Abstract

Experiments of third harmonic generation in rutile TiO2 allowed us to determine the phase-matching angles and the refractive indices of the crystal up to 4500 nm. We also showed that χ16 and χ18 coefficients of the third order electric susceptibility tensor exhibit opposite signs, and that |χ18(616.7nm)| = 9.7 × 10−20 m2V−2.

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  1. D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, “Bell’s theorem without inequalities,” Am. J. Phys.58(12), 1131–1143 (1990).
    [CrossRef]
  2. F. Gravier and B. Boulanger, “Cubic parametric frequency generation in rutile single crystal,” Opt. Express14(24), 11715–11720 (2006).
    [CrossRef] [PubMed]
  3. F. Gravier and B. Boulanger, “Third-order frequency generation in TiO2 rutile and KTiOPO4,” Opt. Mater.30(1), 33–36 (2007).
    [CrossRef]
  4. K. Bencheikh, F. Gravier, J. Douady, J. A. Levenson, and B. Boulanger, “Triple photons: a challenge in nonlinear and quantum optics,” C. R. Phys.8(2), 206–220 (2007).
    [CrossRef]
  5. M. E. Straumanis, T. Ejima, and W. J. James, “The TiO2 phase explored by the lattice constant and density method,” Acta Crystallogr.14(5), 493–497 (1961).
    [CrossRef]
  6. Data from Almaz Optics Inc., www.almazoptics.com/TiO2.htm .
  7. J. R. Devore, “Refractive indices of rutile and sphalerite,” J. Opt. Soc. Am.41(6), 416–417 (1951).
    [CrossRef]
  8. J. Rams, A. Tejeda, and J. M. Cabrera, “Refractive indices of rutile as a function of temperature and wavelength,” J. Appl. Phys.82(3), 994–997 (1997).
    [CrossRef]
  9. D. C. Cronemeyer, “Electrical and optical properties of rutile single crystals,” Phys. Rev.87(5), 876–886 (1952).
    [CrossRef]
  10. N. G. Khadzhiiski and N. I. Koroteev, “Coherent Raman ellipsometry of crystals: determination of the components and the dispersion of the third-order nonlinear susceptibility tensor of rutile,” Opt. Commun.42(6), 423–427 (1982).
    [CrossRef]
  11. R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B Condens. Matter39(5), 3337–3350 (1989).
    [CrossRef] [PubMed]
  12. T. Hashimoto, T. Yoko, and S. Sakka, “Sol-Gel preparation and third-order nonlinear optical properties of TiO2 thin films,” Bull. Chem. Soc. Jpn.67(3), 653–660 (1994).
    [CrossRef]
  13. H. Long, A. Chen, G. Yang, Y. Li, and P. Lu, “Third-order optical nonlinearities in anatase and rutile TiO2 thin films,” Thin Solid Films517(19), 5601–5604 (2009).
    [CrossRef]
  14. M. E. Lines, “Influence of d orbitals on the nonlinear optical response of transparent transition-metal oxides,” Phys. Rev. B Condens. Matter43(14), 11978–11990 (1991).
    [CrossRef] [PubMed]
  15. B. Boulanger, J. P. Fève, and G. Marnier, “Field-factor formalism for the study of the tensorial symmetry of four-wave nonlinear optical parametric interactions in uniaxial and biaxial crystals,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics48(6), 4730–4751 (1993).
    [CrossRef] [PubMed]
  16. J. P. Fève, B. Boulanger, and Y. Guillien, “Efficient energy conversion for cubic third-harmonic generation that is phase matched in KTiOPO4,” Opt. Lett.25(18), 1373–1375 (2000).
    [CrossRef] [PubMed]
  17. Y. Guillien, B. Ménaert, J. P. Fève, P. Segonds, J. Douady, B. Boulanger, and O. Pacaud, “Crystal growth and refined Sellmeier equations over the complete transparency range of RbTiOPO4,” Opt. Mater.22(2), 155–162 (2003).
    [CrossRef]
  18. O. Pacaud, J. P. Fève, B. Boulanger, and B. Ménaert, “Cylindrical KTiOPO4 crystal for enhanced angular tunability of phase-matched optical parametric oscillators,” Opt. Lett.25(10), 737–739 (2000).
    [CrossRef] [PubMed]
  19. A. Hadni, Essentials of Modern Physics Applied to the Study of the Infrared (Pergamon Press, 1967).
  20. R. C. Miller, “Optical second harmonic generation in piezoelectric crystals,” Appl. Phys. Lett.5(1), 17–19 (1964).
    [CrossRef]

2009 (1)

H. Long, A. Chen, G. Yang, Y. Li, and P. Lu, “Third-order optical nonlinearities in anatase and rutile TiO2 thin films,” Thin Solid Films517(19), 5601–5604 (2009).
[CrossRef]

2007 (2)

F. Gravier and B. Boulanger, “Third-order frequency generation in TiO2 rutile and KTiOPO4,” Opt. Mater.30(1), 33–36 (2007).
[CrossRef]

K. Bencheikh, F. Gravier, J. Douady, J. A. Levenson, and B. Boulanger, “Triple photons: a challenge in nonlinear and quantum optics,” C. R. Phys.8(2), 206–220 (2007).
[CrossRef]

2006 (1)

2003 (1)

Y. Guillien, B. Ménaert, J. P. Fève, P. Segonds, J. Douady, B. Boulanger, and O. Pacaud, “Crystal growth and refined Sellmeier equations over the complete transparency range of RbTiOPO4,” Opt. Mater.22(2), 155–162 (2003).
[CrossRef]

2000 (2)

1997 (1)

J. Rams, A. Tejeda, and J. M. Cabrera, “Refractive indices of rutile as a function of temperature and wavelength,” J. Appl. Phys.82(3), 994–997 (1997).
[CrossRef]

1994 (1)

T. Hashimoto, T. Yoko, and S. Sakka, “Sol-Gel preparation and third-order nonlinear optical properties of TiO2 thin films,” Bull. Chem. Soc. Jpn.67(3), 653–660 (1994).
[CrossRef]

1993 (1)

B. Boulanger, J. P. Fève, and G. Marnier, “Field-factor formalism for the study of the tensorial symmetry of four-wave nonlinear optical parametric interactions in uniaxial and biaxial crystals,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics48(6), 4730–4751 (1993).
[CrossRef] [PubMed]

1991 (1)

M. E. Lines, “Influence of d orbitals on the nonlinear optical response of transparent transition-metal oxides,” Phys. Rev. B Condens. Matter43(14), 11978–11990 (1991).
[CrossRef] [PubMed]

1990 (1)

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, “Bell’s theorem without inequalities,” Am. J. Phys.58(12), 1131–1143 (1990).
[CrossRef]

1989 (1)

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B Condens. Matter39(5), 3337–3350 (1989).
[CrossRef] [PubMed]

1982 (1)

N. G. Khadzhiiski and N. I. Koroteev, “Coherent Raman ellipsometry of crystals: determination of the components and the dispersion of the third-order nonlinear susceptibility tensor of rutile,” Opt. Commun.42(6), 423–427 (1982).
[CrossRef]

1964 (1)

R. C. Miller, “Optical second harmonic generation in piezoelectric crystals,” Appl. Phys. Lett.5(1), 17–19 (1964).
[CrossRef]

1961 (1)

M. E. Straumanis, T. Ejima, and W. J. James, “The TiO2 phase explored by the lattice constant and density method,” Acta Crystallogr.14(5), 493–497 (1961).
[CrossRef]

1952 (1)

D. C. Cronemeyer, “Electrical and optical properties of rutile single crystals,” Phys. Rev.87(5), 876–886 (1952).
[CrossRef]

1951 (1)

Adair, R.

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B Condens. Matter39(5), 3337–3350 (1989).
[CrossRef] [PubMed]

Bencheikh, K.

K. Bencheikh, F. Gravier, J. Douady, J. A. Levenson, and B. Boulanger, “Triple photons: a challenge in nonlinear and quantum optics,” C. R. Phys.8(2), 206–220 (2007).
[CrossRef]

Boulanger, B.

K. Bencheikh, F. Gravier, J. Douady, J. A. Levenson, and B. Boulanger, “Triple photons: a challenge in nonlinear and quantum optics,” C. R. Phys.8(2), 206–220 (2007).
[CrossRef]

F. Gravier and B. Boulanger, “Third-order frequency generation in TiO2 rutile and KTiOPO4,” Opt. Mater.30(1), 33–36 (2007).
[CrossRef]

F. Gravier and B. Boulanger, “Cubic parametric frequency generation in rutile single crystal,” Opt. Express14(24), 11715–11720 (2006).
[CrossRef] [PubMed]

Y. Guillien, B. Ménaert, J. P. Fève, P. Segonds, J. Douady, B. Boulanger, and O. Pacaud, “Crystal growth and refined Sellmeier equations over the complete transparency range of RbTiOPO4,” Opt. Mater.22(2), 155–162 (2003).
[CrossRef]

O. Pacaud, J. P. Fève, B. Boulanger, and B. Ménaert, “Cylindrical KTiOPO4 crystal for enhanced angular tunability of phase-matched optical parametric oscillators,” Opt. Lett.25(10), 737–739 (2000).
[CrossRef] [PubMed]

J. P. Fève, B. Boulanger, and Y. Guillien, “Efficient energy conversion for cubic third-harmonic generation that is phase matched in KTiOPO4,” Opt. Lett.25(18), 1373–1375 (2000).
[CrossRef] [PubMed]

B. Boulanger, J. P. Fève, and G. Marnier, “Field-factor formalism for the study of the tensorial symmetry of four-wave nonlinear optical parametric interactions in uniaxial and biaxial crystals,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics48(6), 4730–4751 (1993).
[CrossRef] [PubMed]

Cabrera, J. M.

J. Rams, A. Tejeda, and J. M. Cabrera, “Refractive indices of rutile as a function of temperature and wavelength,” J. Appl. Phys.82(3), 994–997 (1997).
[CrossRef]

Chase, L. L.

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B Condens. Matter39(5), 3337–3350 (1989).
[CrossRef] [PubMed]

Chen, A.

H. Long, A. Chen, G. Yang, Y. Li, and P. Lu, “Third-order optical nonlinearities in anatase and rutile TiO2 thin films,” Thin Solid Films517(19), 5601–5604 (2009).
[CrossRef]

Cronemeyer, D. C.

D. C. Cronemeyer, “Electrical and optical properties of rutile single crystals,” Phys. Rev.87(5), 876–886 (1952).
[CrossRef]

Devore, J. R.

Douady, J.

K. Bencheikh, F. Gravier, J. Douady, J. A. Levenson, and B. Boulanger, “Triple photons: a challenge in nonlinear and quantum optics,” C. R. Phys.8(2), 206–220 (2007).
[CrossRef]

Y. Guillien, B. Ménaert, J. P. Fève, P. Segonds, J. Douady, B. Boulanger, and O. Pacaud, “Crystal growth and refined Sellmeier equations over the complete transparency range of RbTiOPO4,” Opt. Mater.22(2), 155–162 (2003).
[CrossRef]

Ejima, T.

M. E. Straumanis, T. Ejima, and W. J. James, “The TiO2 phase explored by the lattice constant and density method,” Acta Crystallogr.14(5), 493–497 (1961).
[CrossRef]

Fève, J. P.

Y. Guillien, B. Ménaert, J. P. Fève, P. Segonds, J. Douady, B. Boulanger, and O. Pacaud, “Crystal growth and refined Sellmeier equations over the complete transparency range of RbTiOPO4,” Opt. Mater.22(2), 155–162 (2003).
[CrossRef]

J. P. Fève, B. Boulanger, and Y. Guillien, “Efficient energy conversion for cubic third-harmonic generation that is phase matched in KTiOPO4,” Opt. Lett.25(18), 1373–1375 (2000).
[CrossRef] [PubMed]

O. Pacaud, J. P. Fève, B. Boulanger, and B. Ménaert, “Cylindrical KTiOPO4 crystal for enhanced angular tunability of phase-matched optical parametric oscillators,” Opt. Lett.25(10), 737–739 (2000).
[CrossRef] [PubMed]

B. Boulanger, J. P. Fève, and G. Marnier, “Field-factor formalism for the study of the tensorial symmetry of four-wave nonlinear optical parametric interactions in uniaxial and biaxial crystals,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics48(6), 4730–4751 (1993).
[CrossRef] [PubMed]

Gravier, F.

F. Gravier and B. Boulanger, “Third-order frequency generation in TiO2 rutile and KTiOPO4,” Opt. Mater.30(1), 33–36 (2007).
[CrossRef]

K. Bencheikh, F. Gravier, J. Douady, J. A. Levenson, and B. Boulanger, “Triple photons: a challenge in nonlinear and quantum optics,” C. R. Phys.8(2), 206–220 (2007).
[CrossRef]

F. Gravier and B. Boulanger, “Cubic parametric frequency generation in rutile single crystal,” Opt. Express14(24), 11715–11720 (2006).
[CrossRef] [PubMed]

Greenberger, D. M.

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, “Bell’s theorem without inequalities,” Am. J. Phys.58(12), 1131–1143 (1990).
[CrossRef]

Guillien, Y.

Y. Guillien, B. Ménaert, J. P. Fève, P. Segonds, J. Douady, B. Boulanger, and O. Pacaud, “Crystal growth and refined Sellmeier equations over the complete transparency range of RbTiOPO4,” Opt. Mater.22(2), 155–162 (2003).
[CrossRef]

J. P. Fève, B. Boulanger, and Y. Guillien, “Efficient energy conversion for cubic third-harmonic generation that is phase matched in KTiOPO4,” Opt. Lett.25(18), 1373–1375 (2000).
[CrossRef] [PubMed]

Hashimoto, T.

T. Hashimoto, T. Yoko, and S. Sakka, “Sol-Gel preparation and third-order nonlinear optical properties of TiO2 thin films,” Bull. Chem. Soc. Jpn.67(3), 653–660 (1994).
[CrossRef]

Horne, M. A.

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, “Bell’s theorem without inequalities,” Am. J. Phys.58(12), 1131–1143 (1990).
[CrossRef]

James, W. J.

M. E. Straumanis, T. Ejima, and W. J. James, “The TiO2 phase explored by the lattice constant and density method,” Acta Crystallogr.14(5), 493–497 (1961).
[CrossRef]

Khadzhiiski, N. G.

N. G. Khadzhiiski and N. I. Koroteev, “Coherent Raman ellipsometry of crystals: determination of the components and the dispersion of the third-order nonlinear susceptibility tensor of rutile,” Opt. Commun.42(6), 423–427 (1982).
[CrossRef]

Koroteev, N. I.

N. G. Khadzhiiski and N. I. Koroteev, “Coherent Raman ellipsometry of crystals: determination of the components and the dispersion of the third-order nonlinear susceptibility tensor of rutile,” Opt. Commun.42(6), 423–427 (1982).
[CrossRef]

Levenson, J. A.

K. Bencheikh, F. Gravier, J. Douady, J. A. Levenson, and B. Boulanger, “Triple photons: a challenge in nonlinear and quantum optics,” C. R. Phys.8(2), 206–220 (2007).
[CrossRef]

Li, Y.

H. Long, A. Chen, G. Yang, Y. Li, and P. Lu, “Third-order optical nonlinearities in anatase and rutile TiO2 thin films,” Thin Solid Films517(19), 5601–5604 (2009).
[CrossRef]

Lines, M. E.

M. E. Lines, “Influence of d orbitals on the nonlinear optical response of transparent transition-metal oxides,” Phys. Rev. B Condens. Matter43(14), 11978–11990 (1991).
[CrossRef] [PubMed]

Long, H.

H. Long, A. Chen, G. Yang, Y. Li, and P. Lu, “Third-order optical nonlinearities in anatase and rutile TiO2 thin films,” Thin Solid Films517(19), 5601–5604 (2009).
[CrossRef]

Lu, P.

H. Long, A. Chen, G. Yang, Y. Li, and P. Lu, “Third-order optical nonlinearities in anatase and rutile TiO2 thin films,” Thin Solid Films517(19), 5601–5604 (2009).
[CrossRef]

Marnier, G.

B. Boulanger, J. P. Fève, and G. Marnier, “Field-factor formalism for the study of the tensorial symmetry of four-wave nonlinear optical parametric interactions in uniaxial and biaxial crystals,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics48(6), 4730–4751 (1993).
[CrossRef] [PubMed]

Ménaert, B.

Y. Guillien, B. Ménaert, J. P. Fève, P. Segonds, J. Douady, B. Boulanger, and O. Pacaud, “Crystal growth and refined Sellmeier equations over the complete transparency range of RbTiOPO4,” Opt. Mater.22(2), 155–162 (2003).
[CrossRef]

O. Pacaud, J. P. Fève, B. Boulanger, and B. Ménaert, “Cylindrical KTiOPO4 crystal for enhanced angular tunability of phase-matched optical parametric oscillators,” Opt. Lett.25(10), 737–739 (2000).
[CrossRef] [PubMed]

Miller, R. C.

R. C. Miller, “Optical second harmonic generation in piezoelectric crystals,” Appl. Phys. Lett.5(1), 17–19 (1964).
[CrossRef]

Pacaud, O.

Y. Guillien, B. Ménaert, J. P. Fève, P. Segonds, J. Douady, B. Boulanger, and O. Pacaud, “Crystal growth and refined Sellmeier equations over the complete transparency range of RbTiOPO4,” Opt. Mater.22(2), 155–162 (2003).
[CrossRef]

O. Pacaud, J. P. Fève, B. Boulanger, and B. Ménaert, “Cylindrical KTiOPO4 crystal for enhanced angular tunability of phase-matched optical parametric oscillators,” Opt. Lett.25(10), 737–739 (2000).
[CrossRef] [PubMed]

Payne, S. A.

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B Condens. Matter39(5), 3337–3350 (1989).
[CrossRef] [PubMed]

Rams, J.

J. Rams, A. Tejeda, and J. M. Cabrera, “Refractive indices of rutile as a function of temperature and wavelength,” J. Appl. Phys.82(3), 994–997 (1997).
[CrossRef]

Sakka, S.

T. Hashimoto, T. Yoko, and S. Sakka, “Sol-Gel preparation and third-order nonlinear optical properties of TiO2 thin films,” Bull. Chem. Soc. Jpn.67(3), 653–660 (1994).
[CrossRef]

Segonds, P.

Y. Guillien, B. Ménaert, J. P. Fève, P. Segonds, J. Douady, B. Boulanger, and O. Pacaud, “Crystal growth and refined Sellmeier equations over the complete transparency range of RbTiOPO4,” Opt. Mater.22(2), 155–162 (2003).
[CrossRef]

Shimony, A.

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, “Bell’s theorem without inequalities,” Am. J. Phys.58(12), 1131–1143 (1990).
[CrossRef]

Straumanis, M. E.

M. E. Straumanis, T. Ejima, and W. J. James, “The TiO2 phase explored by the lattice constant and density method,” Acta Crystallogr.14(5), 493–497 (1961).
[CrossRef]

Tejeda, A.

J. Rams, A. Tejeda, and J. M. Cabrera, “Refractive indices of rutile as a function of temperature and wavelength,” J. Appl. Phys.82(3), 994–997 (1997).
[CrossRef]

Yang, G.

H. Long, A. Chen, G. Yang, Y. Li, and P. Lu, “Third-order optical nonlinearities in anatase and rutile TiO2 thin films,” Thin Solid Films517(19), 5601–5604 (2009).
[CrossRef]

Yoko, T.

T. Hashimoto, T. Yoko, and S. Sakka, “Sol-Gel preparation and third-order nonlinear optical properties of TiO2 thin films,” Bull. Chem. Soc. Jpn.67(3), 653–660 (1994).
[CrossRef]

Zeilinger, A.

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, “Bell’s theorem without inequalities,” Am. J. Phys.58(12), 1131–1143 (1990).
[CrossRef]

Acta Crystallogr. (1)

M. E. Straumanis, T. Ejima, and W. J. James, “The TiO2 phase explored by the lattice constant and density method,” Acta Crystallogr.14(5), 493–497 (1961).
[CrossRef]

Am. J. Phys. (1)

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, “Bell’s theorem without inequalities,” Am. J. Phys.58(12), 1131–1143 (1990).
[CrossRef]

Appl. Phys. Lett. (1)

R. C. Miller, “Optical second harmonic generation in piezoelectric crystals,” Appl. Phys. Lett.5(1), 17–19 (1964).
[CrossRef]

Bull. Chem. Soc. Jpn. (1)

T. Hashimoto, T. Yoko, and S. Sakka, “Sol-Gel preparation and third-order nonlinear optical properties of TiO2 thin films,” Bull. Chem. Soc. Jpn.67(3), 653–660 (1994).
[CrossRef]

C. R. Phys. (1)

K. Bencheikh, F. Gravier, J. Douady, J. A. Levenson, and B. Boulanger, “Triple photons: a challenge in nonlinear and quantum optics,” C. R. Phys.8(2), 206–220 (2007).
[CrossRef]

J. Appl. Phys. (1)

J. Rams, A. Tejeda, and J. M. Cabrera, “Refractive indices of rutile as a function of temperature and wavelength,” J. Appl. Phys.82(3), 994–997 (1997).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

N. G. Khadzhiiski and N. I. Koroteev, “Coherent Raman ellipsometry of crystals: determination of the components and the dispersion of the third-order nonlinear susceptibility tensor of rutile,” Opt. Commun.42(6), 423–427 (1982).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Opt. Mater. (2)

Y. Guillien, B. Ménaert, J. P. Fève, P. Segonds, J. Douady, B. Boulanger, and O. Pacaud, “Crystal growth and refined Sellmeier equations over the complete transparency range of RbTiOPO4,” Opt. Mater.22(2), 155–162 (2003).
[CrossRef]

F. Gravier and B. Boulanger, “Third-order frequency generation in TiO2 rutile and KTiOPO4,” Opt. Mater.30(1), 33–36 (2007).
[CrossRef]

Phys. Rev. (1)

D. C. Cronemeyer, “Electrical and optical properties of rutile single crystals,” Phys. Rev.87(5), 876–886 (1952).
[CrossRef]

Phys. Rev. B Condens. Matter (2)

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B Condens. Matter39(5), 3337–3350 (1989).
[CrossRef] [PubMed]

M. E. Lines, “Influence of d orbitals on the nonlinear optical response of transparent transition-metal oxides,” Phys. Rev. B Condens. Matter43(14), 11978–11990 (1991).
[CrossRef] [PubMed]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

B. Boulanger, J. P. Fève, and G. Marnier, “Field-factor formalism for the study of the tensorial symmetry of four-wave nonlinear optical parametric interactions in uniaxial and biaxial crystals,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics48(6), 4730–4751 (1993).
[CrossRef] [PubMed]

Thin Solid Films (1)

H. Long, A. Chen, G. Yang, Y. Li, and P. Lu, “Third-order optical nonlinearities in anatase and rutile TiO2 thin films,” Thin Solid Films517(19), 5601–5604 (2009).
[CrossRef]

Other (2)

Data from Almaz Optics Inc., www.almazoptics.com/TiO2.htm .

A. Hadni, Essentials of Modern Physics Applied to the Study of the Infrared (Pergamon Press, 1967).

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Figures (4)

Fig. 1
Fig. 1

(a) Picture of the oriented 4-mm radius TiO2 cylinder with the y-axis as rotation axis; (b) Schematic top view of the THG experimental setup where ω and are the fundamental and third harmonic circular frequencies. HWP is a Half-Wave Plate.

Fig. 2
Fig. 2

Type II THG phase-matching curve of rutile TiO2. Black squares are experimental data from the cylinder experiment and the solid red line corresponds to their numerical interpolation. Color dashed lines are phase-matching curves calculated from data of [2,68].

Fig. 3
Fig. 3

Ordinary no and extraordinary ne principal refractive indices of TiO2 as a function of wavelength from present work in solid lines, and from [69] in symbols (experiments) and dashed lines (calculations).

Fig. 4
Fig. 4

Type II THG conversion efficiency of rutile TiO2 as a function of the phase-matching angle for fundamental energies ξω = 16µJ (black dots) and 1.9µJ (blue triangles). In the insert is shown the magnitude of the effective coefficient χeff(3) where the black squares correspond to values determined from conversion efficiencies experimental data and Eq. (4); the dashed red and solid blue lines are calculations considering χ16 and χ18 with same and opposite signs respectively.

Equations (9)

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

Δk= ω c [ 3 n ( o ) ( θ AP ,3ω ) n ( o ) ( θ AP ,ω )2 n ( e ) ( θ AP ,ω ) ]=0
θ AP =acos[ ( ( n o ( ω ) n e ( 3ω ) ) 2 4 ( 3 n o ( ω ) n o ( 3ω ) ) 2 ( n o ( ω ) n e ( ω ) ) 2 1 ( n o ( ω ) n e ( ω ) ) 2 ) 1/2 ]
χ eff ( 3 ) ( θ AP , ω, 3ω)=[ sin 2 ( θ AP ρ( θ AP , ω) ) ]. χ 16 (3ω)+[ cos 2 ( θ AP ρ( θ AP , ω) ) ]. χ 18 (3ω)
η= 128. μ 0 3π. ε 0 [ χ eff (3) ] 2 λ ω 2 T ω (o) [ T ω (e) ] 2 T 3ω (o) n ω (o) [ n ω (e) ] 2 n 3ω (o) τ 3ω τ ω 3 w 3ω 2 w ω 6 G(β) L 2 [ ξ ω (L) ] 2
G(β)= 6 π + F 2 (u,β)du
F( u,β )= e u 2 β 0 β e [ 2 (u+σ) 2 ]  dσ
n o 2 ( λ )=3.2089+ 3.4000× 10 5 1.2270× 10 5 λ 2 3.2545× 10 8 λ 2
n e 2 ( λ )=2.9713+ 5.1891× 10 5 1.2280× 10 5 λ 2 4.2950× 10 8 λ 2
Δ 18 = | χ 18 (3ω) | ( n e 2 ( ω )1 ) 2 ( n o 2 ( ω )1 )( n o 2 ( 3ω )1 ) =9.1× 10 23   m 2 V 2

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