Abstract

Field-assisted ion exchange has been used to extend the profile repertoire and to speed the ion exchange process for gradient-index (GRIN) applications. Profiles are predicted for various ion mobility ratios and time-varying electric fields. Profile control is demonstrated by silver for sodium exchange in an aluminosilicate glass. Diffusion depths of the order of a millimeter are obtained in a few hours using modest field strengths.

© 1985 Optical Society of America

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References

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  1. D. T. Moore, “Gradient-Index Optics: A Review,” Appl. Opt. 19, 1035 (1980).
    [CrossRef] [PubMed]
  2. P. O. McLaughlin et al., “Design of a Gradient-Index Binocular Objective,” Proc. Soc. Photo-Opt. Instrum. Eng. 237, 369 (1980).
  3. L. G. Atkinson, S. N. Houde-Walter, D. T. Moore, D. P. Ryan, J. M. Stagaman, “Design of a Gradient-Index Photographic Objective,” Appl. Opt. 21, (1982).
    [CrossRef] [PubMed]
  4. D. Forer, “Gradient-Index Eyepiece Design,” Appl. Opt. 22, 407 (1983).
    [CrossRef] [PubMed]
  5. L. G. Atkinson, J. D. Downie, D. T. Moore, J.M. Stagaman, L. L. Voci, “Gradient-Index Wide-Angle Photographic Objective Design,” Appl. Opt. 23, 1735 (1984).
    [CrossRef]
  6. M. Abou-El-Liel, A. R. Cooper, “Analysis of Field-Assisted Binary Ion Exchange,” J. Am. Ceram. Soc. 62, 390 (1979).
    [CrossRef]
  7. H. J. Lilienhof et al., “Field Induced Index Profiles of Multi-mode Ion-Exchanged Strip Waveguides,” IEEE J. Quantum Electron. QE-18, 1877 (1982).
    [CrossRef]
  8. J. R. Engel, M. Tomozawa, “Nernst-Einstein Relation in Sodium Silicate Glass,” J. Am. Ceram. Soc. 58, (1975).
    [CrossRef]
  9. T. Kaneko, H. Yamamoto, “On Ionic Penetration of Silver Film into Glasses under the Electric Field,” in Proceedings, Tenth International Congress in Glass, Kyoto, Japan (1974), pp. 8–79–8–86.
  10. J. Crank, The Mathematics of Diffusion (Oxford U. P.London, 1975), p. 175.
  11. D. T. Moore, “Design of Singlets with Continuously Varying Indices of Refraction,” J. Opt. Soc. Am. 61, 886 (1971).
    [CrossRef]
  12. R. H. Doremus, Glass Science (Wiley, New York, 1973), p. 148.
  13. H. Bloom, The Chemistry of Molten Salts (Benjamin, New York, 1967).
  14. Gradient Index Optical Glass Lenses, Annual Report, July 1975 to Dec. 1976, NSF Research contract ENG 74-11993-A01, Principal Investigator: D. T. Moore.
  15. R. H. Doremus, “Exchange and Diffusion of Ions in Glass,” J. Phys. Chem. 68, 2212 (1964).
    [CrossRef]

1984 (1)

1983 (1)

1982 (2)

L. G. Atkinson, S. N. Houde-Walter, D. T. Moore, D. P. Ryan, J. M. Stagaman, “Design of a Gradient-Index Photographic Objective,” Appl. Opt. 21, (1982).
[CrossRef] [PubMed]

H. J. Lilienhof et al., “Field Induced Index Profiles of Multi-mode Ion-Exchanged Strip Waveguides,” IEEE J. Quantum Electron. QE-18, 1877 (1982).
[CrossRef]

1980 (2)

D. T. Moore, “Gradient-Index Optics: A Review,” Appl. Opt. 19, 1035 (1980).
[CrossRef] [PubMed]

P. O. McLaughlin et al., “Design of a Gradient-Index Binocular Objective,” Proc. Soc. Photo-Opt. Instrum. Eng. 237, 369 (1980).

1979 (1)

M. Abou-El-Liel, A. R. Cooper, “Analysis of Field-Assisted Binary Ion Exchange,” J. Am. Ceram. Soc. 62, 390 (1979).
[CrossRef]

1975 (1)

J. R. Engel, M. Tomozawa, “Nernst-Einstein Relation in Sodium Silicate Glass,” J. Am. Ceram. Soc. 58, (1975).
[CrossRef]

1971 (1)

1964 (1)

R. H. Doremus, “Exchange and Diffusion of Ions in Glass,” J. Phys. Chem. 68, 2212 (1964).
[CrossRef]

Abou-El-Liel, M.

M. Abou-El-Liel, A. R. Cooper, “Analysis of Field-Assisted Binary Ion Exchange,” J. Am. Ceram. Soc. 62, 390 (1979).
[CrossRef]

Atkinson, L. G.

L. G. Atkinson, J. D. Downie, D. T. Moore, J.M. Stagaman, L. L. Voci, “Gradient-Index Wide-Angle Photographic Objective Design,” Appl. Opt. 23, 1735 (1984).
[CrossRef]

L. G. Atkinson, S. N. Houde-Walter, D. T. Moore, D. P. Ryan, J. M. Stagaman, “Design of a Gradient-Index Photographic Objective,” Appl. Opt. 21, (1982).
[CrossRef] [PubMed]

Bloom, H.

H. Bloom, The Chemistry of Molten Salts (Benjamin, New York, 1967).

Cooper, A. R.

M. Abou-El-Liel, A. R. Cooper, “Analysis of Field-Assisted Binary Ion Exchange,” J. Am. Ceram. Soc. 62, 390 (1979).
[CrossRef]

Crank, J.

J. Crank, The Mathematics of Diffusion (Oxford U. P.London, 1975), p. 175.

Doremus, R. H.

R. H. Doremus, “Exchange and Diffusion of Ions in Glass,” J. Phys. Chem. 68, 2212 (1964).
[CrossRef]

R. H. Doremus, Glass Science (Wiley, New York, 1973), p. 148.

Downie, J. D.

Engel, J. R.

J. R. Engel, M. Tomozawa, “Nernst-Einstein Relation in Sodium Silicate Glass,” J. Am. Ceram. Soc. 58, (1975).
[CrossRef]

Forer, D.

Houde-Walter, S. N.

L. G. Atkinson, S. N. Houde-Walter, D. T. Moore, D. P. Ryan, J. M. Stagaman, “Design of a Gradient-Index Photographic Objective,” Appl. Opt. 21, (1982).
[CrossRef] [PubMed]

Kaneko, T.

T. Kaneko, H. Yamamoto, “On Ionic Penetration of Silver Film into Glasses under the Electric Field,” in Proceedings, Tenth International Congress in Glass, Kyoto, Japan (1974), pp. 8–79–8–86.

Lilienhof, H. J.

H. J. Lilienhof et al., “Field Induced Index Profiles of Multi-mode Ion-Exchanged Strip Waveguides,” IEEE J. Quantum Electron. QE-18, 1877 (1982).
[CrossRef]

McLaughlin, P. O.

P. O. McLaughlin et al., “Design of a Gradient-Index Binocular Objective,” Proc. Soc. Photo-Opt. Instrum. Eng. 237, 369 (1980).

Moore, D. T.

L. G. Atkinson, J. D. Downie, D. T. Moore, J.M. Stagaman, L. L. Voci, “Gradient-Index Wide-Angle Photographic Objective Design,” Appl. Opt. 23, 1735 (1984).
[CrossRef]

L. G. Atkinson, S. N. Houde-Walter, D. T. Moore, D. P. Ryan, J. M. Stagaman, “Design of a Gradient-Index Photographic Objective,” Appl. Opt. 21, (1982).
[CrossRef] [PubMed]

D. T. Moore, “Gradient-Index Optics: A Review,” Appl. Opt. 19, 1035 (1980).
[CrossRef] [PubMed]

D. T. Moore, “Design of Singlets with Continuously Varying Indices of Refraction,” J. Opt. Soc. Am. 61, 886 (1971).
[CrossRef]

Gradient Index Optical Glass Lenses, Annual Report, July 1975 to Dec. 1976, NSF Research contract ENG 74-11993-A01, Principal Investigator: D. T. Moore.

Ryan, D. P.

L. G. Atkinson, S. N. Houde-Walter, D. T. Moore, D. P. Ryan, J. M. Stagaman, “Design of a Gradient-Index Photographic Objective,” Appl. Opt. 21, (1982).
[CrossRef] [PubMed]

Stagaman, J. M.

L. G. Atkinson, S. N. Houde-Walter, D. T. Moore, D. P. Ryan, J. M. Stagaman, “Design of a Gradient-Index Photographic Objective,” Appl. Opt. 21, (1982).
[CrossRef] [PubMed]

Stagaman, J.M.

Tomozawa, M.

J. R. Engel, M. Tomozawa, “Nernst-Einstein Relation in Sodium Silicate Glass,” J. Am. Ceram. Soc. 58, (1975).
[CrossRef]

Voci, L. L.

Yamamoto, H.

T. Kaneko, H. Yamamoto, “On Ionic Penetration of Silver Film into Glasses under the Electric Field,” in Proceedings, Tenth International Congress in Glass, Kyoto, Japan (1974), pp. 8–79–8–86.

Appl. Opt. (4)

IEEE J. Quantum Electron. (1)

H. J. Lilienhof et al., “Field Induced Index Profiles of Multi-mode Ion-Exchanged Strip Waveguides,” IEEE J. Quantum Electron. QE-18, 1877 (1982).
[CrossRef]

J. Am. Ceram. Soc. (2)

J. R. Engel, M. Tomozawa, “Nernst-Einstein Relation in Sodium Silicate Glass,” J. Am. Ceram. Soc. 58, (1975).
[CrossRef]

M. Abou-El-Liel, A. R. Cooper, “Analysis of Field-Assisted Binary Ion Exchange,” J. Am. Ceram. Soc. 62, 390 (1979).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. Chem. (1)

R. H. Doremus, “Exchange and Diffusion of Ions in Glass,” J. Phys. Chem. 68, 2212 (1964).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

P. O. McLaughlin et al., “Design of a Gradient-Index Binocular Objective,” Proc. Soc. Photo-Opt. Instrum. Eng. 237, 369 (1980).

Other (5)

R. H. Doremus, Glass Science (Wiley, New York, 1973), p. 148.

H. Bloom, The Chemistry of Molten Salts (Benjamin, New York, 1967).

Gradient Index Optical Glass Lenses, Annual Report, July 1975 to Dec. 1976, NSF Research contract ENG 74-11993-A01, Principal Investigator: D. T. Moore.

T. Kaneko, H. Yamamoto, “On Ionic Penetration of Silver Film into Glasses under the Electric Field,” in Proceedings, Tenth International Congress in Glass, Kyoto, Japan (1974), pp. 8–79–8–86.

J. Crank, The Mathematics of Diffusion (Oxford U. P.London, 1975), p. 175.

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Figures (11)

Fig. 1
Fig. 1

Solution to Eq. (2) with constant boundary conditions. The electric field is constant in both magnitude and direction. The drift to diffusion ratio (μE/D) is ~45 cm−1. (Equal ionic mobility is assumed.)

Fig. 2
Fig. 2

Complementary error function at equal time intervals.

Fig. 3
Fig. 3

Same as Fig. 2 except a ramped electric field has been applied.

Fig. 4
Fig. 4

Solution to Eq. (4) with constant boundary conditions. The magnitude of the applied field is constant, and its direction is indicated by arrows. The profiles are shown at equal time intervals, and the numbers indicate the movement of the profile front. The drift to diffusion ratio (μE/D) is ~80 cm−1. (Equal ionic mobility is assumed.) See text.

Fig. 5
Fig. 5

Calculated profile resulting from a field-assisted ion exchange with a forward-reverse-forward applied field. Profiles are shown at the end of each field application. The drift to diffusion ratio (μE/D) is ~45 cm−1. The ionic mobility of the diffusant is equal to the ionic mobility of the glass constituent.

Fig. 6
Fig. 6

Same as in Fig. 5, except that the ionic mobility of the glass constituent is 20 times higher than that of the diffusant.

Fig. 7
Fig. 7

Same as in Figs. 5 and 6 except that the ionic mobility of the diffusant is twice that of the glass constituent.

Fig. 8
Fig. 8

Experimental configuration used to prevent leakage currents.

Fig. 9
Fig. 9

Normalized concentration distance curves for various mobility ratios (nonfield-assisted). The number on each curve is the ionic mobility of the diffusant ion divided by that of the glass constituent ion. The open circles are interferometric data using D0 = 1.99 × 10−8 cm2 sec−1.

Fig. 10
Fig. 10

Forward-reverse field application. The solid line is the calculated profile using D0 = 1.99 × 10−8 cm2 sec−1 and M = 5 × 10−2. The open circles are the interferometric data.

Fig. 11
Fig. 11

Forward-reverse-forward field application. The solid line is the calculated profile using D0 = 1.99 × 10−8 cm2 sec−1 and M = 5 × 10−2. The open circles are the interferometric data.

Tables (1)

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Table I Characteristics of Glasses

Equations (5)

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

C t + M J 0 C 0 [ C 0 + ( M 1 ) C ] 2 · C x = x { D 0 C 0 [ C 0 + ( M 1 ] C ] · C x } ,
μ = D e / k T ,
C t = D 0 2 C x 2 μ E C x .
C ( x , t ) = 1 2 C 0 { exp ( μ E x D ) · erfc ( x + μ E t 2 D t ) + erfc ( x μ E T 2 D t ) } ,
erfc ( z ) = 2 π z exp ( y 2 ) d y .

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