Skip to main content
Erschienen in: Journal of Materials Science: Materials in Electronics 18/2019

22.06.2019

A generalized Drude–Lorentz model for refractive index behavior of tellurite glasses

verfasst von: Anderson Gonçalves, Maurício A. Ribeiro, Jaqueline V. Gunha, Aloisi Somer, Vitor S. Zanuto, Nelson G. C. Astrath, Daniele T. Dias, Maike A. F. dos Santos, Carlos Jacinto, Ervin K. Lenzi, Andressa Novatski

Erschienen in: Journal of Materials Science: Materials in Electronics | Ausgabe 18/2019

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

An extension of Drude–Lorentz model based on the fractional approach was used to investigate quantitative measurement of refractive index as a function of wavelength of Tellurite glasses. Tellurite glass samples were synthesized by conventional melt-quenching method with the composition of 65TeO2–15Li2O–20ZnO undoped and doped with different concentrations of Er2O3. Refractive index measurements were performed using the Brewster angle technique with polarized lasers at 442, 532, 594 and 633 nm as light source. From the Sellmeier’s coefficient it was possible to obtain the behavior of refractive index from 0.35 to 1.8 μm. The analytical solution obtained from the generalized Drude–Lorentz model was used to investigate the experimental data of refractive index behavior obtained by the two-pole Sellmeier’s equation showing that the mean polarizability increases with Er2O3 concentration and this behavior can be related to a collective fractal character of the material.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat A. Mori, Y. Ohishi, S. Sudo, Erbium-doped tellurite glass fibre laser and amplifier. Electron. Lett. 33(10), 863 (1997)CrossRef A. Mori, Y. Ohishi, S. Sudo, Erbium-doped tellurite glass fibre laser and amplifier. Electron. Lett. 33(10), 863 (1997)CrossRef
2.
Zurück zum Zitat J. Wang, E. Vogel, E. Snitzer, Tellurite glass: a new candidate for fiber devices. Opt. Mater. 3(3), 187 (1994)CrossRef J. Wang, E. Vogel, E. Snitzer, Tellurite glass: a new candidate for fiber devices. Opt. Mater. 3(3), 187 (1994)CrossRef
3.
Zurück zum Zitat S. Shen, A. Jha, X. Liu, M. Naftaly, K. Bindra, H.J. Bookey, A.K. Kar, Tellurite glasses for broadband amplifiers and integrated optics. J. Am. Ceram. Soc. 85(6), 1391 (2002)CrossRef S. Shen, A. Jha, X. Liu, M. Naftaly, K. Bindra, H.J. Bookey, A.K. Kar, Tellurite glasses for broadband amplifiers and integrated optics. J. Am. Ceram. Soc. 85(6), 1391 (2002)CrossRef
4.
Zurück zum Zitat D. Zhou, R. Wang, Z. Yang, Z. Song, Z. Yin, J. Qiu, Spectroscopic properties of Tm3+ doped TeO2–R2O–La2O3 glasses for 1.47 μm optical amplifiers. J. Non-Cryst. Solids 357(11–13), 2409 (2011)CrossRef D. Zhou, R. Wang, Z. Yang, Z. Song, Z. Yin, J. Qiu, Spectroscopic properties of Tm3+ doped TeO2–R2O–La2O3 glasses for 1.47 μm optical amplifiers. J. Non-Cryst. Solids 357(11–13), 2409 (2011)CrossRef
5.
Zurück zum Zitat L.R. Kassab, M.J. Bell, Lanthanide-Based Multifunctional Materials (Elsevier, Amsterdam, 2018), pp. 263–289CrossRef L.R. Kassab, M.J. Bell, Lanthanide-Based Multifunctional Materials (Elsevier, Amsterdam, 2018), pp. 263–289CrossRef
6.
Zurück zum Zitat N. Jaba, A. Kanoun, H. Mejri, A. Selmi, S. Alaya, H. Maaref, Infrared to visible up-conversion study for erbium-doped zinc tellurite glasses. J. Phys. 12(20), 4523 (2000) N. Jaba, A. Kanoun, H. Mejri, A. Selmi, S. Alaya, H. Maaref, Infrared to visible up-conversion study for erbium-doped zinc tellurite glasses. J. Phys. 12(20), 4523 (2000)
7.
8.
Zurück zum Zitat R.A. El-Mallawany, Tellurite Glasses Handbook: Physical Properties and Data (CRC Press, Boca Raton, 2016)CrossRef R.A. El-Mallawany, Tellurite Glasses Handbook: Physical Properties and Data (CRC Press, Boca Raton, 2016)CrossRef
9.
Zurück zum Zitat G.N. Conti, V.K. Tikhomirov, M. Bettinelli, S. Berneschi, M. Brenci, B. Chen, S. Pelli, A. Speghini, A.B. Seddon, G.C. Righini, Characterization of ion-exchanged waveguides in tungsten tellurite and zinc tellurite Er3+-doped glasses. Opt. Eng. 42(10), 2805 (2003)CrossRef G.N. Conti, V.K. Tikhomirov, M. Bettinelli, S. Berneschi, M. Brenci, B. Chen, S. Pelli, A. Speghini, A.B. Seddon, G.C. Righini, Characterization of ion-exchanged waveguides in tungsten tellurite and zinc tellurite Er3+-doped glasses. Opt. Eng. 42(10), 2805 (2003)CrossRef
10.
Zurück zum Zitat A. Gonçalves, V.S. Zanuto, G.A.S. Flizikowski, A.N. Medina, F.L. Hegeto, A. Somer, J.L. Gomes Jr., J.V. Gunha, G.K. Cruz, C. Jacinto, N.G.C. Astrath, A. Novatski, Luminescence and upconversion processes in Er3+-doped tellurite glasses. J. Lumin. 201, 110 (2018)CrossRef A. Gonçalves, V.S. Zanuto, G.A.S. Flizikowski, A.N. Medina, F.L. Hegeto, A. Somer, J.L. Gomes Jr., J.V. Gunha, G.K. Cruz, C. Jacinto, N.G.C. Astrath, A. Novatski, Luminescence and upconversion processes in Er3+-doped tellurite glasses. J. Lumin. 201, 110 (2018)CrossRef
11.
Zurück zum Zitat A. Hasegawa, F. Tappert, Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion. Appl. Phys. Lett. 23(3), 142 (1973)CrossRef A. Hasegawa, F. Tappert, Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion. Appl. Phys. Lett. 23(3), 142 (1973)CrossRef
12.
Zurück zum Zitat R. Betts, T. Tjugiarto, Y. Xue, P. Chu, Nonlinear refractive index in erbium doped optical fiber: theory and experiment. IEEE J. Quantum Electron. 27(4), 908 (1991)CrossRef R. Betts, T. Tjugiarto, Y. Xue, P. Chu, Nonlinear refractive index in erbium doped optical fiber: theory and experiment. IEEE J. Quantum Electron. 27(4), 908 (1991)CrossRef
13.
Zurück zum Zitat A. Hasegawa, F. Tappert, Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion. Appl. Phys. Lett. 23(4), 171 (1973)CrossRef A. Hasegawa, F. Tappert, Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion. Appl. Phys. Lett. 23(4), 171 (1973)CrossRef
14.
Zurück zum Zitat S. Rida, H. El-Sherbiny, A. Arafa, On the solution of the fractional nonlinear schrödinger equation. Phys. Lett. A 372(5), 553 (2008)CrossRef S. Rida, H. El-Sherbiny, A. Arafa, On the solution of the fractional nonlinear schrödinger equation. Phys. Lett. A 372(5), 553 (2008)CrossRef
15.
Zurück zum Zitat A. Bhrawy, M. Abdelkawy, A fully spectral collocation approximation for multi-dimensional fractional Schrödinger equations. J. Comput. Phys. 294, 462 (2015)CrossRef A. Bhrawy, M. Abdelkawy, A fully spectral collocation approximation for multi-dimensional fractional Schrödinger equations. J. Comput. Phys. 294, 462 (2015)CrossRef
16.
Zurück zum Zitat L.R. Evangelista, E.K. Lenzi, Fractional Diffusion Equations and Anomalous Diffusion (Cambridge University Press, Cambridge, 2018)CrossRef L.R. Evangelista, E.K. Lenzi, Fractional Diffusion Equations and Anomalous Diffusion (Cambridge University Press, Cambridge, 2018)CrossRef
18.
Zurück zum Zitat S. Das, A new look at formulation of charge storage in capacitors and application to classical capacitor and fractional capacitor theory. Asian J. Res. Rev. Phys. 1(3), 1 (2018) S. Das, A new look at formulation of charge storage in capacitors and application to classical capacitor and fractional capacitor theory. Asian J. Res. Rev. Phys. 1(3), 1 (2018)
19.
Zurück zum Zitat G. Baumann, Fractals in Biology and Medicine (Springer, Berlin, 2005) G. Baumann, Fractals in Biology and Medicine (Springer, Berlin, 2005)
20.
Zurück zum Zitat B.I. Henry, S.L. Wearne, Fractional reaction–diffusion. Physica A 276(3–4), 448 (2000)CrossRef B.I. Henry, S.L. Wearne, Fractional reaction–diffusion. Physica A 276(3–4), 448 (2000)CrossRef
21.
Zurück zum Zitat R. Metzler, J. Klafter, The random walk’s guide to anomalous diffusion: a fractional dynamics approach. Phys. Rep. 339(1), 1 (2000)CrossRef R. Metzler, J. Klafter, The random walk’s guide to anomalous diffusion: a fractional dynamics approach. Phys. Rep. 339(1), 1 (2000)CrossRef
22.
Zurück zum Zitat J. Hristov, Derivatives with non-singular kernels from the Caputo–Fabrizio definition and beyond: appraising analysis with emphasis on diffusion models. Front. Fract. Calc. 1, 270 (2017) J. Hristov, Derivatives with non-singular kernels from the Caputo–Fabrizio definition and beyond: appraising analysis with emphasis on diffusion models. Front. Fract. Calc. 1, 270 (2017)
23.
Zurück zum Zitat S. Burov, E. Barkai, Fractional langevin equation: overdamped, underdamped, and critical behaviors. Phys. Rev. E 78, 031112 (2008)CrossRef S. Burov, E. Barkai, Fractional langevin equation: overdamped, underdamped, and critical behaviors. Phys. Rev. E 78, 031112 (2008)CrossRef
24.
Zurück zum Zitat S. Burov, E. Barkai, Critical exponent of the fractional Langevin equation. Phys. Rev. Lett. 100, 070601 (2008)CrossRef S. Burov, E. Barkai, Critical exponent of the fractional Langevin equation. Phys. Rev. Lett. 100, 070601 (2008)CrossRef
25.
Zurück zum Zitat I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, vol. 198 (Elsevier, Amsterdam, 1998) I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, vol. 198 (Elsevier, Amsterdam, 1998)
26.
Zurück zum Zitat R. Hilfer, Experimental evidence for fractional time evolution in glass forming materials. Chem. Phys. 284(1–2), 399 (2002)CrossRef R. Hilfer, Experimental evidence for fractional time evolution in glass forming materials. Chem. Phys. 284(1–2), 399 (2002)CrossRef
27.
Zurück zum Zitat M. Di Paola, A. Pirrotta, A. Valenza, Visco-elastic behavior through fractional calculus: an easier method for best fitting experimental results. Mech. Mater. 43(12), 799 (2011)CrossRef M. Di Paola, A. Pirrotta, A. Valenza, Visco-elastic behavior through fractional calculus: an easier method for best fitting experimental results. Mech. Mater. 43(12), 799 (2011)CrossRef
28.
Zurück zum Zitat J.R. Reitz, F.J. Milford, R.W. Christy, Foundations of Electromagnetic Theory (Addison-Wesley Publishing Company, Boston, 2008) J.R. Reitz, F.J. Milford, R.W. Christy, Foundations of Electromagnetic Theory (Addison-Wesley Publishing Company, Boston, 2008)
29.
Zurück zum Zitat M.N.R. Jauhariyah, W. Setyarsih, M. Yantidewi, A. Marzuki, Cari, in, International Seminar on Sensors, Instrumentation, Measurement and Metrology (ISSIMM) 2016, 71–74 (2016) M.N.R. Jauhariyah, W. Setyarsih, M. Yantidewi, A. Marzuki, Cari, in, International Seminar on Sensors, Instrumentation, Measurement and Metrology (ISSIMM) 2016, 71–74 (2016)
30.
Zurück zum Zitat A. Novatski, A. Somer, A. Gonçalves, R.L.S. Piazzetta, J.V. Gunha, A.V.C. Andrade, E.K. Lenzi, A.N. Medina, N.G.C. Astrath, R. El-Mallawany, Thermal and optical properties of lithium–zinc–tellurite glasses. Mater. Chem. Phys. 231, 150 (2019)CrossRef A. Novatski, A. Somer, A. Gonçalves, R.L.S. Piazzetta, J.V. Gunha, A.V.C. Andrade, E.K. Lenzi, A.N. Medina, N.G.C. Astrath, R. El-Mallawany, Thermal and optical properties of lithium–zinc–tellurite glasses. Mater. Chem. Phys. 231, 150 (2019)CrossRef
31.
Zurück zum Zitat T.J. Wang, Z.H. Kang, H.Z. Zhang, Z.S. Feng, F.G. Wu, H.Y. Zang, Y. Jiang, J.Y. Gao, Y. Andreev, G. Lanskii et al., Sellmeier equations for green, yellow, and orange colored Hg Ga 2 S 4 crystals. Appl. Phys. Lett. 90(18), 181913 (2007)CrossRef T.J. Wang, Z.H. Kang, H.Z. Zhang, Z.S. Feng, F.G. Wu, H.Y. Zang, Y. Jiang, J.Y. Gao, Y. Andreev, G. Lanskii et al., Sellmeier equations for green, yellow, and orange colored Hg Ga 2 S 4 crystals. Appl. Phys. Lett. 90(18), 181913 (2007)CrossRef
32.
Zurück zum Zitat G. Ghosh, Sellmeier coefficients and chromatic dispersions for some tellurite glasses. J. Am. Ceram. Soc. 78(10), 2828 (1995)CrossRef G. Ghosh, Sellmeier coefficients and chromatic dispersions for some tellurite glasses. J. Am. Ceram. Soc. 78(10), 2828 (1995)CrossRef
33.
Zurück zum Zitat G. Ghosh, Sellmeier coefficients and dispersion of thermo-optic coefficients for some optical glasses. Appl. Opt. 36(7), 1540 (1997)CrossRef G. Ghosh, Sellmeier coefficients and dispersion of thermo-optic coefficients for some optical glasses. Appl. Opt. 36(7), 1540 (1997)CrossRef
34.
Zurück zum Zitat H. Desirena, A. Schlzgen, S. Sabet, G. Ramos-Ortiz, E. de la Rosa, N. Peyghambarian, Effect of alkali metal oxides R2O (R = Li, Na, K, Rb and Cs) and network intermediate MO (M = Zn, Mg, Ba and Pb) in tellurite glasses. Opt. Mater. 31(6), 784 (2009)CrossRef H. Desirena, A. Schlzgen, S. Sabet, G. Ramos-Ortiz, E. de la Rosa, N. Peyghambarian, Effect of alkali metal oxides R2O (R = Li, Na, K, Rb and Cs) and network intermediate MO (M = Zn, Mg, Ba and Pb) in tellurite glasses. Opt. Mater. 31(6), 784 (2009)CrossRef
35.
Zurück zum Zitat R.N. Brown, Material dispersion in heavy metal oxide glasses containing Bi2O3. J. Non-Cryst. Solids 92(1), 89 (1987)CrossRef R.N. Brown, Material dispersion in heavy metal oxide glasses containing Bi2O3. J. Non-Cryst. Solids 92(1), 89 (1987)CrossRef
36.
Zurück zum Zitat J. McCloy, B. Riley, B. Johnson, M. Schweiger, H.A. Qiao, N. Carlie, The predictive power of electronic polarizability for tailoring the refractivity of high-index glasses: optical basicity versus the single oscillator model. J. Am. Ceram. Soc. 93(6), 1650 (2010) J. McCloy, B. Riley, B. Johnson, M. Schweiger, H.A. Qiao, N. Carlie, The predictive power of electronic polarizability for tailoring the refractivity of high-index glasses: optical basicity versus the single oscillator model. J. Am. Ceram. Soc. 93(6), 1650 (2010)
37.
Zurück zum Zitat R.D. Shannon, R.C. Shannon, O. Medenbach, R.X. Fischer, Refractive index and dispersion of fluorides and oxides. J. Phys. Chem. Ref. Data 31(4), 931 (2002)CrossRef R.D. Shannon, R.C. Shannon, O. Medenbach, R.X. Fischer, Refractive index and dispersion of fluorides and oxides. J. Phys. Chem. Ref. Data 31(4), 931 (2002)CrossRef
38.
Zurück zum Zitat H. Takebe, S. Pujino, K. Morinaga, Refractive-index dispersion of tellurite glasses in the region from 0.40 to 1.71 μm. J. Am. Ceram. Soc. 77(9), 2455 (1994)CrossRef H. Takebe, S. Pujino, K. Morinaga, Refractive-index dispersion of tellurite glasses in the region from 0.40 to 1.71 μm. J. Am. Ceram. Soc. 77(9), 2455 (1994)CrossRef
39.
Zurück zum Zitat S. Umar, M. Halimah, K. Chan, A. Latif, Polarizability, optical basicity and electric susceptibility of Er3+ doped silicate borotellurite glasses. J. Non-Cryst. Solids 471, 101 (2017)CrossRef S. Umar, M. Halimah, K. Chan, A. Latif, Polarizability, optical basicity and electric susceptibility of Er3+ doped silicate borotellurite glasses. J. Non-Cryst. Solids 471, 101 (2017)CrossRef
40.
Zurück zum Zitat V. Dimitrov, S. Sakka, Electronic oxide polarizability and optical basicity of simple oxides. I. J. Appl. Phys. 79(3), 1736 (1996)CrossRef V. Dimitrov, S. Sakka, Electronic oxide polarizability and optical basicity of simple oxides. I. J. Appl. Phys. 79(3), 1736 (1996)CrossRef
41.
Zurück zum Zitat V. Dimitrov, T. Komatsu, Classification of oxide glasses: a polarizability approach. J. Solid State Chem. 178(3), 831 (2005)CrossRef V. Dimitrov, T. Komatsu, Classification of oxide glasses: a polarizability approach. J. Solid State Chem. 178(3), 831 (2005)CrossRef
42.
Zurück zum Zitat S. Butera, M. Di Paola, A physically based connection between fractional calculus and fractal geometry. Ann. Phys. 350, 146 (2014)CrossRef S. Butera, M. Di Paola, A physically based connection between fractional calculus and fractal geometry. Ann. Phys. 350, 146 (2014)CrossRef
43.
Zurück zum Zitat V.M. Shalaev, R. Botet, R. Jullien, Resonant light scattering by fractal clusters. Phys. Rev. B 44(22), 12216 (1991)CrossRef V.M. Shalaev, R. Botet, R. Jullien, Resonant light scattering by fractal clusters. Phys. Rev. B 44(22), 12216 (1991)CrossRef
Metadaten
Titel
A generalized Drude–Lorentz model for refractive index behavior of tellurite glasses
verfasst von
Anderson Gonçalves
Maurício A. Ribeiro
Jaqueline V. Gunha
Aloisi Somer
Vitor S. Zanuto
Nelson G. C. Astrath
Daniele T. Dias
Maike A. F. dos Santos
Carlos Jacinto
Ervin K. Lenzi
Andressa Novatski
Publikationsdatum
22.06.2019
Verlag
Springer US
Erschienen in
Journal of Materials Science: Materials in Electronics / Ausgabe 18/2019
Print ISSN: 0957-4522
Elektronische ISSN: 1573-482X
DOI
https://doi.org/10.1007/s10854-019-01696-0

Weitere Artikel der Ausgabe 18/2019

Journal of Materials Science: Materials in Electronics 18/2019 Zur Ausgabe

Neuer Inhalt