorphous media,” Phys. Rev. B 77, 165102 (2008).
[Crossref]

H. J. Peng, E. J. Adles, J.-F. Wang, and D. E. Aspnes, “Relative bulk and interface contributions to optical second-harmonic generation in silicon,” Phys. Rev. B 72, 205203 (2005).
[Crossref]

G. D. Powell, J.-F. Wang, and D. E. Aspnes, “Simplified bond-hyperpolarizability model of second harmonic generation,” Phys. Rev. B 65, 205320 (2002).
[Crossref]

Bauer, K.-D.

Bloembergen, N.

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev. 174, 813–822 (1968).
[Crossref]

Boatner, L. A.

Y. Yan, M. M. Al-Jassim, M. F. Chisholm, L. A. Boatner, S. J. Pennycook, and M. Oxley, “[11¯00]/(1102) twin boundaries in wurtzite ZnO and group-III-nitrides,” Phys. Rev. B 71, 041309(R) (2005).
[Crossref]

Bottomley, D. J.

Boukhachema, M.

C. Mrabet, A. Mahdhib, M. Boukhachema, M. Amlouka, and T. Manoubia, “Effects of surface oxygen vacancies content on wettability of zinc oxide nanorods doped with lanthanum,” J. Alloys Compd. 688, 122–132 (2016).
[Crossref]

Bragas, A. V.

G. Grinblat, M. Rahmani, E. Cortes, M. Caldarola, D. Comedi, S. A. Maier, and A. V. Bragas, “High-efficiency second harmonic generation from a single hybrid ZnO nanowire/Au plasmonic nano-oligomer,” Nano Lett. 14, 6660–6665 (2014).
[Crossref]

Caldarola, M.

G. Grinblat, M. Rahmani, E. Cortes, M. Caldarola, D. Comedi, S. A. Maier, and A. V. Bragas, “High-efficiency second harmonic generation from a single hybrid ZnO nanowire/Au plasmonic nano-oligomer,” Nano Lett. 14, 6660–6665 (2014).
[Crossref]

Centrin, M.

M. C. Laciprente and M. Centrin, “Second harmonic generation from ZnO films and nanostructures,” Appl. Phys. Rev. 2, 031302 (2015).
[Crossref]

Chang, R.

K. Y. Lo, S. Lo, Y. C. Feng, T. Tite, J. Y. Huang, Y. J. Huang, R. Chang, and S. Chu, “Optical second harmonic generation from the twin boundary of ZnO thin films grown on silicon,” Appl. Phys. Lett 92, 091909 (2008).
[Crossref]

Chang, R. K.

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev. 174, 813–822 (1968).
[Crossref]

Chisholm, M. F.

Y. Yan, M. M. Al-Jassim, M. F. Chisholm, L. A. Boatner, S. J. Pennycook, and M. Oxley, “[11¯00]/(1102) twin boundaries in wurtzite ZnO and group-III-nitrides,” Phys. Rev. B 71, 041309(R) (2005).
[Crossref]

Chu, S.

K. Y. Lo, S. Lo, Y. C. Feng, T. Tite, J. Y. Huang, Y. J. Huang, R. Chang, and S. Chu, “Optical second harmonic generation from the twin boundary of ZnO thin films grown on silicon,” Appl. Phys. Lett 92, 091909 (2008).
[Crossref]

Comedi, D.

G. Grinblat, M. Rahmani, E. Cortes, M. Caldarola, D. Comedi, S. A. Maier, and A. V. Bragas, “High-efficiency second harmonic generation from a single hybrid ZnO nanowire/Au plasmonic nano-oligomer,” Nano Lett. 14, 6660–6665 (2014).
[Crossref]

Cortes, E.

G. Grinblat, M. Rahmani, E. Cortes, M. Caldarola, D. Comedi, S. A. Maier, and A. V. Bragas, “High-efficiency second harmonic generation from a single hybrid ZnO nanowire/Au plasmonic nano-oligomer,” Nano Lett. 14, 6660–6665 (2014).
[Crossref]

Downer, M. C.

B. S. Mendoza, J. Wei, and M. C. Downer, “Blue-shift of E2 critical point resonance in optical second-harmonic spectrum of Si nanocrystals,” Phys. Status Solidi B 249, 1166–1172 (2012).
[Crossref]

J. Kwon and M. C. Downer, “Second harmonic and reflectance anisotropy spectroscopy of vicinal Si(001)/SiO2 interfaces: experiment and simplified microscope model,” Phys. Rev. B 73, 195330 (2006).
[Crossref]

Escobedo-Alatorre, J. J.

E. S. Jatirian-Foltides, J. J. Escobedo-Alatorre, P. A. Márquez-Aguilar, H. Hardhienata, K. Hingerl, and A. Alejo-Molinaa, “About the calculation of the second-order susceptibility tensorial elements for crystals using group theory,” Rev. Mex. Fis. E 62, 5–13 (2016).

Ewald, P.

P. Ewald, “Theory of dispersion, reflection, and refraction,” Ann. Phys. 354, 1–38 (1916).
[Crossref]

Fazli, M.

F. B. Afruz, M. J. Tafreshi, M. R. Mohammadizadeh, and M. Fazli, “Structural and electronic properties of hydrogen doped wurtzite ZnO,” Comput. Mater. Sci. 143, 232–239 (2018).
[Crossref]

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K. Y. Lo, S. Lo, Y. C. Feng, T. Tite, J. Y. Huang, Y. J. Huang, R. Chang, and S. Chu, “Optical second harmonic generation from the twin boundary of ZnO thin films grown on silicon,” Appl. Phys. Lett 92, 091909 (2008).
[Crossref]

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K. Y. Lo, Y. J. Huang, Z. C. Feng, W. E. Fenwick, M. Pan, and I. T. Ferguson, “Reflective second harmonic generation from ZnO thin films: a study on the Zn-O bonding,” Appl. Phys. Lett. 90, 161904 (2007).
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K. Y. Lo, Y. J. Huang, Z. C. Feng, W. E. Fenwick, M. Pan, and I. T. Ferguson, “Reflective second harmonic generation from ZnO thin films: a study on the Zn-O bonding,” Appl. Phys. Lett. 90, 161904 (2007).
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Ferguson, I. T.

K. Y. Lo, Y. J. Huang, Z. C. Feng, W. E. Fenwick, M. Pan, and I. T. Ferguson, “Reflective second harmonic generation from ZnO thin films: a study on the Zn-O bonding,” Appl. Phys. Lett. 90, 161904 (2007).
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H. Linnenbank, Y. Grynko, J. Foerstner, and S. Linden, “Second harmonic generation spectroscopy on hybrid plasmonic/dielectric nanoantennas,” Light: Sci. Appl. 5, e16013 (2016).
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P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
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G. Grinblat, M. Rahmani, E. Cortes, M. Caldarola, D. Comedi, S. A. Maier, and A. V. Bragas, “High-efficiency second harmonic generation from a single hybrid ZnO nanowire/Au plasmonic nano-oligomer,” Nano Lett. 14, 6660–6665 (2014).
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H. Linnenbank, Y. Grynko, J. Foerstner, and S. Linden, “Second harmonic generation spectroscopy on hybrid plasmonic/dielectric nanoantennas,” Light: Sci. Appl. 5, e16013 (2016).
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Guo, C.

Y. Ogata, A. Vorobyev, and C. Guo, “Optical third harmonic generation using nickel nanostructure-covered microcube structures,” Materials 11, 501 (2018).
[Crossref]

Y. Ogata and C. Guo, “Nonlinear optics on nano/micro-hierarchical structures on metals: focus on symmetric and plasmonic effects,” Nano Rev. Exp. 8, 1339545 (2017).
[Crossref]

Hardhienata, H.

H. Hardhienata, T. I. Sumaryada, B. Pesendorfer, and H. Alatas, “Bond model of second and third harmonic generation in body and face centered crystal structures,” Adv. Mater. Sci. Eng. 2018, 7153247 (2018).
[Crossref]

E. S. Jatirian-Foltides, J. J. Escobedo-Alatorre, P. A. Márquez-Aguilar, H. Hardhienata, K. Hingerl, and A. Alejo-Molinaa, “About the calculation of the second-order susceptibility tensorial elements for crystals using group theory,” Rev. Mex. Fis. E 62, 5–13 (2016).

H. Hardhienata, A. Alejo-Molina, C. Reitböck, A. Prylepa, D. Stifter, and K. Hingerl, “Bulk dipolar contribution to second-harmonic generation in zincblende,” J. Opt. Soc. Am. B 33, 195–201 (2016).
[Crossref]

C. Reitböck, D. Stifter, A. Alejo-Molina, K. Hingerl, and H. Hardhienata, “Bulk quadrupole and interface dipole contribution for second harmonic generation in Si(111),” J. Opt. 18, 035501 (2016).
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H. Hardhienata, “How nonlinear optics can be simplified to study molecular deposition and surface vicinality of a Si(001) interface,” IOP Conf. Series: Earth Environ. Sci. 31, 012017 (2016).
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A. Alejo-Molina, K. Hingerl, and H. Hardhienata, “Model of third harmonic generation and electric field induced optical second harmonic using the simplified bond-hyperpolarizability model,” J. Opt. Soc. Am. B 32, 562–570 (2015).
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A. Alejo-Molina, H. Hardhienata, and K. Hingerl, “Simplified bond hyperpolarizability model of second harmonic generation, group theory, and Neumann’s principle,” J. Opt. Soc. Am. B 31, 526–533 (2014).
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H. Hardhienata, A. Prylepa, D. Stifter, and K. Hingerl, “Simplified bond-hyperpolarizability model of second-harmonic-generation in Si(111): theory and experiment,” J. Phys. 423, 012046 (2013).
[Crossref]

Hill, A. E.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
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Hingerl, K.

K.-D. Bauer and K. Hingerl, “Bulk quadrupole contribution to second harmonic generation from classical oscillator model in silicon,” Opt. Express 25, 26567–26580 (2017).
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H. Hardhienata, A. Alejo-Molina, C. Reitböck, A. Prylepa, D. Stifter, and K. Hingerl, “Bulk dipolar contribution to second-harmonic generation in zincblende,” J. Opt. Soc. Am. B 33, 195–201 (2016).
[Crossref]

E. S. Jatirian-Foltides, J. J. Escobedo-Alatorre, P. A. Márquez-Aguilar, H. Hardhienata, K. Hingerl, and A. Alejo-Molinaa, “About the calculation of the second-order susceptibility tensorial elements for crystals using group theory,” Rev. Mex. Fis. E 62, 5–13 (2016).

C. Reitböck, D. Stifter, A. Alejo-Molina, K. Hingerl, and H. Hardhienata, “Bulk quadrupole and interface dipole contribution for second harmonic generation in Si(111),” J. Opt. 18, 035501 (2016).
[Crossref]

A. Alejo-Molina, K. Hingerl, and H. Hardhienata, “Model of third harmonic generation and electric field induced optical second harmonic using the simplified bond-hyperpolarizability model,” J. Opt. Soc. Am. B 32, 562–570 (2015).
[Crossref]

A. Alejo-Molina, H. Hardhienata, and K. Hingerl, “Simplified bond hyperpolarizability model of second harmonic generation, group theory, and Neumann’s principle,” J. Opt. Soc. Am. B 31, 526–533 (2014).
[Crossref]

H. Hardhienata, A. Prylepa, D. Stifter, and K. Hingerl, “Simplified bond-hyperpolarizability model of second-harmonic-generation in Si(111): theory and experiment,” J. Phys. 423, 012046 (2013).
[Crossref]

Huang, J. Y.

K. Y. Lo, S. Lo, Y. C. Feng, T. Tite, J. Y. Huang, Y. J. Huang, R. Chang, and S. Chu, “Optical second harmonic generation from the twin boundary of ZnO thin films grown on silicon,” Appl. Phys. Lett 92, 091909 (2008).
[Crossref]

Huang, Y. J.

K. Y. Lo, S. Lo, Y. C. Feng, T. Tite, J. Y. Huang, Y. J. Huang, R. Chang, and S. Chu, “Optical second harmonic generation from the twin boundary of ZnO thin films grown on silicon,” Appl. Phys. Lett 92, 091909 (2008).
[Crossref]

K. Y. Lo, Y. J. Huang, Z. C. Feng, W. E. Fenwick, M. Pan, and I. T. Ferguson, “Reflective second harmonic generation from ZnO thin films: a study on the Zn-O bonding,” Appl. Phys. Lett. 90, 161904 (2007).
[Crossref]

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E. S. Jatirian-Foltides, J. J. Escobedo-Alatorre, P. A. Márquez-Aguilar, H. Hardhienata, K. Hingerl, and A. Alejo-Molinaa, “About the calculation of the second-order susceptibility tensorial elements for crystals using group theory,” Rev. Mex. Fis. E 62, 5–13 (2016).

Jha, S. S.

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev. 174, 813–822 (1968).
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J. C. Johnson, H. Yan, R. D. Schaller, P. B. Petersen, P. Yang, and R. J. Saykally, “Near-field imaging of nonlinear optical mixing in single zinc oxide nanowires,” Nano Lett. 2, 279–283 (2002).
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N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev. 174, 813–822 (1968).
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Linden, S.

H. Linnenbank, Y. Grynko, J. Foerstner, and S. Linden, “Second harmonic generation spectroscopy on hybrid plasmonic/dielectric nanoantennas,” Light: Sci. Appl. 5, e16013 (2016).
[Crossref]

Linnenbank, H.

H. Linnenbank, Y. Grynko, J. Foerstner, and S. Linden, “Second harmonic generation spectroscopy on hybrid plasmonic/dielectric nanoantennas,” Light: Sci. Appl. 5, e16013 (2016).
[Crossref]

Litwin, J. A.

J. A. Litwin, J. E. Sipe, and H. M. van Driel, “Picosecond and nanosecond laser-induced second-harmonic generation from centrosymmetric semiconductors,” Phys. Rev. B 31, 5543–5546 (1984).
[Crossref]

Lo, K. Y.

K. Y. Lo, S. Lo, Y. C. Feng, T. Tite, J. Y. Huang, Y. J. Huang, R. Chang, and S. Chu, “Optical second harmonic generation from the twin boundary of ZnO thin films grown on silicon,” Appl. Phys. Lett 92, 091909 (2008).
[Crossref]

K. Y. Lo, Y. J. Huang, Z. C. Feng, W. E. Fenwick, M. Pan, and I. T. Ferguson, “Reflective second harmonic generation from ZnO thin films: a study on the Zn-O bonding,” Appl. Phys. Lett. 90, 161904 (2007).
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Lo, S.

K. Y. Lo, S. Lo, Y. C. Feng, T. Tite, J. Y. Huang, Y. J. Huang, R. Chang, and S. Chu, “Optical second harmonic generation from the twin boundary of ZnO thin films grown on silicon,” Appl. Phys. Lett 92, 091909 (2008).
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Lüpke, G.

Mahdhib, A.

C. Mrabet, A. Mahdhib, M. Boukhachema, M. Amlouka, and T. Manoubia, “Effects of surface oxygen vacancies content on wettability of zinc oxide nanorods doped with lanthanum,” J. Alloys Compd. 688, 122–132 (2016).
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Maier, S. A.

G. Grinblat, M. Rahmani, E. Cortes, M. Caldarola, D. Comedi, S. A. Maier, and A. V. Bragas, “High-efficiency second harmonic generation from a single hybrid ZnO nanowire/Au plasmonic nano-oligomer,” Nano Lett. 14, 6660–6665 (2014).
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Manoubia, T.

C. Mrabet, A. Mahdhib, M. Boukhachema, M. Amlouka, and T. Manoubia, “Effects of surface oxygen vacancies content on wettability of zinc oxide nanorods doped with lanthanum,” J. Alloys Compd. 688, 122–132 (2016).
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A. A. Maradudin and D. L. Mills, “Scattering and absorption of electromagnetic radiation by a semi-infinite medium in the presence of surface roughness,” Phys. Rev. B 11, 1392–1415 (1975).
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E. S. Jatirian-Foltides, J. J. Escobedo-Alatorre, P. A. Márquez-Aguilar, H. Hardhienata, K. Hingerl, and A. Alejo-Molinaa, “About the calculation of the second-order susceptibility tensorial elements for crystals using group theory,” Rev. Mex. Fis. E 62, 5–13 (2016).

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J. F. McGilp, “Using steps at the Si, SiO2 interface to test simple bond models of the optical second-harmonic response,” J. Phys. Condens. Matter 19, 016006 (2007).
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B. S. Mendoza, J. Wei, and M. C. Downer, “Blue-shift of E2 critical point resonance in optical second-harmonic spectrum of Si nanocrystals,” Phys. Status Solidi B 249, 1166–1172 (2012).
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B. S. Mendoza and W. L. Mochán, “Local field effect in the second harmonic generation spectra of Si surfaces,” Phys. Rev. B 53, R10473 (1996).
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B. S. Mendoza and W. L. Mochán, “Exactly solvable model of surface second harmonic generation,” Phys. Rev. B 53, 4999–5006 (1996).
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A. A. Maradudin and D. L. Mills, “Scattering and absorption of electromagnetic radiation by a semi-infinite medium in the presence of surface roughness,” Phys. Rev. B 11, 1392–1415 (1975).
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Y. Ogata, N. Anh Tuan, Y. Miyauchi, and G. Mizutani, “Optical second harmonic generation from Pt nanowires with boomerang-like cross-sectional shapes,” J. Appl. Phys. 110, 044301 (2011).
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Mizrahi, V.

V. Mizrahi and J. E. Sipe, “Phenomenological treatment of surface second-harmonic generation,” J. Opt. Soc. Am. B 5, 660–667 (1988).
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V. Mizrahi and J. E. Sipe, “Phenomenological treatment of surface second-harmonic generation,” J. Opt. Soc. Am. B 5, 233402 (1988).
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Y. Ogata, N. Anh Tuan, Y. Miyauchi, and G. Mizutani, “Optical second harmonic generation from Pt nanowires with boomerang-like cross-sectional shapes,” J. Appl. Phys. 110, 044301 (2011).
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Mochán, W. L.

B. S. Mendoza and W. L. Mochán, “Exactly solvable model of surface second harmonic generation,” Phys. Rev. B 53, 4999–5006 (1996).
[Crossref]

B. S. Mendoza and W. L. Mochán, “Local field effect in the second harmonic generation spectra of Si surfaces,” Phys. Rev. B 53, R10473 (1996).
[Crossref]

Mohammadizadeh, M. R.

F. B. Afruz, M. J. Tafreshi, M. R. Mohammadizadeh, and M. Fazli, “Structural and electronic properties of hydrogen doped wurtzite ZnO,” Comput. Mater. Sci. 143, 232–239 (2018).
[Crossref]

Moss, D. J.

J. E. Sipe, D. J. Moss, and H. M. van Driel, “Phenomenological theory of optical second- and third-harmonic generation from cubic centrosymmetric crystals,” Phys. Rev. B 35, 1129–1141 (1987).
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Mrabet, C.

C. Mrabet, A. Mahdhib, M. Boukhachema, M. Amlouka, and T. Manoubia, “Effects of surface oxygen vacancies content on wettability of zinc oxide nanorods doped with lanthanum,” J. Alloys Compd. 688, 122–132 (2016).
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Ogata, Y.

Y. Ogata, A. Vorobyev, and C. Guo, “Optical third harmonic generation using nickel nanostructure-covered microcube structures,” Materials 11, 501 (2018).
[Crossref]

Y. Ogata and C. Guo, “Nonlinear optics on nano/micro-hierarchical structures on metals: focus on symmetric and plasmonic effects,” Nano Rev. Exp. 8, 1339545 (2017).
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Y. Ogata, “Optical second harmonic generation from nanostructure-covered micro-cubes on nickel,” Opt. Mater. Express 6, 1520–1529 (2016).
[Crossref]

Y. Ogata, N. Anh Tuan, Y. Miyauchi, and G. Mizutani, “Optical second harmonic generation from Pt nanowires with boomerang-like cross-sectional shapes,” J. Appl. Phys. 110, 044301 (2011).
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C. W. Oseen, “The interaction between two electric dipoles and the rotation of the polarization plane in crystals and liquids,” Ann. Phys. 353, 1–56 (1915).
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Oxley, M.

Y. Yan, M. M. Al-Jassim, M. F. Chisholm, L. A. Boatner, S. J. Pennycook, and M. Oxley, “[11¯00]/(1102) twin boundaries in wurtzite ZnO and group-III-nitrides,” Phys. Rev. B 71, 041309(R) (2005).
[Crossref]

Pan, M.

K. Y. Lo, Y. J. Huang, Z. C. Feng, W. E. Fenwick, M. Pan, and I. T. Ferguson, “Reflective second harmonic generation from ZnO thin films: a study on the Zn-O bonding,” Appl. Phys. Lett. 90, 161904 (2007).
[Crossref]

Peng, H. J.

H. J. Peng, E. J. Adles, J.-F. Wang, and D. E. Aspnes, “Relative bulk and interface contributions to optical second-harmonic generation in silicon,” Phys. Rev. B 72, 205203 (2005).
[Crossref]

Pennycook, S. J.

Y. Yan, M. M. Al-Jassim, M. F. Chisholm, L. A. Boatner, S. J. Pennycook, and M. Oxley, “[11¯00]/(1102) twin boundaries in wurtzite ZnO and group-III-nitrides,” Phys. Rev. B 71, 041309(R) (2005).
[Crossref]

Pesendorfer, B.

H. Hardhienata, T. I. Sumaryada, B. Pesendorfer, and H. Alatas, “Bond model of second and third harmonic generation in body and face centered crystal structures,” Adv. Mater. Sci. Eng. 2018, 7153247 (2018).
[Crossref]

Peters, C. W.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
[Crossref]

Petersen, P. B.

J. C. Johnson, H. Yan, R. D. Schaller, P. B. Petersen, P. Yang, and R. J. Saykally, “Near-field imaging of nonlinear optical mixing in single zinc oxide nanowires,” Nano Lett. 2, 279–283 (2002).
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Powell, G. D.

G. D. Powell, J.-F. Wang, and D. E. Aspnes, “Simplified bond-hyperpolarizability model of second harmonic generation,” Phys. Rev. B 65, 205320 (2002).
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Prylepa, A.

H. Hardhienata, A. Alejo-Molina, C. Reitböck, A. Prylepa, D. Stifter, and K. Hingerl, “Bulk dipolar contribution to second-harmonic generation in zincblende,” J. Opt. Soc. Am. B 33, 195–201 (2016).
[Crossref]

H. Hardhienata, A. Prylepa, D. Stifter, and K. Hingerl, “Simplified bond-hyperpolarizability model of second-harmonic-generation in Si(111): theory and experiment,” J. Phys. 423, 012046 (2013).
[Crossref]

Rahmani, M.

G. Grinblat, M. Rahmani, E. Cortes, M. Caldarola, D. Comedi, S. A. Maier, and A. V. Bragas, “High-efficiency second harmonic generation from a single hybrid ZnO nanowire/Au plasmonic nano-oligomer,” Nano Lett. 14, 6660–6665 (2014).
[Crossref]

Reitböck, C.

C. Reitböck, D. Stifter, A. Alejo-Molina, K. Hingerl, and H. Hardhienata, “Bulk quadrupole and interface dipole contribution for second harmonic generation in Si(111),” J. Opt. 18, 035501 (2016).
[Crossref]

H. Hardhienata, A. Alejo-Molina, C. Reitböck, A. Prylepa, D. Stifter, and K. Hingerl, “Bulk dipolar contribution to second-harmonic generation in zincblende,” J. Opt. Soc. Am. B 33, 195–201 (2016).
[Crossref]

Saykally, R. J.

J. C. Johnson, H. Yan, R. D. Schaller, P. B. Petersen, P. Yang, and R. J. Saykally, “Near-field imaging of nonlinear optical mixing in single zinc oxide nanowires,” Nano Lett. 2, 279–283 (2002).
[Crossref]

Schaller, R. D.

J. C. Johnson, H. Yan, R. D. Schaller, P. B. Petersen, P. Yang, and R. J. Saykally, “Near-field imaging of nonlinear optical mixing in single zinc oxide nanowires,” Nano Lett. 2, 279–283 (2002).
[Crossref]

Sipe, J. E.

V. Mizrahi and J. E. Sipe, “Phenomenological treatment of surface second-harmonic generation,” J. Opt. Soc. Am. B 5, 233402 (1988).
[Crossref]

V. Mizrahi and J. E. Sipe, “Phenomenological treatment of surface second-harmonic generation,” J. Opt. Soc. Am. B 5, 660–667 (1988).
[Crossref]

J. E. Sipe, D. J. Moss, and H. M. van Driel, “Phenomenological theory of optical second- and third-harmonic generation from cubic centrosymmetric crystals,” Phys. Rev. B 35, 1129–1141 (1987).
[Crossref]

J. A. Litwin, J. E. Sipe, and H. M. van Driel, “Picosecond and nanosecond laser-induced second-harmonic generation from centrosymmetric semiconductors,” Phys. Rev. B 31, 5543–5546 (1984).
[Crossref]

Stifter, D.

C. Reitböck, D. Stifter, A. Alejo-Molina, K. Hingerl, and H. Hardhienata, “Bulk quadrupole and interface dipole contribution for second harmonic generation in Si(111),” J. Opt. 18, 035501 (2016).
[Crossref]

H. Hardhienata, A. Alejo-Molina, C. Reitböck, A. Prylepa, D. Stifter, and K. Hingerl, “Bulk dipolar contribution to second-harmonic generation in zincblende,” J. Opt. Soc. Am. B 33, 195–201 (2016).
[Crossref]

H. Hardhienata, A. Prylepa, D. Stifter, and K. Hingerl, “Simplified bond-hyperpolarizability model of second-harmonic-generation in Si(111): theory and experiment,” J. Phys. 423, 012046 (2013).
[Crossref]

Sumaryada, T. I.

H. Hardhienata, T. I. Sumaryada, B. Pesendorfer, and H. Alatas, “Bond model of second and third harmonic generation in body and face centered crystal structures,” Adv. Mater. Sci. Eng. 2018, 7153247 (2018).
[Crossref]

Tafreshi, M. J.

F. B. Afruz, M. J. Tafreshi, M. R. Mohammadizadeh, and M. Fazli, “Structural and electronic properties of hydrogen doped wurtzite ZnO,” Comput. Mater. Sci. 143, 232–239 (2018).
[Crossref]

Tite, T.

K. Y. Lo, S. Lo, Y. C. Feng, T. Tite, J. Y. Huang, Y. J. Huang, R. Chang, and S. Chu, “Optical second harmonic generation from the twin boundary of ZnO thin films grown on silicon,” Appl. Phys. Lett 92, 091909 (2008).
[Crossref]

van Driel, H. M.

G. Lüpke, D. J. Bottomley, and H. M. van Driel, “Second- and third-harmonic generation from cubic centrosymmetric crystals with vicinal faces: phenomenological theory and experiment,” J. Opt. Soc. Am. B 11, 33–44 (1994).
[Crossref]

J. E. Sipe, D. J. Moss, and H. M. van Driel, “Phenomenological theory of optical second- and third-harmonic generation from cubic centrosymmetric crystals,” Phys. Rev. B 35, 1129–1141 (1987).
[Crossref]

J. A. Litwin, J. E. Sipe, and H. M. van Driel, “Picosecond and nanosecond laser-induced second-harmonic generation from centrosymmetric semiconductors,” Phys. Rev. B 31, 5543–5546 (1984).
[Crossref]

Vorobyev, A.

Y. Ogata, A. Vorobyev, and C. Guo, “Optical third harmonic generation using nickel nanostructure-covered microcube structures,” Materials 11, 501 (2018).
[Crossref]

Wang, J.-F.

H. J. Peng, E. J. Adles, J.-F. Wang, and D. E. Aspnes, “Relative bulk and interface contributions to optical second-harmonic generation in silicon,” Phys. Rev. B 72, 205203 (2005).
[Crossref]

G. D. Powell, J.-F. Wang, and D. E. Aspnes, “Simplified bond-hyperpolarizability model of second harmonic generation,” Phys. Rev. B 65, 205320 (2002).
[Crossref]

Wei, J.

B. S. Mendoza, J. Wei, and M. C. Downer, “Blue-shift of E2 critical point resonance in optical second-harmonic spectrum of Si nanocrystals,” Phys. Status Solidi B 249, 1166–1172 (2012).
[Crossref]

Weinreich, G.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–119 (1961).
[Crossref]

Yan, H.

J. C. Johnson, H. Yan, R. D. Schaller, P. B. Petersen, P. Yang, and R. J. Saykally, “Near-field imaging of nonlinear optical mixing in single zinc oxide nanowires,” Nano Lett. 2, 279–283 (2002).
[Crossref]

Yan, Y.

Y. Yan, M. M. Al-Jassim, M. F. Chisholm, L. A. Boatner, S. J. Pennycook, and M. Oxley, “[11¯00]/(1102) twin boundaries in wurtzite ZnO and group-III-nitrides,” Phys. Rev. B 71, 041309(R) (2005).
[Crossref]

Yang, P.

J. C. Johnson, H. Yan, R. D. Schaller, P. B. Petersen, P. Yang, and R. J. Saykally, “Near-field imaging of nonlinear optical mixing in single zinc oxide nanowires,” Nano Lett. 2, 279–283 (2002).
[Crossref]

Adv. Mater. Sci. Eng. (1)

H. Hardhienata, T. I. Sumaryada, B. Pesendorfer, and H. Alatas, “Bond model of second and third harmonic generation in body and face centered crystal structures,” Adv. Mater. Sci. Eng. 2018, 7153247 (2018).
[Crossref]

Ann. Phys. (2)

P. Ewald, “Theory of dispersion, reflection, and refraction,” Ann. Phys. 354, 1–38 (1916).
[Crossref]

C. W. Oseen, “The interaction between two electric dipoles and the rotation of the polarization plane in crystals and liquids,” Ann. Phys. 353, 1–56 (1915).
[Crossref]

Appl. Phys. Lett (1)

K. Y. Lo, S. Lo, Y. C. Feng, T. Tite, J. Y. Huang, Y. J. Huang, R. Chang, and S. Chu, “Optical second harmonic generation from the twin boundary of ZnO thin films grown on silicon,” Appl. Phys. Lett 92, 091909 (2008).
[Crossref]

Appl. Phys. Lett. (1)

K. Y. Lo, Y. J. Huang, Z. C. Feng, W. E. Fenwick, M. Pan, and I. T. Ferguson, “Reflective second harmonic generation from ZnO thin films: a study on the Zn-O bonding,” Appl. Phys. Lett. 90, 161904 (2007).
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Appl. Phys. Rev. (1)

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Figures (6)

Fig. 1.
Fig. 1. Orientation of the ZnO(0002) structure and bond vector direction in a ZnO bulk wurtzite structure; the red atoms/arrows denote Zn whereas the blue atoms/arrows represents O. Viewed in terms of (a) the standard crystal orientation, (b) bond vector directions representing the two Zn and O atoms in the insert, (c) top view of the bond atoms and bond vectors, and (d) orientation of the atomic bonds viewed from the top but tilted lightly to show opposing bond between the top and layer below.
Fig. 2.
Fig. 2. (a) ZnO surface atomic orientation with Zn at the very top. (b) Surface bond vector orientations. (c) Effective surface bond vectors.
Fig. 3.
Fig. 3. Fully relaxed structures for the (a) head to tail twin boundary configuration from top taken from [40]; (b) three-dimensional SBHM bond vector orientation of head to tail twin boundary; and (c) SBHM effective head to tail twin boundary bond vectors.
Fig. 4.
Fig. 4. Coordinate system of the incoming and outgoing polarization. The z-axis is pointing to the ZnO(0002) direction.
Fig. 5.
Fig. 5. SS-RSHG intensity in (a) unreduced surface structure (C3v), (b) twin boundary (C1v), (c) ZnO thin film via SBHM, and (d) ZnO thin film obtained via experiment in [26].
Fig. 6.
Fig. 6. (Left) Affected oxygen atoms at the ZnO rough surface denoted by yellow circles, and (right) SBHM pp-polarization RASHG intensity far field showing a gradual decrease starting from zero vacancies (green), 50% oxygen vacancies (red), and 70% oxygen vacancies (blue).

Equations (69)

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b^1bulk=z^,
b^2bulk=sin(β)x^+cos(β)z^,
b^3bulk=12sin(β)x^123sin(β)y^+cos(β)z^,
b^4bulk=12sin(β)x^+123sin(β)y^+cos(β)z^,
b^5bulk=sin(β)x^+cos(β)z^,
b^6bulk=12sin(β)x^+123sin(β)y^+cos(β)z^,
b^7bulk=12sin(β)x^123sin(β)y^+cos(β)z^,
b^8bulk=b^1bulk,b^9bulk=b^2bulk,b^10bulk=b^4bulk,b^11bulk=b^3bulk,b^12bulk=b^5bulk,b^13bulk=b^7bulk,b^14bulk=b^6bulk.
PSHGbulk=1(V/N)j=17α2Znbulkb^jbulk(ϕ)(b^jbulk(ϕ)·Eloc(ω))2+1(V/N)j=814α2Obulkb^jbulk(ϕ)(b^jbulk(ϕ)·Eloc(ω))2,
PSHGbulk=χZnbulk(2)Eloc(ω)Eloc(ω)+χObulk(2)Eloc(ω)Eloc(ω).
α2ZnObulk=|α2Znbulkα2Obulk|.
PSHGbulk=1(V/N)j=17α2ZnObulkb^jbulk(ϕ)(b^jbulk(ϕ)·Eloc(ω))2=χZnObulk(2)Eloc(ω)Eloc(ω).
PSHGbulkQuad=χZnObulkQuad(3)Eloc(ω)bEloc(ω),
b^1surf=z^,
b^2surf=sin(β)x^+cos(β)z^,
b^3surf=12sin(β)x^123sin(β)y^+cos(β)z^,
b^4surf=12sin(β)x^+123sin(β)y^+cos(β)z^.
PSHGsurf=1(V/N)j=14α2ZnOsurfb^jsurf(ϕ)(b^jsurf(ϕ)·Eloc(ω))2=χZnOsurf(2)Eloc(ω)Eloc(ω),
4b^1TB=12sin(β)x^cos(β)y^12sin(β)z^,
b^2TB=(3+cos(β))sin(β)22x^+(3cos(2β))4y^(3+cos(β))sin(β)22z^,
b^3TB=(3+cos(β))sin(β)22x^+(3cos(2β))4y^+(3cos(β))sin(β)22z^,
b4TB=2cos(β)sin(β)x^cos(2β)y^2cos(β)sin(β)z^,
b^5TB=(3+3cos(β))sin(β)22x^+(13cos(2β))4y^+(33cos(β))sin(β)22z^,
b^6TB=(33cos(β))sin(β)22x^+(13cos(2β))4y^(3+3cos(β))sin(β)22z^,
b^7TB=y^,
b^8TB=12sin(β)x^+cos(β)y^+12sin(β)z^,
b^9TB=(3+cos(β))sin(β)22x^+(3+cos(2β))4y^+(3+cos(β))sin(β)22z^,
b^10TB=(3+cos(β))sin(β)22x^+(3+cos(2β))4y^+(3cos(β))sin(β)22z^,
b^11TB=2cos(β)sin(β)x^+cos(2β)y^+2cos(β)sin(β)z^,
b^12TB=(3+3cos(β))sin(β)22x^+(1+3cos(2β))4y^(33cos(β))sin(β)22z^,
b^13TB=(33cos(β))sin(β)22x^+(1+3cos(2β))4y^+(3+3cos(β))sin(β)22z^,
b^14TB=y^.
PSHG-TB=1(V/N)j=114α2ZnO-TBb^jTB(ϕ)(b^jTB(ϕ)·Eloc(ω))2=χZnO-TB(2)Eloc(ω)Eloc(ω),
χijk(2)bulk=((00χzxx000χzxx00)(00000χzxx0χzxx0)(χzxx000χzxx000χzzz)).
χijk(2)surf=((0χxyxχxzxχxyx00χxzx00)(χyxx000χyyyχxzx0χxzx0)(χzxx000χzxx000χzzz)).
χZnO-TB(2)=((χxxx000χxyyχxzy0χxzyχxzz)(0χxyyχxzyχxyy00χxzy00)(0χxzyχxzzχxzy00χxzz00)).
χZnObulk(2)=α2ZnObulk(V/N)j=17b^jbulk×b^jbulk×b^jbulk,
χZnObulk(2)=α2ZnObulk(V/N)×((003cos(β)sin(β)20003cos(β)sin(β)200)(000003cos(β)sin(β)203cos(β)sin(β)20)(3cos(β)sin(β)20003cos(β)sin(β)20001+6cos(β)3)).
χZnOsurf(2)=α2ZnOsurf(V/N)j=17b^jsurf×b^jsurf×b^jsurf.
χZnOsurf(2)=α2ZnOsurf(V/N)×((34sin(β)3032cos(β)sin(β)2034sin(β)3032cos(β)sin(β)200)(034sin(β)3034sin(β)3032cos(β)sin(β)2032cos(β)sin(β)20)(32cos(β)sin(β)200032cos(β)sin(β)20001+3cos(β)3)),
χZnO-TB(2)=α2ZnO-TB(V/N)j=17b^jTB×b^jTB×b^jTB,
χxxx=α2ZnO-TB2(V/N)(1+9cos(β)+15cos(β)3)sin(β)3,
χxyy=χyxy=χyxx=α2ZnO-TB162(V/N)(8sin(β)+27sin(2β)+8sin(3β)+12sin(4β)+15sin(6β)),
χxzy=χxyz=χyzx=χyxz=χzyx=χzxy=α2ZnO-TB(V/N)18(9+8cos(β)+24cos(2β)+15cos(4β)sin(β)2),
χxzz=χzxz=χzzx=α2ZnO-TB2(V/N)(13cos(β)+15cos(β)3)sin(β)3.
fss=(|ts(ω)|2|ts(2ω)|),
ts=2ε(n)ε(0)sin2(θ)ε(n)ε(0)sin2(θ)+ε(n+1)ε(0)sin2(θ).
Effss-bulk(total)=0,
Effss-bulk(bond1)=0,
Effss-bulk(bond2)=fssαZnObulksin(β)3sin(ϕ)3y^,
Effss-bulk(bond3)=18fssαZnObulksin(β)3(3cos(ϕ)+sin(ϕ))3y^,
Effss-bulk(bond4)=18fssαZnObulksin(β)3(3cos(ϕ)sin(ϕ))3y^,
Effss-bulk(bond5)=fssαZnObulksin(β)3sin(ϕ)3y^,
Effss-bulk(bond6)=18fss18αZnObulksin(β)3(3cos(ϕ)sin(ϕ))3y^,
Effss-bulk(bond7)=18fssαZnObulksin(β)3(3cos(ϕ)sin(ϕ))3y^.
Effss-surf=c1αZnOsurfsin(3ϕ)y^,
Effss-TB=eiψαZnO-TB((c2)sin(ϕ)(c3)sin(ϕ))y^,
ISS-surf+TB=(eiψαZnO-TB(c2sin(ϕ)+c3sin(3ϕ))+c1αZnOsurfsin(3ϕ))2.
ISS-experiment=(aeiψsin(ϕ)+bsin(3ϕ))2,
F=qjEloc(ω)·b^jeiωtκ1(xx0)κ2(xx0)2bdxdt=md2xdt2,
x=x0+Δx1eiωt+Δx2ei2ωt+Δx3ei3ωt+,
p2j=qjΔx2b^j=qjκ2Δx12κ14mω22ibωb^j=α2j(b^j·Eloc(ω))2b^j,
b^j(ϕ)=Rz(ϕ)·b^j,
Rz(ϕ)=(cos(ϕ)sin(ϕ)0sin(ϕ)cos(ϕ)0001).
PSHG=N(V/N)j=1npj=N(V/N)j=1nα2jb^j(ϕ)(b^j(ϕ)·Eloc(ω))2,
Ep=(cos(θin)0sin(θin)),
Es=(010),
k=(sin(θout)0cos(θout)).
Eff=k2eikrr(I¯k^k^)·PSHG,