Abstract

We have measured the surface index change and birefringence in K+–Na+ ion-exchanged waveguides and compared the results with theory. The contribution to the index change caused by the polarizability/volume changes (Δnp) is calculated using two theoretical models which use empirical relations based on the glass composition. In both cases, we encounter large discrepancies between the predicted and measured values which are attributed to the inherent deficiency in the models, which assume free expansion of the glass in calculating the volume changes. Recognizing that the net volume change is much smaller, we accurately measure its value and show that both models can be used to predict Δnp with the same accuracy, provided that the correct volume change is used. We show that the limitation in accuracy is dictated by measurement errors and uncertainties in the values of the ionic radii and polarizabilities. We also present a unique and systematic method for determining the compressive stress generated in the glass resulting from ion exchange.

© 1991 Optical Society of America

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References

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  1. M. L. Huggins, K. H. Sun, “Calculation of Denisty and Optical Constants of a Glass From Its Composition in Weight Percentage,” J. Am. Ceram. Soc. 26, 4–11 (1943).
    [CrossRef]
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    [CrossRef] [PubMed]
  3. A. A. Appen, Chemie des Glases (Verlag Chemie, Leningrad, 1974).
  4. H. Scholzer, Glas Natur, Struktur und Eigenschaften (Springer-VerlagBerlin, 1977).
  5. M. Abou-el Leil, F. Leonberger, “A Model for Ion-Exchanged Waveguides in Glass,” J. Am. Ceram. Soc. 71, 497–502 (1988).
    [CrossRef]
  6. H. M. Garfinkel, “Ion-Exchange Equilibria Between Glass and Molten Salts,” J. Phys. Chem. 72, 4175–4181 (1968).
    [CrossRef]
  7. R. V. Ramaswamy, R. Srivastava, P. Chludzinski, T. J. Anderson, “Influence of Ag+–Na+ Ion-Exchange Equilibrium on Waveguide Index Profile,” IEEE J. Quantum Electron, QE-24, 780–786 (1988).
    [CrossRef]
  8. J. Albert, G. L. Yip, “Stress Induced Index Change for K+–Na+ Ion Exchange in Glass,” Electron. Lett. 23, 737–738 (1987).
    [CrossRef]
  9. A. Brandenburg, “Stress in Ion-Exchanged Glass Waveguides,” IEEE/OSA J. Lightwave Technol. LT-4, 1580–1593 (1986).
    [CrossRef]
  10. A. Miliou, H. Zhenguang, H. C. Cheng, R. Srivastava, R. V. Ramaswamy, “Fiber-Compatible K+–Na+ Ion-Exchange Channel Waveguides: Fabrication and Characterization,” IEEE J. Quantum Electron. QE-25, 1889–1897 (1989).
    [CrossRef]
  11. H. A. Lorentz, “Ueber die Beziehung zwischender Fortpflan-zungsgeschwindigkeit des Lichtes und de Körperdichte,” Anna-len der Physic, 9, 641–665 (1880); L. Lorenz, “Ueber die Refractionsconstante,” Annalen der Physik, 11, 70–103 (1880).
    [CrossRef]
  12. M. L. Huggins, “The Density of Silicate Glasses as a Function of Composition,” J. Opt. Soc. Am. 30, 420–430 (1940).
    [CrossRef]
  13. M. L. Huggins, “The Refractive Index of Silicate Glasses as a Function of Composition,” J. Opt. Soc. Am. 30, 495–504 (1940).
    [CrossRef]
  14. T. Kaneko, “Dilation of Glass by Ion-Exchange,” J. Mater. Sci. Lett. 5, 1011–1012 (1986).
    [CrossRef]
  15. K. Tsutsumi, H. Hirai, Y. Yuba, “Characteristics of Swelling of Sodium-Potassium Ion-Exchanged Glass Waveguides,” Electron. Lett. 22, 1299–1300 (1986).
    [CrossRef]
  16. J. W. Dally, W. F. Riley, Experimental Stress Analysis (McGraw-Hill, New York, 1965), pp. 204–206.
  17. A. Y. Sane, A. R. Cooper, “Anomalous Stress Profiles in Ion-Exchanged Glass,” J. Am. Ceram. Soc. 61, 359–362 (1982).
    [CrossRef]
  18. B. A. Boley, J. H. Weiner, Theory of Thermal Stresses (Wiley, New York, 1960), pp. 288–291.
  19. K. S. Chiang, “Construction of Refractive-Index Profiles of Planar Dielectric Waveguides From the Distribution of Effective Indexes,” IEEE/OSA J. Lightwave Technol. LT-3, 385–391 (1985).
    [CrossRef]

1989

A. Miliou, H. Zhenguang, H. C. Cheng, R. Srivastava, R. V. Ramaswamy, “Fiber-Compatible K+–Na+ Ion-Exchange Channel Waveguides: Fabrication and Characterization,” IEEE J. Quantum Electron. QE-25, 1889–1897 (1989).
[CrossRef]

1988

M. Abou-el Leil, F. Leonberger, “A Model for Ion-Exchanged Waveguides in Glass,” J. Am. Ceram. Soc. 71, 497–502 (1988).
[CrossRef]

R. V. Ramaswamy, R. Srivastava, P. Chludzinski, T. J. Anderson, “Influence of Ag+–Na+ Ion-Exchange Equilibrium on Waveguide Index Profile,” IEEE J. Quantum Electron, QE-24, 780–786 (1988).
[CrossRef]

1987

J. Albert, G. L. Yip, “Stress Induced Index Change for K+–Na+ Ion Exchange in Glass,” Electron. Lett. 23, 737–738 (1987).
[CrossRef]

1986

A. Brandenburg, “Stress in Ion-Exchanged Glass Waveguides,” IEEE/OSA J. Lightwave Technol. LT-4, 1580–1593 (1986).
[CrossRef]

T. Kaneko, “Dilation of Glass by Ion-Exchange,” J. Mater. Sci. Lett. 5, 1011–1012 (1986).
[CrossRef]

K. Tsutsumi, H. Hirai, Y. Yuba, “Characteristics of Swelling of Sodium-Potassium Ion-Exchanged Glass Waveguides,” Electron. Lett. 22, 1299–1300 (1986).
[CrossRef]

1985

K. S. Chiang, “Construction of Refractive-Index Profiles of Planar Dielectric Waveguides From the Distribution of Effective Indexes,” IEEE/OSA J. Lightwave Technol. LT-3, 385–391 (1985).
[CrossRef]

1983

1982

A. Y. Sane, A. R. Cooper, “Anomalous Stress Profiles in Ion-Exchanged Glass,” J. Am. Ceram. Soc. 61, 359–362 (1982).
[CrossRef]

1968

H. M. Garfinkel, “Ion-Exchange Equilibria Between Glass and Molten Salts,” J. Phys. Chem. 72, 4175–4181 (1968).
[CrossRef]

1943

M. L. Huggins, K. H. Sun, “Calculation of Denisty and Optical Constants of a Glass From Its Composition in Weight Percentage,” J. Am. Ceram. Soc. 26, 4–11 (1943).
[CrossRef]

1940

1880

H. A. Lorentz, “Ueber die Beziehung zwischender Fortpflan-zungsgeschwindigkeit des Lichtes und de Körperdichte,” Anna-len der Physic, 9, 641–665 (1880); L. Lorenz, “Ueber die Refractionsconstante,” Annalen der Physik, 11, 70–103 (1880).
[CrossRef]

Abou-el Leil, M.

M. Abou-el Leil, F. Leonberger, “A Model for Ion-Exchanged Waveguides in Glass,” J. Am. Ceram. Soc. 71, 497–502 (1988).
[CrossRef]

Albert, J.

J. Albert, G. L. Yip, “Stress Induced Index Change for K+–Na+ Ion Exchange in Glass,” Electron. Lett. 23, 737–738 (1987).
[CrossRef]

Anderson, T. J.

R. V. Ramaswamy, R. Srivastava, P. Chludzinski, T. J. Anderson, “Influence of Ag+–Na+ Ion-Exchange Equilibrium on Waveguide Index Profile,” IEEE J. Quantum Electron, QE-24, 780–786 (1988).
[CrossRef]

Appen, A. A.

A. A. Appen, Chemie des Glases (Verlag Chemie, Leningrad, 1974).

Boley, B. A.

B. A. Boley, J. H. Weiner, Theory of Thermal Stresses (Wiley, New York, 1960), pp. 288–291.

Brandenburg, A.

A. Brandenburg, “Stress in Ion-Exchanged Glass Waveguides,” IEEE/OSA J. Lightwave Technol. LT-4, 1580–1593 (1986).
[CrossRef]

Cheng, H. C.

A. Miliou, H. Zhenguang, H. C. Cheng, R. Srivastava, R. V. Ramaswamy, “Fiber-Compatible K+–Na+ Ion-Exchange Channel Waveguides: Fabrication and Characterization,” IEEE J. Quantum Electron. QE-25, 1889–1897 (1989).
[CrossRef]

Chiang, K. S.

K. S. Chiang, “Construction of Refractive-Index Profiles of Planar Dielectric Waveguides From the Distribution of Effective Indexes,” IEEE/OSA J. Lightwave Technol. LT-3, 385–391 (1985).
[CrossRef]

Chludzinski, P.

R. V. Ramaswamy, R. Srivastava, P. Chludzinski, T. J. Anderson, “Influence of Ag+–Na+ Ion-Exchange Equilibrium on Waveguide Index Profile,” IEEE J. Quantum Electron, QE-24, 780–786 (1988).
[CrossRef]

Cooper, A. R.

A. Y. Sane, A. R. Cooper, “Anomalous Stress Profiles in Ion-Exchanged Glass,” J. Am. Ceram. Soc. 61, 359–362 (1982).
[CrossRef]

Dally, J. W.

J. W. Dally, W. F. Riley, Experimental Stress Analysis (McGraw-Hill, New York, 1965), pp. 204–206.

Fantone, S. D.

Garfinkel, H. M.

H. M. Garfinkel, “Ion-Exchange Equilibria Between Glass and Molten Salts,” J. Phys. Chem. 72, 4175–4181 (1968).
[CrossRef]

Hirai, H.

K. Tsutsumi, H. Hirai, Y. Yuba, “Characteristics of Swelling of Sodium-Potassium Ion-Exchanged Glass Waveguides,” Electron. Lett. 22, 1299–1300 (1986).
[CrossRef]

Huggins, M. L.

Kaneko, T.

T. Kaneko, “Dilation of Glass by Ion-Exchange,” J. Mater. Sci. Lett. 5, 1011–1012 (1986).
[CrossRef]

Leonberger, F.

M. Abou-el Leil, F. Leonberger, “A Model for Ion-Exchanged Waveguides in Glass,” J. Am. Ceram. Soc. 71, 497–502 (1988).
[CrossRef]

Lorentz, H. A.

H. A. Lorentz, “Ueber die Beziehung zwischender Fortpflan-zungsgeschwindigkeit des Lichtes und de Körperdichte,” Anna-len der Physic, 9, 641–665 (1880); L. Lorenz, “Ueber die Refractionsconstante,” Annalen der Physik, 11, 70–103 (1880).
[CrossRef]

Miliou, A.

A. Miliou, H. Zhenguang, H. C. Cheng, R. Srivastava, R. V. Ramaswamy, “Fiber-Compatible K+–Na+ Ion-Exchange Channel Waveguides: Fabrication and Characterization,” IEEE J. Quantum Electron. QE-25, 1889–1897 (1989).
[CrossRef]

Ramaswamy, R. V.

A. Miliou, H. Zhenguang, H. C. Cheng, R. Srivastava, R. V. Ramaswamy, “Fiber-Compatible K+–Na+ Ion-Exchange Channel Waveguides: Fabrication and Characterization,” IEEE J. Quantum Electron. QE-25, 1889–1897 (1989).
[CrossRef]

R. V. Ramaswamy, R. Srivastava, P. Chludzinski, T. J. Anderson, “Influence of Ag+–Na+ Ion-Exchange Equilibrium on Waveguide Index Profile,” IEEE J. Quantum Electron, QE-24, 780–786 (1988).
[CrossRef]

Riley, W. F.

J. W. Dally, W. F. Riley, Experimental Stress Analysis (McGraw-Hill, New York, 1965), pp. 204–206.

Sane, A. Y.

A. Y. Sane, A. R. Cooper, “Anomalous Stress Profiles in Ion-Exchanged Glass,” J. Am. Ceram. Soc. 61, 359–362 (1982).
[CrossRef]

Scholzer, H.

H. Scholzer, Glas Natur, Struktur und Eigenschaften (Springer-VerlagBerlin, 1977).

Srivastava, R.

A. Miliou, H. Zhenguang, H. C. Cheng, R. Srivastava, R. V. Ramaswamy, “Fiber-Compatible K+–Na+ Ion-Exchange Channel Waveguides: Fabrication and Characterization,” IEEE J. Quantum Electron. QE-25, 1889–1897 (1989).
[CrossRef]

R. V. Ramaswamy, R. Srivastava, P. Chludzinski, T. J. Anderson, “Influence of Ag+–Na+ Ion-Exchange Equilibrium on Waveguide Index Profile,” IEEE J. Quantum Electron, QE-24, 780–786 (1988).
[CrossRef]

Sun, K. H.

M. L. Huggins, K. H. Sun, “Calculation of Denisty and Optical Constants of a Glass From Its Composition in Weight Percentage,” J. Am. Ceram. Soc. 26, 4–11 (1943).
[CrossRef]

Tsutsumi, K.

K. Tsutsumi, H. Hirai, Y. Yuba, “Characteristics of Swelling of Sodium-Potassium Ion-Exchanged Glass Waveguides,” Electron. Lett. 22, 1299–1300 (1986).
[CrossRef]

Weiner, J. H.

B. A. Boley, J. H. Weiner, Theory of Thermal Stresses (Wiley, New York, 1960), pp. 288–291.

Yip, G. L.

J. Albert, G. L. Yip, “Stress Induced Index Change for K+–Na+ Ion Exchange in Glass,” Electron. Lett. 23, 737–738 (1987).
[CrossRef]

Yuba, Y.

K. Tsutsumi, H. Hirai, Y. Yuba, “Characteristics of Swelling of Sodium-Potassium Ion-Exchanged Glass Waveguides,” Electron. Lett. 22, 1299–1300 (1986).
[CrossRef]

Zhenguang, H.

A. Miliou, H. Zhenguang, H. C. Cheng, R. Srivastava, R. V. Ramaswamy, “Fiber-Compatible K+–Na+ Ion-Exchange Channel Waveguides: Fabrication and Characterization,” IEEE J. Quantum Electron. QE-25, 1889–1897 (1989).
[CrossRef]

Anna-len der Physic

H. A. Lorentz, “Ueber die Beziehung zwischender Fortpflan-zungsgeschwindigkeit des Lichtes und de Körperdichte,” Anna-len der Physic, 9, 641–665 (1880); L. Lorenz, “Ueber die Refractionsconstante,” Annalen der Physik, 11, 70–103 (1880).
[CrossRef]

Appl. Opt.

Electron. Lett.

K. Tsutsumi, H. Hirai, Y. Yuba, “Characteristics of Swelling of Sodium-Potassium Ion-Exchanged Glass Waveguides,” Electron. Lett. 22, 1299–1300 (1986).
[CrossRef]

J. Albert, G. L. Yip, “Stress Induced Index Change for K+–Na+ Ion Exchange in Glass,” Electron. Lett. 23, 737–738 (1987).
[CrossRef]

IEEE J. Quantum Electron

R. V. Ramaswamy, R. Srivastava, P. Chludzinski, T. J. Anderson, “Influence of Ag+–Na+ Ion-Exchange Equilibrium on Waveguide Index Profile,” IEEE J. Quantum Electron, QE-24, 780–786 (1988).
[CrossRef]

IEEE J. Quantum Electron.

A. Miliou, H. Zhenguang, H. C. Cheng, R. Srivastava, R. V. Ramaswamy, “Fiber-Compatible K+–Na+ Ion-Exchange Channel Waveguides: Fabrication and Characterization,” IEEE J. Quantum Electron. QE-25, 1889–1897 (1989).
[CrossRef]

IEEE/OSA J. Lightwave Technol.

A. Brandenburg, “Stress in Ion-Exchanged Glass Waveguides,” IEEE/OSA J. Lightwave Technol. LT-4, 1580–1593 (1986).
[CrossRef]

K. S. Chiang, “Construction of Refractive-Index Profiles of Planar Dielectric Waveguides From the Distribution of Effective Indexes,” IEEE/OSA J. Lightwave Technol. LT-3, 385–391 (1985).
[CrossRef]

J. Am. Ceram. Soc.

M. L. Huggins, K. H. Sun, “Calculation of Denisty and Optical Constants of a Glass From Its Composition in Weight Percentage,” J. Am. Ceram. Soc. 26, 4–11 (1943).
[CrossRef]

A. Y. Sane, A. R. Cooper, “Anomalous Stress Profiles in Ion-Exchanged Glass,” J. Am. Ceram. Soc. 61, 359–362 (1982).
[CrossRef]

M. Abou-el Leil, F. Leonberger, “A Model for Ion-Exchanged Waveguides in Glass,” J. Am. Ceram. Soc. 71, 497–502 (1988).
[CrossRef]

J. Mater. Sci. Lett.

T. Kaneko, “Dilation of Glass by Ion-Exchange,” J. Mater. Sci. Lett. 5, 1011–1012 (1986).
[CrossRef]

J. Opt. Soc. Am.

J. Phys. Chem.

H. M. Garfinkel, “Ion-Exchange Equilibria Between Glass and Molten Salts,” J. Phys. Chem. 72, 4175–4181 (1968).
[CrossRef]

Other

A. A. Appen, Chemie des Glases (Verlag Chemie, Leningrad, 1974).

H. Scholzer, Glas Natur, Struktur und Eigenschaften (Springer-VerlagBerlin, 1977).

J. W. Dally, W. F. Riley, Experimental Stress Analysis (McGraw-Hill, New York, 1965), pp. 204–206.

B. A. Boley, J. H. Weiner, Theory of Thermal Stresses (Wiley, New York, 1960), pp. 288–291.

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Figures (1)

Fig. 1
Fig. 1

Geometry of stress-induced index change.

Tables (6)

Tables Icon

Table I Binary Exchange Cation Pairs

Tables Icon

Table II Glass Composition (wt %)

Tables Icon

Table III Comparison of the Two Models

Tables Icon

Table IV Comparison of Δnp in Three Glasses; Values Multiplied by 103

Tables Icon

Table V Glass Constants

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Table VI Comparison of ΔVeqV, ΔVeqV′, and Δnp in the Three Glasses for the Three Approaches for the K+–Na+ Exchange

Equations (21)

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

n 2 1 n 2 + 2 = R V ,
( n 1 ) = R V ,
n ( f ) = 1 + R + Δ R V + Δ V ,
Δ n p = 1 V ( Δ R R Δ V V ) ,
Δ n p = ( n R ) V Δ R + ( n V ) R Δ V , Δ n P = ( n 2 + 2 ) 2 6 n V ( Δ R n 2 1 n 2 + 2 Δ V ) .
Δ V str = Δ V Δ V eq ,
Δ V str = Δ V Δ V eq .
Δ V eq 2 3 Δ V .
Δ n s TE = C 1 σ y + C 2 ( σ x + σ z ) ,
Δ n s TM = C 1 σ x + C 2 ( σ y + σ z ) ,
σ x = 0 , σ y = σ z = σ o .
σ o = E β ( 1 ν ) [ C ( x ) 1 2 d 0 2 d C ( x ) d x ] ,
Δ V str V = Δ V str V = ε x + ε y + ε z = 2 σ o E ( 1 2 ν ) ,
δ n = ( Δ n s TM Δ n s TE ) surface .
δ n = ( C 2 C 1 ) σ o ( 0 ) ,
( Δ V eq / Δ V ) = S Δ h N δ .
δ = 4 π 3 ( r A 3 r B 3 ) ,
N = S 0 n A ( x ) d x ,
n A ( 0 ) = f n B 0 ,
Δ n p m = Δ n t TE Δ n s TE = Δ n t TM Δ n s TM .
Δ n p m = Δ n t TE Δ n s TE = Δ n t TM Δ n s TM ;

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