Abstract

Optical nonlinearity or the nonlinear hyperpolarizability of amorphous materials (e.g., glasses) is related directly to the complex third-order susceptibility. The imaginary part of third-order susceptibility affects negatively the maximum data rate in telecommunication systems. In addition, many transition metals containing glasses have bandgaps with semiconductor-like behavior. So, due to the necessity of operation near the absorption band edge, the study of optical nonlinearity and band structure in glasses is very essential. In this work, we investigated the relationship between the imaginary third-order nonlinear susceptibility and the bandgap of some different series of prepared oxide glasses. A universal empirical formula is given to correlate the imaginary part of the third-order nonlinear susceptibility of the glasses and their optical bandgaps. The obtained nonlinearity is discussed in view of available theories and mechanisms.

© 2009 Optical Society of America

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  1. R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2003).
  2. V. Dimitrov and S. Sakka, “Linear and nonlinear optical properties of simple oxides. II,” J. Appl. Phys. 79, 1741-1745(1996).
    [CrossRef]
  3. H. Ticha´ and L. Tichy´, “Semiempirical relation between non-linear susceptibility (refractive index), linear refractive index and optical gap and its application to amorphous chalcogenides,” J. Optoelectron. Adv. Mater. 4, 381-386 (2002).
  4. N. L. Böling, A. J. Glass, and A. Owyoung, “Empirical relationships for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. 14, 601-608 (1978).
    [CrossRef]
  5. K. Petkov and P. J. S. Ewen, “Photoinduced changes in the linear and non-linear optical properties of chalcogenide glasses,” J. Non-Cryst. Solids 249, 150-159 (1999).
    [CrossRef]
  6. K. S. Bindra, H. T. Bookey, A. K. Kar, B. S. Wherrett, X. Liu, and A. Jha, “Nonlinear optical properties of chalcogenide glasses: Observation of multiphoton absorption,” Appl. Phys. Lett. 79, 1939-1941 (2001).
    [CrossRef]
  7. R. C. Miller, “Optical second harmonic generation in piezoelectric crystals,” Appl. Phys. Lett. 5, 17-19 (1964).
    [CrossRef]
  8. D. Hobbs, D. Weaire, S. McMurry, and O. Zuchuat, “The computation of linear and nonlinear optical constants of semiconductors,” J. Phys. Condens. Matter 8, 4691-4708 (1996).
    [CrossRef]
  9. S. Suehara, T. Konishi, and S. Inoue, “Ab initio calculation of the refractive index and third-order nonlinear optical susceptibility of typical glass formers using the bond additivity model,” Phys. Rev. B 73, 092203 (2006).
    [CrossRef]
  10. M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65, 96-99 (1990).
    [CrossRef] [PubMed]
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    [CrossRef]
  15. T. Cassano, R. Tommasi, M. Ferrara, F. Babudri, G. M. Farimol, and F. Naso, “Substituent-dependence of the optical nonlinearities in poly(2,5-dialkoxy-p-phenylenevinylene) polymers investigated by the Z-scan technique,” Chem. Phys. 272, 111-118 (2001).
    [CrossRef]
  16. E. A. Davis and N. F. Mott, “Conduction in noncrystalline systems V. Conductivity, optical absorption and photoconductivity in amorphous semiconductors,” Philos. Mag. 22903-922 (1970).
    [CrossRef]
  17. M. Abdel-Baki, F. A. Abdel Wahab, and F. El-Diasty, “Optical characterization of xTiO2─(60−x)SiO2─40Na2O glasses: I. linear and nonlinear dispersion properties,” Mater. Chem. Phys. 96, 201-210 (2006).
    [CrossRef]
  18. F. El-Diasty, F. A. Abdel Wahab, and M. Abdel-Baki, “Optical bandgap studies on lithium aluminum silicate glasses doped with Cr3+ ions,” J. Appl. Phys. 100, 093511 (2006).
    [CrossRef]
  19. M. Abdel-Baki and F. El-Diasty, “Linear and nonlinear refractive-index properties of silicate glasses doped with BaO: fundamental absorption edge investigation,” Phys. Chem. Glasses 48, 74-78 (2007).
  20. M. Abdel-Baki, F. A. Abdel Wahab, A. Radi, and F. El-Diasty, “Factors affecting optical dispersion in borate glass systems,” J. Phys. Chem. Solids 68, 1457-1470 (2007).
    [CrossRef]
  21. B. Edlén, “The refractive index of air,” Metrologia 2, 71-79 (1966).
    [CrossRef]
  22. M. A. Khashan and A. M. El-Naggar, “A new method of finding the optical constants of a solid from the reflectance and transmittance spectrograms of its slab,” Opt. Commun. 174, 445-453 (2000).
    [CrossRef]
  23. E. M. Vogel, M. J. Weber, and D. M. Krol, “Nonlinear optical phenomena in glass,” Phys. Chem. Glasses 32231-254 (1991).
  24. M. Lines, “Oxide glasses for fast photonic switching: A comparative study,” J. Appl. Phys. 69, 6876-6884 (1991).
    [CrossRef]
  25. C. Chen and G. Z. Liu, “Recent advances in nonlinear optical and electro-optical materials,” Annu. Rev. Mater. Sci. 16, 203-243 (1986).
    [CrossRef]
  26. H. Kimura and A. Miyazaki, “Composition dependence of third-order nonlinear optical properties on BaO─B2O3─Al2O3 and BaO─B2O3─Ga2O3 glasses,” Mater. Res. Bull. 36, 1847-1853 (2001).
    [CrossRef]
  27. J. R. Tessman and A. H. Kahn, “Electronic polarizabilities of ions in crystals,” Phys. Rev. 92, 890-895 (1953).
    [CrossRef]
  28. M. Abdel-Baki, F. El-Diasty, and F. A. Abdel Wahab, Opt. “Optical characterization of xTiO2─(60−x)SiO2─40Na2O glasses: II. Absorption edge, Fermi level, electronic polarizability and optical basicity,” Opt. Commun. 261, 65-70 (2006).
    [CrossRef]
  29. A. Abou Shama, M. S. Abd El Keriem, M. Abdel-Baki, and F. El-Diasty, “RDF analysis, Positron annihilation and Raman spectroscopy of xTiO2─(60−x)SiO2─40Na2O nonlinear optical glasses: III. Non-bridging oxygen bonds tracing and structure analysis,” J. Non-Cryst. Solids 353, 2708-2716 (2007).
    [CrossRef]
  30. H. Nasu, O. Sugimoto, J. Matsuoka, and K. Kamiya, “Non-resonant-type third-order optical non-linearity of alkali silicate and alkali aluminosilicate glasses-contribution of individual chemical species in the glasses to χ(3),” J. Non-Cryst. Solids 182, 321-327 (1995).
    [CrossRef]
  31. Q. Liu, X. Zhao, F. Gan, J. Mi, and S. Quin, “Femtosecond optical Kerr effect study of amorphous chalcogenide films,” J. Non-Cryst. Solids 352, 2351-2354 (2006).
    [CrossRef]

2007

K. Tanaka, “Nonlinear optics in glasses: How can we analyze?,” J. Phys. Chem. Solids 68, 896-900 (2007).
[CrossRef]

M. Abdel-Baki and F. El-Diasty, “Linear and nonlinear refractive-index properties of silicate glasses doped with BaO: fundamental absorption edge investigation,” Phys. Chem. Glasses 48, 74-78 (2007).

M. Abdel-Baki, F. A. Abdel Wahab, A. Radi, and F. El-Diasty, “Factors affecting optical dispersion in borate glass systems,” J. Phys. Chem. Solids 68, 1457-1470 (2007).
[CrossRef]

A. Abou Shama, M. S. Abd El Keriem, M. Abdel-Baki, and F. El-Diasty, “RDF analysis, Positron annihilation and Raman spectroscopy of xTiO2─(60−x)SiO2─40Na2O nonlinear optical glasses: III. Non-bridging oxygen bonds tracing and structure analysis,” J. Non-Cryst. Solids 353, 2708-2716 (2007).
[CrossRef]

2006

M. Abdel-Baki, F. El-Diasty, and F. A. Abdel Wahab, Opt. “Optical characterization of xTiO2─(60−x)SiO2─40Na2O glasses: II. Absorption edge, Fermi level, electronic polarizability and optical basicity,” Opt. Commun. 261, 65-70 (2006).
[CrossRef]

Q. Liu, X. Zhao, F. Gan, J. Mi, and S. Quin, “Femtosecond optical Kerr effect study of amorphous chalcogenide films,” J. Non-Cryst. Solids 352, 2351-2354 (2006).
[CrossRef]

M. Abdel-Baki, F. A. Abdel Wahab, and F. El-Diasty, “Optical characterization of xTiO2─(60−x)SiO2─40Na2O glasses: I. linear and nonlinear dispersion properties,” Mater. Chem. Phys. 96, 201-210 (2006).
[CrossRef]

F. El-Diasty, F. A. Abdel Wahab, and M. Abdel-Baki, “Optical bandgap studies on lithium aluminum silicate glasses doped with Cr3+ ions,” J. Appl. Phys. 100, 093511 (2006).
[CrossRef]

S. Suehara, T. Konishi, and S. Inoue, “Ab initio calculation of the refractive index and third-order nonlinear optical susceptibility of typical glass formers using the bond additivity model,” Phys. Rev. B 73, 092203 (2006).
[CrossRef]

2002

H. Ticha´ and L. Tichy´, “Semiempirical relation between non-linear susceptibility (refractive index), linear refractive index and optical gap and its application to amorphous chalcogenides,” J. Optoelectron. Adv. Mater. 4, 381-386 (2002).

2001

K. S. Bindra, H. T. Bookey, A. K. Kar, B. S. Wherrett, X. Liu, and A. Jha, “Nonlinear optical properties of chalcogenide glasses: Observation of multiphoton absorption,” Appl. Phys. Lett. 79, 1939-1941 (2001).
[CrossRef]

T. Cassano, R. Tommasi, M. Ferrara, F. Babudri, G. M. Farimol, and F. Naso, “Substituent-dependence of the optical nonlinearities in poly(2,5-dialkoxy-p-phenylenevinylene) polymers investigated by the Z-scan technique,” Chem. Phys. 272, 111-118 (2001).
[CrossRef]

H. Kimura and A. Miyazaki, “Composition dependence of third-order nonlinear optical properties on BaO─B2O3─Al2O3 and BaO─B2O3─Ga2O3 glasses,” Mater. Res. Bull. 36, 1847-1853 (2001).
[CrossRef]

2000

M. A. Khashan and A. M. El-Naggar, “A new method of finding the optical constants of a solid from the reflectance and transmittance spectrograms of its slab,” Opt. Commun. 174, 445-453 (2000).
[CrossRef]

1999

K. Petkov and P. J. S. Ewen, “Photoinduced changes in the linear and non-linear optical properties of chalcogenide glasses,” J. Non-Cryst. Solids 249, 150-159 (1999).
[CrossRef]

1996

V. Dimitrov and S. Sakka, “Linear and nonlinear optical properties of simple oxides. II,” J. Appl. Phys. 79, 1741-1745(1996).
[CrossRef]

D. Hobbs, D. Weaire, S. McMurry, and O. Zuchuat, “The computation of linear and nonlinear optical constants of semiconductors,” J. Phys. Condens. Matter 8, 4691-4708 (1996).
[CrossRef]

1995

H. Nasu, O. Sugimoto, J. Matsuoka, and K. Kamiya, “Non-resonant-type third-order optical non-linearity of alkali silicate and alkali aluminosilicate glasses-contribution of individual chemical species in the glasses to χ(3),” J. Non-Cryst. Solids 182, 321-327 (1995).
[CrossRef]

1991

E. M. Vogel, M. J. Weber, and D. M. Krol, “Nonlinear optical phenomena in glass,” Phys. Chem. Glasses 32231-254 (1991).

M. Lines, “Oxide glasses for fast photonic switching: A comparative study,” J. Appl. Phys. 69, 6876-6884 (1991).
[CrossRef]

1990

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65, 96-99 (1990).
[CrossRef] [PubMed]

1986

C. Chen and G. Z. Liu, “Recent advances in nonlinear optical and electro-optical materials,” Annu. Rev. Mater. Sci. 16, 203-243 (1986).
[CrossRef]

1984

1981

M. Weiler, “Nonparabolicity and exciton effects in two-photon absorption in zincblende semiconductors,” Solid State Commun. 39, 937-940 (1981).
[CrossRef]

1978

N. L. Böling, A. J. Glass, and A. Owyoung, “Empirical relationships for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. 14, 601-608 (1978).
[CrossRef]

1970

E. A. Davis and N. F. Mott, “Conduction in noncrystalline systems V. Conductivity, optical absorption and photoconductivity in amorphous semiconductors,” Philos. Mag. 22903-922 (1970).
[CrossRef]

1966

B. Edlén, “The refractive index of air,” Metrologia 2, 71-79 (1966).
[CrossRef]

1964

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

1953

J. R. Tessman and A. H. Kahn, “Electronic polarizabilities of ions in crystals,” Phys. Rev. 92, 890-895 (1953).
[CrossRef]

Abd El Keriem, M. S.

A. Abou Shama, M. S. Abd El Keriem, M. Abdel-Baki, and F. El-Diasty, “RDF analysis, Positron annihilation and Raman spectroscopy of xTiO2─(60−x)SiO2─40Na2O nonlinear optical glasses: III. Non-bridging oxygen bonds tracing and structure analysis,” J. Non-Cryst. Solids 353, 2708-2716 (2007).
[CrossRef]

Abdel Wahab, F. A.

M. Abdel-Baki, F. A. Abdel Wahab, A. Radi, and F. El-Diasty, “Factors affecting optical dispersion in borate glass systems,” J. Phys. Chem. Solids 68, 1457-1470 (2007).
[CrossRef]

F. El-Diasty, F. A. Abdel Wahab, and M. Abdel-Baki, “Optical bandgap studies on lithium aluminum silicate glasses doped with Cr3+ ions,” J. Appl. Phys. 100, 093511 (2006).
[CrossRef]

M. Abdel-Baki, F. A. Abdel Wahab, and F. El-Diasty, “Optical characterization of xTiO2─(60−x)SiO2─40Na2O glasses: I. linear and nonlinear dispersion properties,” Mater. Chem. Phys. 96, 201-210 (2006).
[CrossRef]

M. Abdel-Baki, F. El-Diasty, and F. A. Abdel Wahab, Opt. “Optical characterization of xTiO2─(60−x)SiO2─40Na2O glasses: II. Absorption edge, Fermi level, electronic polarizability and optical basicity,” Opt. Commun. 261, 65-70 (2006).
[CrossRef]

Abdel-Baki, M.

M. Abdel-Baki and F. El-Diasty, “Linear and nonlinear refractive-index properties of silicate glasses doped with BaO: fundamental absorption edge investigation,” Phys. Chem. Glasses 48, 74-78 (2007).

M. Abdel-Baki, F. A. Abdel Wahab, A. Radi, and F. El-Diasty, “Factors affecting optical dispersion in borate glass systems,” J. Phys. Chem. Solids 68, 1457-1470 (2007).
[CrossRef]

A. Abou Shama, M. S. Abd El Keriem, M. Abdel-Baki, and F. El-Diasty, “RDF analysis, Positron annihilation and Raman spectroscopy of xTiO2─(60−x)SiO2─40Na2O nonlinear optical glasses: III. Non-bridging oxygen bonds tracing and structure analysis,” J. Non-Cryst. Solids 353, 2708-2716 (2007).
[CrossRef]

M. Abdel-Baki, F. A. Abdel Wahab, and F. El-Diasty, “Optical characterization of xTiO2─(60−x)SiO2─40Na2O glasses: I. linear and nonlinear dispersion properties,” Mater. Chem. Phys. 96, 201-210 (2006).
[CrossRef]

F. El-Diasty, F. A. Abdel Wahab, and M. Abdel-Baki, “Optical bandgap studies on lithium aluminum silicate glasses doped with Cr3+ ions,” J. Appl. Phys. 100, 093511 (2006).
[CrossRef]

M. Abdel-Baki, F. El-Diasty, and F. A. Abdel Wahab, Opt. “Optical characterization of xTiO2─(60−x)SiO2─40Na2O glasses: II. Absorption edge, Fermi level, electronic polarizability and optical basicity,” Opt. Commun. 261, 65-70 (2006).
[CrossRef]

Abou Shama, A.

A. Abou Shama, M. S. Abd El Keriem, M. Abdel-Baki, and F. El-Diasty, “RDF analysis, Positron annihilation and Raman spectroscopy of xTiO2─(60−x)SiO2─40Na2O nonlinear optical glasses: III. Non-bridging oxygen bonds tracing and structure analysis,” J. Non-Cryst. Solids 353, 2708-2716 (2007).
[CrossRef]

Babudri, F.

T. Cassano, R. Tommasi, M. Ferrara, F. Babudri, G. M. Farimol, and F. Naso, “Substituent-dependence of the optical nonlinearities in poly(2,5-dialkoxy-p-phenylenevinylene) polymers investigated by the Z-scan technique,” Chem. Phys. 272, 111-118 (2001).
[CrossRef]

Bindra, K. S.

K. S. Bindra, H. T. Bookey, A. K. Kar, B. S. Wherrett, X. Liu, and A. Jha, “Nonlinear optical properties of chalcogenide glasses: Observation of multiphoton absorption,” Appl. Phys. Lett. 79, 1939-1941 (2001).
[CrossRef]

Böling, N. L.

N. L. Böling, A. J. Glass, and A. Owyoung, “Empirical relationships for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. 14, 601-608 (1978).
[CrossRef]

Bookey, H. T.

K. S. Bindra, H. T. Bookey, A. K. Kar, B. S. Wherrett, X. Liu, and A. Jha, “Nonlinear optical properties of chalcogenide glasses: Observation of multiphoton absorption,” Appl. Phys. Lett. 79, 1939-1941 (2001).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2003).

Cassano, T.

T. Cassano, R. Tommasi, M. Ferrara, F. Babudri, G. M. Farimol, and F. Naso, “Substituent-dependence of the optical nonlinearities in poly(2,5-dialkoxy-p-phenylenevinylene) polymers investigated by the Z-scan technique,” Chem. Phys. 272, 111-118 (2001).
[CrossRef]

Chen, C.

C. Chen and G. Z. Liu, “Recent advances in nonlinear optical and electro-optical materials,” Annu. Rev. Mater. Sci. 16, 203-243 (1986).
[CrossRef]

Davis, E. A.

E. A. Davis and N. F. Mott, “Conduction in noncrystalline systems V. Conductivity, optical absorption and photoconductivity in amorphous semiconductors,” Philos. Mag. 22903-922 (1970).
[CrossRef]

Dimitrov, V.

V. Dimitrov and S. Sakka, “Linear and nonlinear optical properties of simple oxides. II,” J. Appl. Phys. 79, 1741-1745(1996).
[CrossRef]

Edlén, B.

B. Edlén, “The refractive index of air,” Metrologia 2, 71-79 (1966).
[CrossRef]

El-Diasty, F.

M. Abdel-Baki, F. A. Abdel Wahab, A. Radi, and F. El-Diasty, “Factors affecting optical dispersion in borate glass systems,” J. Phys. Chem. Solids 68, 1457-1470 (2007).
[CrossRef]

M. Abdel-Baki and F. El-Diasty, “Linear and nonlinear refractive-index properties of silicate glasses doped with BaO: fundamental absorption edge investigation,” Phys. Chem. Glasses 48, 74-78 (2007).

A. Abou Shama, M. S. Abd El Keriem, M. Abdel-Baki, and F. El-Diasty, “RDF analysis, Positron annihilation and Raman spectroscopy of xTiO2─(60−x)SiO2─40Na2O nonlinear optical glasses: III. Non-bridging oxygen bonds tracing and structure analysis,” J. Non-Cryst. Solids 353, 2708-2716 (2007).
[CrossRef]

M. Abdel-Baki, F. A. Abdel Wahab, and F. El-Diasty, “Optical characterization of xTiO2─(60−x)SiO2─40Na2O glasses: I. linear and nonlinear dispersion properties,” Mater. Chem. Phys. 96, 201-210 (2006).
[CrossRef]

F. El-Diasty, F. A. Abdel Wahab, and M. Abdel-Baki, “Optical bandgap studies on lithium aluminum silicate glasses doped with Cr3+ ions,” J. Appl. Phys. 100, 093511 (2006).
[CrossRef]

M. Abdel-Baki, F. El-Diasty, and F. A. Abdel Wahab, Opt. “Optical characterization of xTiO2─(60−x)SiO2─40Na2O glasses: II. Absorption edge, Fermi level, electronic polarizability and optical basicity,” Opt. Commun. 261, 65-70 (2006).
[CrossRef]

El-Naggar, A. M.

M. A. Khashan and A. M. El-Naggar, “A new method of finding the optical constants of a solid from the reflectance and transmittance spectrograms of its slab,” Opt. Commun. 174, 445-453 (2000).
[CrossRef]

Ewen, P. J. S.

K. Petkov and P. J. S. Ewen, “Photoinduced changes in the linear and non-linear optical properties of chalcogenide glasses,” J. Non-Cryst. Solids 249, 150-159 (1999).
[CrossRef]

Farimol, G. M.

T. Cassano, R. Tommasi, M. Ferrara, F. Babudri, G. M. Farimol, and F. Naso, “Substituent-dependence of the optical nonlinearities in poly(2,5-dialkoxy-p-phenylenevinylene) polymers investigated by the Z-scan technique,” Chem. Phys. 272, 111-118 (2001).
[CrossRef]

Ferrara, M.

T. Cassano, R. Tommasi, M. Ferrara, F. Babudri, G. M. Farimol, and F. Naso, “Substituent-dependence of the optical nonlinearities in poly(2,5-dialkoxy-p-phenylenevinylene) polymers investigated by the Z-scan technique,” Chem. Phys. 272, 111-118 (2001).
[CrossRef]

Gan, F.

Q. Liu, X. Zhao, F. Gan, J. Mi, and S. Quin, “Femtosecond optical Kerr effect study of amorphous chalcogenide films,” J. Non-Cryst. Solids 352, 2351-2354 (2006).
[CrossRef]

Glass, A. J.

N. L. Böling, A. J. Glass, and A. Owyoung, “Empirical relationships for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. 14, 601-608 (1978).
[CrossRef]

Hagan, D. J.

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65, 96-99 (1990).
[CrossRef] [PubMed]

Hobbs, D.

D. Hobbs, D. Weaire, S. McMurry, and O. Zuchuat, “The computation of linear and nonlinear optical constants of semiconductors,” J. Phys. Condens. Matter 8, 4691-4708 (1996).
[CrossRef]

Inoue, S.

S. Suehara, T. Konishi, and S. Inoue, “Ab initio calculation of the refractive index and third-order nonlinear optical susceptibility of typical glass formers using the bond additivity model,” Phys. Rev. B 73, 092203 (2006).
[CrossRef]

Jha, A.

K. S. Bindra, H. T. Bookey, A. K. Kar, B. S. Wherrett, X. Liu, and A. Jha, “Nonlinear optical properties of chalcogenide glasses: Observation of multiphoton absorption,” Appl. Phys. Lett. 79, 1939-1941 (2001).
[CrossRef]

Kahn, A. H.

J. R. Tessman and A. H. Kahn, “Electronic polarizabilities of ions in crystals,” Phys. Rev. 92, 890-895 (1953).
[CrossRef]

Kamiya, K.

H. Nasu, O. Sugimoto, J. Matsuoka, and K. Kamiya, “Non-resonant-type third-order optical non-linearity of alkali silicate and alkali aluminosilicate glasses-contribution of individual chemical species in the glasses to χ(3),” J. Non-Cryst. Solids 182, 321-327 (1995).
[CrossRef]

Kar, A. K.

K. S. Bindra, H. T. Bookey, A. K. Kar, B. S. Wherrett, X. Liu, and A. Jha, “Nonlinear optical properties of chalcogenide glasses: Observation of multiphoton absorption,” Appl. Phys. Lett. 79, 1939-1941 (2001).
[CrossRef]

Khashan, M. A.

M. A. Khashan and A. M. El-Naggar, “A new method of finding the optical constants of a solid from the reflectance and transmittance spectrograms of its slab,” Opt. Commun. 174, 445-453 (2000).
[CrossRef]

Kimura, H.

H. Kimura and A. Miyazaki, “Composition dependence of third-order nonlinear optical properties on BaO─B2O3─Al2O3 and BaO─B2O3─Ga2O3 glasses,” Mater. Res. Bull. 36, 1847-1853 (2001).
[CrossRef]

Konishi, T.

S. Suehara, T. Konishi, and S. Inoue, “Ab initio calculation of the refractive index and third-order nonlinear optical susceptibility of typical glass formers using the bond additivity model,” Phys. Rev. B 73, 092203 (2006).
[CrossRef]

Krol, D. M.

E. M. Vogel, M. J. Weber, and D. M. Krol, “Nonlinear optical phenomena in glass,” Phys. Chem. Glasses 32231-254 (1991).

Lines, M.

M. Lines, “Oxide glasses for fast photonic switching: A comparative study,” J. Appl. Phys. 69, 6876-6884 (1991).
[CrossRef]

Liu, G. Z.

C. Chen and G. Z. Liu, “Recent advances in nonlinear optical and electro-optical materials,” Annu. Rev. Mater. Sci. 16, 203-243 (1986).
[CrossRef]

Liu, Q.

Q. Liu, X. Zhao, F. Gan, J. Mi, and S. Quin, “Femtosecond optical Kerr effect study of amorphous chalcogenide films,” J. Non-Cryst. Solids 352, 2351-2354 (2006).
[CrossRef]

Liu, X.

K. S. Bindra, H. T. Bookey, A. K. Kar, B. S. Wherrett, X. Liu, and A. Jha, “Nonlinear optical properties of chalcogenide glasses: Observation of multiphoton absorption,” Appl. Phys. Lett. 79, 1939-1941 (2001).
[CrossRef]

Matsuoka, J.

H. Nasu, O. Sugimoto, J. Matsuoka, and K. Kamiya, “Non-resonant-type third-order optical non-linearity of alkali silicate and alkali aluminosilicate glasses-contribution of individual chemical species in the glasses to χ(3),” J. Non-Cryst. Solids 182, 321-327 (1995).
[CrossRef]

McMurry, S.

D. Hobbs, D. Weaire, S. McMurry, and O. Zuchuat, “The computation of linear and nonlinear optical constants of semiconductors,” J. Phys. Condens. Matter 8, 4691-4708 (1996).
[CrossRef]

Mi, J.

Q. Liu, X. Zhao, F. Gan, J. Mi, and S. Quin, “Femtosecond optical Kerr effect study of amorphous chalcogenide films,” J. Non-Cryst. Solids 352, 2351-2354 (2006).
[CrossRef]

Miller, R. C.

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

Miyazaki, A.

H. Kimura and A. Miyazaki, “Composition dependence of third-order nonlinear optical properties on BaO─B2O3─Al2O3 and BaO─B2O3─Ga2O3 glasses,” Mater. Res. Bull. 36, 1847-1853 (2001).
[CrossRef]

Mott, N. F.

E. A. Davis and N. F. Mott, “Conduction in noncrystalline systems V. Conductivity, optical absorption and photoconductivity in amorphous semiconductors,” Philos. Mag. 22903-922 (1970).
[CrossRef]

Naso, F.

T. Cassano, R. Tommasi, M. Ferrara, F. Babudri, G. M. Farimol, and F. Naso, “Substituent-dependence of the optical nonlinearities in poly(2,5-dialkoxy-p-phenylenevinylene) polymers investigated by the Z-scan technique,” Chem. Phys. 272, 111-118 (2001).
[CrossRef]

Nasu, H.

H. Nasu, O. Sugimoto, J. Matsuoka, and K. Kamiya, “Non-resonant-type third-order optical non-linearity of alkali silicate and alkali aluminosilicate glasses-contribution of individual chemical species in the glasses to χ(3),” J. Non-Cryst. Solids 182, 321-327 (1995).
[CrossRef]

Owyoung, A.

N. L. Böling, A. J. Glass, and A. Owyoung, “Empirical relationships for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. 14, 601-608 (1978).
[CrossRef]

Petkov, K.

K. Petkov and P. J. S. Ewen, “Photoinduced changes in the linear and non-linear optical properties of chalcogenide glasses,” J. Non-Cryst. Solids 249, 150-159 (1999).
[CrossRef]

Quin, S.

Q. Liu, X. Zhao, F. Gan, J. Mi, and S. Quin, “Femtosecond optical Kerr effect study of amorphous chalcogenide films,” J. Non-Cryst. Solids 352, 2351-2354 (2006).
[CrossRef]

Radi, A.

M. Abdel-Baki, F. A. Abdel Wahab, A. Radi, and F. El-Diasty, “Factors affecting optical dispersion in borate glass systems,” J. Phys. Chem. Solids 68, 1457-1470 (2007).
[CrossRef]

Sakka, S.

V. Dimitrov and S. Sakka, “Linear and nonlinear optical properties of simple oxides. II,” J. Appl. Phys. 79, 1741-1745(1996).
[CrossRef]

Sheik-Bahae, M.

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65, 96-99 (1990).
[CrossRef] [PubMed]

M. Sheik-Bahae and E. W. Van Stryland, in: E.Garmire and A.Kost, eds., Semiconductors and Semimetals (Academic, 1999), Vol. 58, Chap. 4.

Suehara, S.

S. Suehara, T. Konishi, and S. Inoue, “Ab initio calculation of the refractive index and third-order nonlinear optical susceptibility of typical glass formers using the bond additivity model,” Phys. Rev. B 73, 092203 (2006).
[CrossRef]

Sugimoto, O.

H. Nasu, O. Sugimoto, J. Matsuoka, and K. Kamiya, “Non-resonant-type third-order optical non-linearity of alkali silicate and alkali aluminosilicate glasses-contribution of individual chemical species in the glasses to χ(3),” J. Non-Cryst. Solids 182, 321-327 (1995).
[CrossRef]

Tanaka, K.

K. Tanaka, “Nonlinear optics in glasses: How can we analyze?,” J. Phys. Chem. Solids 68, 896-900 (2007).
[CrossRef]

Tessman, J. R.

J. R. Tessman and A. H. Kahn, “Electronic polarizabilities of ions in crystals,” Phys. Rev. 92, 890-895 (1953).
[CrossRef]

Ticha´, H.

H. Ticha´ and L. Tichy´, “Semiempirical relation between non-linear susceptibility (refractive index), linear refractive index and optical gap and its application to amorphous chalcogenides,” J. Optoelectron. Adv. Mater. 4, 381-386 (2002).

Tichy´, L.

H. Ticha´ and L. Tichy´, “Semiempirical relation between non-linear susceptibility (refractive index), linear refractive index and optical gap and its application to amorphous chalcogenides,” J. Optoelectron. Adv. Mater. 4, 381-386 (2002).

Tommasi, R.

T. Cassano, R. Tommasi, M. Ferrara, F. Babudri, G. M. Farimol, and F. Naso, “Substituent-dependence of the optical nonlinearities in poly(2,5-dialkoxy-p-phenylenevinylene) polymers investigated by the Z-scan technique,” Chem. Phys. 272, 111-118 (2001).
[CrossRef]

Van Stryland, E. W.

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65, 96-99 (1990).
[CrossRef] [PubMed]

M. Sheik-Bahae and E. W. Van Stryland, in: E.Garmire and A.Kost, eds., Semiconductors and Semimetals (Academic, 1999), Vol. 58, Chap. 4.

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E. M. Vogel, M. J. Weber, and D. M. Krol, “Nonlinear optical phenomena in glass,” Phys. Chem. Glasses 32231-254 (1991).

Weaire, D.

D. Hobbs, D. Weaire, S. McMurry, and O. Zuchuat, “The computation of linear and nonlinear optical constants of semiconductors,” J. Phys. Condens. Matter 8, 4691-4708 (1996).
[CrossRef]

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E. M. Vogel, M. J. Weber, and D. M. Krol, “Nonlinear optical phenomena in glass,” Phys. Chem. Glasses 32231-254 (1991).

Weiler, M.

M. Weiler, “Nonparabolicity and exciton effects in two-photon absorption in zincblende semiconductors,” Solid State Commun. 39, 937-940 (1981).
[CrossRef]

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K. S. Bindra, H. T. Bookey, A. K. Kar, B. S. Wherrett, X. Liu, and A. Jha, “Nonlinear optical properties of chalcogenide glasses: Observation of multiphoton absorption,” Appl. Phys. Lett. 79, 1939-1941 (2001).
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[CrossRef]

Zhao, X.

Q. Liu, X. Zhao, F. Gan, J. Mi, and S. Quin, “Femtosecond optical Kerr effect study of amorphous chalcogenide films,” J. Non-Cryst. Solids 352, 2351-2354 (2006).
[CrossRef]

Zuchuat, O.

D. Hobbs, D. Weaire, S. McMurry, and O. Zuchuat, “The computation of linear and nonlinear optical constants of semiconductors,” J. Phys. Condens. Matter 8, 4691-4708 (1996).
[CrossRef]

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[CrossRef]

Appl. Phys. Lett.

K. S. Bindra, H. T. Bookey, A. K. Kar, B. S. Wherrett, X. Liu, and A. Jha, “Nonlinear optical properties of chalcogenide glasses: Observation of multiphoton absorption,” Appl. Phys. Lett. 79, 1939-1941 (2001).
[CrossRef]

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

Chem. Phys.

T. Cassano, R. Tommasi, M. Ferrara, F. Babudri, G. M. Farimol, and F. Naso, “Substituent-dependence of the optical nonlinearities in poly(2,5-dialkoxy-p-phenylenevinylene) polymers investigated by the Z-scan technique,” Chem. Phys. 272, 111-118 (2001).
[CrossRef]

IEEE J. Quantum Electron.

N. L. Böling, A. J. Glass, and A. Owyoung, “Empirical relationships for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. 14, 601-608 (1978).
[CrossRef]

J. Appl. Phys.

V. Dimitrov and S. Sakka, “Linear and nonlinear optical properties of simple oxides. II,” J. Appl. Phys. 79, 1741-1745(1996).
[CrossRef]

F. El-Diasty, F. A. Abdel Wahab, and M. Abdel-Baki, “Optical bandgap studies on lithium aluminum silicate glasses doped with Cr3+ ions,” J. Appl. Phys. 100, 093511 (2006).
[CrossRef]

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[CrossRef]

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A. Abou Shama, M. S. Abd El Keriem, M. Abdel-Baki, and F. El-Diasty, “RDF analysis, Positron annihilation and Raman spectroscopy of xTiO2─(60−x)SiO2─40Na2O nonlinear optical glasses: III. Non-bridging oxygen bonds tracing and structure analysis,” J. Non-Cryst. Solids 353, 2708-2716 (2007).
[CrossRef]

H. Nasu, O. Sugimoto, J. Matsuoka, and K. Kamiya, “Non-resonant-type third-order optical non-linearity of alkali silicate and alkali aluminosilicate glasses-contribution of individual chemical species in the glasses to χ(3),” J. Non-Cryst. Solids 182, 321-327 (1995).
[CrossRef]

Q. Liu, X. Zhao, F. Gan, J. Mi, and S. Quin, “Femtosecond optical Kerr effect study of amorphous chalcogenide films,” J. Non-Cryst. Solids 352, 2351-2354 (2006).
[CrossRef]

K. Petkov and P. J. S. Ewen, “Photoinduced changes in the linear and non-linear optical properties of chalcogenide glasses,” J. Non-Cryst. Solids 249, 150-159 (1999).
[CrossRef]

J. Opt. Soc. Am. B

J. Optoelectron. Adv. Mater.

H. Ticha´ and L. Tichy´, “Semiempirical relation between non-linear susceptibility (refractive index), linear refractive index and optical gap and its application to amorphous chalcogenides,” J. Optoelectron. Adv. Mater. 4, 381-386 (2002).

J. Phys. Chem. Solids

K. Tanaka, “Nonlinear optics in glasses: How can we analyze?,” J. Phys. Chem. Solids 68, 896-900 (2007).
[CrossRef]

M. Abdel-Baki, F. A. Abdel Wahab, A. Radi, and F. El-Diasty, “Factors affecting optical dispersion in borate glass systems,” J. Phys. Chem. Solids 68, 1457-1470 (2007).
[CrossRef]

J. Phys. Condens. Matter

D. Hobbs, D. Weaire, S. McMurry, and O. Zuchuat, “The computation of linear and nonlinear optical constants of semiconductors,” J. Phys. Condens. Matter 8, 4691-4708 (1996).
[CrossRef]

Mater. Chem. Phys.

M. Abdel-Baki, F. A. Abdel Wahab, and F. El-Diasty, “Optical characterization of xTiO2─(60−x)SiO2─40Na2O glasses: I. linear and nonlinear dispersion properties,” Mater. Chem. Phys. 96, 201-210 (2006).
[CrossRef]

Mater. Res. Bull.

H. Kimura and A. Miyazaki, “Composition dependence of third-order nonlinear optical properties on BaO─B2O3─Al2O3 and BaO─B2O3─Ga2O3 glasses,” Mater. Res. Bull. 36, 1847-1853 (2001).
[CrossRef]

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[CrossRef]

Opt. Commun.

M. A. Khashan and A. M. El-Naggar, “A new method of finding the optical constants of a solid from the reflectance and transmittance spectrograms of its slab,” Opt. Commun. 174, 445-453 (2000).
[CrossRef]

M. Abdel-Baki, F. El-Diasty, and F. A. Abdel Wahab, Opt. “Optical characterization of xTiO2─(60−x)SiO2─40Na2O glasses: II. Absorption edge, Fermi level, electronic polarizability and optical basicity,” Opt. Commun. 261, 65-70 (2006).
[CrossRef]

Philos. Mag.

E. A. Davis and N. F. Mott, “Conduction in noncrystalline systems V. Conductivity, optical absorption and photoconductivity in amorphous semiconductors,” Philos. Mag. 22903-922 (1970).
[CrossRef]

Phys. Chem. Glasses

M. Abdel-Baki and F. El-Diasty, “Linear and nonlinear refractive-index properties of silicate glasses doped with BaO: fundamental absorption edge investigation,” Phys. Chem. Glasses 48, 74-78 (2007).

E. M. Vogel, M. J. Weber, and D. M. Krol, “Nonlinear optical phenomena in glass,” Phys. Chem. Glasses 32231-254 (1991).

Phys. Rev.

J. R. Tessman and A. H. Kahn, “Electronic polarizabilities of ions in crystals,” Phys. Rev. 92, 890-895 (1953).
[CrossRef]

Phys. Rev. B

S. Suehara, T. Konishi, and S. Inoue, “Ab initio calculation of the refractive index and third-order nonlinear optical susceptibility of typical glass formers using the bond additivity model,” Phys. Rev. B 73, 092203 (2006).
[CrossRef]

Phys. Rev. Lett.

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65, 96-99 (1990).
[CrossRef] [PubMed]

Solid State Commun.

M. Weiler, “Nonparabolicity and exciton effects in two-photon absorption in zincblende semiconductors,” Solid State Commun. 39, 937-940 (1981).
[CrossRef]

Other

R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2003).

M. Sheik-Bahae and E. W. Van Stryland, in: E.Garmire and A.Kost, eds., Semiconductors and Semimetals (Academic, 1999), Vol. 58, Chap. 4.

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Figures (1)

Fig. 1
Fig. 1

Imaginary part of third-order susceptibility, Im χ ( 3 ) , and the optical bandgap energy, E g , of the different studied glass series. The imbedded numbers refer to the different studied glass samples.

Tables (1)

Tables Icon

Table 1 Linear Refractive Index, n, Imaginary Third-Order Susceptibility, Im χ ( 3 ) (Both Calculated at λ = 587.56 nm ) and Optical Bandgap Energy, E g

Equations (14)

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

n 2 ( 10 13 esu ) = 391 n 1 v d 5 / 4 .
n 2 ( 10 13 esu ) = 3 g S ( n 2 + 2 ) 1.5 ( n 2 1 ) 2 h 2 e 2 12 nm E d E 0 2 ,
n 2 ( ω ) = 1.7 × 10 14 ( n 2 + 2 ) 3 ( n 2 1 ) ( d n E s ) 2 f ( ω E g ) ,
χ ( 3 ) = ( n 2 1 4 π ) 4 × 10 10 .
n 2 = K E p 1 / 2 G / ( n 2 E g 4 ) ,
β = K E p 1 / 2 F / ( n 2 E g 3 ) ,
F = [ ( 2 ω / E g ) 1 ] 3 / 2 ( 2 ω / E g ) 5 .
P = P 0 + χ ( 1 ) E + χ ( 2 ) E E + χ ( 3 ) E E E ,
Re | χ ( 3 ) | = 2 ε 0 c n 2 n 2 ,
Im | χ ( 3 ) | = ε 0 c n 2 λ 2 π β .
α ( ω ) = α 0 ( ω E g ) m / ω ,
n = n air [ 1 + R 1 R + 4 R ( 1 R ) 2 k 2 n air 2 ] ,
n air = 1 + 10 4 [ 0.834213 + 240.603 130 λ 2 + 1.5997 38.9 λ 2 ] ,
Im χ ( 3 ) ( 10 12 esu ) = 166 37.6 E g ( eV ) .

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