Abstract

We report optimization of the processing conditions for fabrication of single-mode Ag+–Na+ ion-exchanged waveguides in a soda-lime glass. The surface-index change, the mobility and diffusion coefficient of Ag+ have been measured at low melt concentrations and the results used for calculation of the index profile using a new simple numerical method for solving the diffusion equation in a two-step process where the index profile is buried by applying an electric field in the second step. The calculated profile is in agreement with that measured. This correlation allows solution of the Helmholtz equation for given process parameters. Single-mode waveguides with desired mode-field distribution have been designed and fabricated with optimized performance and fiber compatibility at 1.3 μm.

© 1988 Optical Society of America

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References

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  1. R. K. Lagu, R. V. Ramaswamy, “Process and Waveguide Parameter Relationships for the Design of Planar Silver Ion-Exchanged Glass Waveguides,” J. Lightwave Tech. LT-4, 176 (1986).
    [Crossref]
  2. R. V. Ramaswamy, S. I. Najafi, IEEE J. Quantum Electron. QE-22, 883 (1986).
    [Crossref]
  3. R. V. Ramaswamy, R. Srivastava, P. Chludzinski, T. J. Anderson, “Influence of Ag+–Na+ Ion-Exchange Equilibrium On Waveguide Index Profiles,” IEEE J. Quantum Electron., to be published.
  4. R. V. Ramaswamy, R. Srivastava, P. Chludzinski, “Influence of Ag+–Na+ Ion-Exchange Equilibrium on the Index Profile of Single-Mode Glass Waveguides,” Tech. Dig. GRIN ’87, Reno, Nev. Paper ThB4-1.
  5. G. Stewart, P. J. R. Laybourn, “Fabrication of Ion-Exchanged Optical Waveguides from Dilute Silver Nitrate Melts,” IEEE J. Quantum Electron. QE-14, 930 (1978).
    [Crossref]
  6. R. G. Eguchi, E. A. Mounders, I. K. Naik, “Fabrication of Low-Loss Waveguides in BK-7 by Ion Exchange,” Proc. Soc. Photo-Opt. Instrum. Eng. 408, 21 (1983).
  7. H. J. Lilienhof, E. Voges, D. Ritter, B. Pantschew, “Field-Induced Index Profiles of Multimode Ion-Exchanged Strip Waveguides,” IEEE J. Quantum Electron. QE-18, 1877 (1982).
    [Crossref]
  8. R. G. Walker, C. D. W. Wilkinson, J. A. H. Wilkinson, “Integrated Optical Waveguiding Structures Made by Silver Ion-Exchange in Glass. 1: The Propagation Characteristics of Stripe Ion-Exchange Waveguides; a Theoretical and Experimental Investigation,” Appl. Opt. 22, 1923 (1983).
    [Crossref] [PubMed]
  9. J. Crank, Mathematics of Diffusion (Oxford, U.P., London, 1956).
  10. M. Abou-el-Leil, A. R. Cooper, “Analysis of Field-Assisted Binary Ion Exchange,” J. Am. Ceram. Soc. 62, 390 (1979).
    [Crossref]
  11. R. H. Doremus, “Exchange and Diffusion of Ions in Glass,” J. Phys. Chem. 68, 2212 (1964).
    [Crossref]
  12. J. M. White, P. F. Heidrich, “Optical Waveguide Refractive Index Profiles Determined from Measurement of Mode Indices: a Simple Analysis,” Appl. Opt. 15, 151 (1976).
    [Crossref] [PubMed]
  13. R. K. Lagu, V. Ramaswamy, “Fabrication of Single-Mode Glass Waveguides by Electrolyte Release of Silver Ions,” Appl. Phys. Lett. 45, 117 (1984).
    [Crossref]
  14. R. K. Lagu, S. I. Najafi, V. Ramaswamy, “In Situ Measurement of Ionic Concentration During Fabrication of Ion-Exchanged Waveguides,” Appl. Opt. 23, 3925 (1984).
    [Crossref] [PubMed]
  15. E. Rodriguez, R. V. Ramaswamy, R. Srivastava, U. Florida; unpublished.

1986 (2)

R. K. Lagu, R. V. Ramaswamy, “Process and Waveguide Parameter Relationships for the Design of Planar Silver Ion-Exchanged Glass Waveguides,” J. Lightwave Tech. LT-4, 176 (1986).
[Crossref]

R. V. Ramaswamy, S. I. Najafi, IEEE J. Quantum Electron. QE-22, 883 (1986).
[Crossref]

1984 (2)

R. K. Lagu, V. Ramaswamy, “Fabrication of Single-Mode Glass Waveguides by Electrolyte Release of Silver Ions,” Appl. Phys. Lett. 45, 117 (1984).
[Crossref]

R. K. Lagu, S. I. Najafi, V. Ramaswamy, “In Situ Measurement of Ionic Concentration During Fabrication of Ion-Exchanged Waveguides,” Appl. Opt. 23, 3925 (1984).
[Crossref] [PubMed]

1983 (2)

1982 (1)

H. J. Lilienhof, E. Voges, D. Ritter, B. Pantschew, “Field-Induced Index Profiles of Multimode Ion-Exchanged Strip Waveguides,” IEEE J. Quantum Electron. QE-18, 1877 (1982).
[Crossref]

1979 (1)

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

1978 (1)

G. Stewart, P. J. R. Laybourn, “Fabrication of Ion-Exchanged Optical Waveguides from Dilute Silver Nitrate Melts,” IEEE J. Quantum Electron. QE-14, 930 (1978).
[Crossref]

1976 (1)

1964 (1)

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

Abou-el-Leil, M.

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

Anderson, T. J.

R. V. Ramaswamy, R. Srivastava, P. Chludzinski, T. J. Anderson, “Influence of Ag+–Na+ Ion-Exchange Equilibrium On Waveguide Index Profiles,” IEEE J. Quantum Electron., to be published.

Chludzinski, P.

R. V. Ramaswamy, R. Srivastava, P. Chludzinski, “Influence of Ag+–Na+ Ion-Exchange Equilibrium on the Index Profile of Single-Mode Glass Waveguides,” Tech. Dig. GRIN ’87, Reno, Nev. Paper ThB4-1.

R. V. Ramaswamy, R. Srivastava, P. Chludzinski, T. J. Anderson, “Influence of Ag+–Na+ Ion-Exchange Equilibrium On Waveguide Index Profiles,” IEEE J. Quantum Electron., to be published.

Cooper, A. R.

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

Crank, J.

J. Crank, Mathematics of Diffusion (Oxford, U.P., London, 1956).

Doremus, R. H.

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

Eguchi, R. G.

R. G. Eguchi, E. A. Mounders, I. K. Naik, “Fabrication of Low-Loss Waveguides in BK-7 by Ion Exchange,” Proc. Soc. Photo-Opt. Instrum. Eng. 408, 21 (1983).

Heidrich, P. F.

Lagu, R. K.

R. K. Lagu, R. V. Ramaswamy, “Process and Waveguide Parameter Relationships for the Design of Planar Silver Ion-Exchanged Glass Waveguides,” J. Lightwave Tech. LT-4, 176 (1986).
[Crossref]

R. K. Lagu, V. Ramaswamy, “Fabrication of Single-Mode Glass Waveguides by Electrolyte Release of Silver Ions,” Appl. Phys. Lett. 45, 117 (1984).
[Crossref]

R. K. Lagu, S. I. Najafi, V. Ramaswamy, “In Situ Measurement of Ionic Concentration During Fabrication of Ion-Exchanged Waveguides,” Appl. Opt. 23, 3925 (1984).
[Crossref] [PubMed]

Laybourn, P. J. R.

G. Stewart, P. J. R. Laybourn, “Fabrication of Ion-Exchanged Optical Waveguides from Dilute Silver Nitrate Melts,” IEEE J. Quantum Electron. QE-14, 930 (1978).
[Crossref]

Lilienhof, H. J.

H. J. Lilienhof, E. Voges, D. Ritter, B. Pantschew, “Field-Induced Index Profiles of Multimode Ion-Exchanged Strip Waveguides,” IEEE J. Quantum Electron. QE-18, 1877 (1982).
[Crossref]

Mounders, E. A.

R. G. Eguchi, E. A. Mounders, I. K. Naik, “Fabrication of Low-Loss Waveguides in BK-7 by Ion Exchange,” Proc. Soc. Photo-Opt. Instrum. Eng. 408, 21 (1983).

Naik, I. K.

R. G. Eguchi, E. A. Mounders, I. K. Naik, “Fabrication of Low-Loss Waveguides in BK-7 by Ion Exchange,” Proc. Soc. Photo-Opt. Instrum. Eng. 408, 21 (1983).

Najafi, S. I.

Pantschew, B.

H. J. Lilienhof, E. Voges, D. Ritter, B. Pantschew, “Field-Induced Index Profiles of Multimode Ion-Exchanged Strip Waveguides,” IEEE J. Quantum Electron. QE-18, 1877 (1982).
[Crossref]

Ramaswamy, R. V.

R. K. Lagu, R. V. Ramaswamy, “Process and Waveguide Parameter Relationships for the Design of Planar Silver Ion-Exchanged Glass Waveguides,” J. Lightwave Tech. LT-4, 176 (1986).
[Crossref]

R. V. Ramaswamy, S. I. Najafi, IEEE J. Quantum Electron. QE-22, 883 (1986).
[Crossref]

R. V. Ramaswamy, R. Srivastava, P. Chludzinski, T. J. Anderson, “Influence of Ag+–Na+ Ion-Exchange Equilibrium On Waveguide Index Profiles,” IEEE J. Quantum Electron., to be published.

R. V. Ramaswamy, R. Srivastava, P. Chludzinski, “Influence of Ag+–Na+ Ion-Exchange Equilibrium on the Index Profile of Single-Mode Glass Waveguides,” Tech. Dig. GRIN ’87, Reno, Nev. Paper ThB4-1.

E. Rodriguez, R. V. Ramaswamy, R. Srivastava, U. Florida; unpublished.

Ramaswamy, V.

R. K. Lagu, V. Ramaswamy, “Fabrication of Single-Mode Glass Waveguides by Electrolyte Release of Silver Ions,” Appl. Phys. Lett. 45, 117 (1984).
[Crossref]

R. K. Lagu, S. I. Najafi, V. Ramaswamy, “In Situ Measurement of Ionic Concentration During Fabrication of Ion-Exchanged Waveguides,” Appl. Opt. 23, 3925 (1984).
[Crossref] [PubMed]

Ritter, D.

H. J. Lilienhof, E. Voges, D. Ritter, B. Pantschew, “Field-Induced Index Profiles of Multimode Ion-Exchanged Strip Waveguides,” IEEE J. Quantum Electron. QE-18, 1877 (1982).
[Crossref]

Rodriguez, E.

E. Rodriguez, R. V. Ramaswamy, R. Srivastava, U. Florida; unpublished.

Srivastava, R.

E. Rodriguez, R. V. Ramaswamy, R. Srivastava, U. Florida; unpublished.

R. V. Ramaswamy, R. Srivastava, P. Chludzinski, “Influence of Ag+–Na+ Ion-Exchange Equilibrium on the Index Profile of Single-Mode Glass Waveguides,” Tech. Dig. GRIN ’87, Reno, Nev. Paper ThB4-1.

R. V. Ramaswamy, R. Srivastava, P. Chludzinski, T. J. Anderson, “Influence of Ag+–Na+ Ion-Exchange Equilibrium On Waveguide Index Profiles,” IEEE J. Quantum Electron., to be published.

Stewart, G.

G. Stewart, P. J. R. Laybourn, “Fabrication of Ion-Exchanged Optical Waveguides from Dilute Silver Nitrate Melts,” IEEE J. Quantum Electron. QE-14, 930 (1978).
[Crossref]

Voges, E.

H. J. Lilienhof, E. Voges, D. Ritter, B. Pantschew, “Field-Induced Index Profiles of Multimode Ion-Exchanged Strip Waveguides,” IEEE J. Quantum Electron. QE-18, 1877 (1982).
[Crossref]

Walker, R. G.

White, J. M.

Wilkinson, C. D. W.

Wilkinson, J. A. H.

Appl. Opt. (3)

Appl. Phys. Lett. (1)

R. K. Lagu, V. Ramaswamy, “Fabrication of Single-Mode Glass Waveguides by Electrolyte Release of Silver Ions,” Appl. Phys. Lett. 45, 117 (1984).
[Crossref]

IEEE J. Quantum Electron. (3)

H. J. Lilienhof, E. Voges, D. Ritter, B. Pantschew, “Field-Induced Index Profiles of Multimode Ion-Exchanged Strip Waveguides,” IEEE J. Quantum Electron. QE-18, 1877 (1982).
[Crossref]

R. V. Ramaswamy, S. I. Najafi, IEEE J. Quantum Electron. QE-22, 883 (1986).
[Crossref]

G. Stewart, P. J. R. Laybourn, “Fabrication of Ion-Exchanged Optical Waveguides from Dilute Silver Nitrate Melts,” IEEE J. Quantum Electron. QE-14, 930 (1978).
[Crossref]

J. Am. Ceram. Soc. (1)

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

J. Lightwave Tech. (1)

R. K. Lagu, R. V. Ramaswamy, “Process and Waveguide Parameter Relationships for the Design of Planar Silver Ion-Exchanged Glass Waveguides,” J. Lightwave Tech. LT-4, 176 (1986).
[Crossref]

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)

R. G. Eguchi, E. A. Mounders, I. K. Naik, “Fabrication of Low-Loss Waveguides in BK-7 by Ion Exchange,” Proc. Soc. Photo-Opt. Instrum. Eng. 408, 21 (1983).

Other (4)

R. V. Ramaswamy, R. Srivastava, P. Chludzinski, T. J. Anderson, “Influence of Ag+–Na+ Ion-Exchange Equilibrium On Waveguide Index Profiles,” IEEE J. Quantum Electron., to be published.

R. V. Ramaswamy, R. Srivastava, P. Chludzinski, “Influence of Ag+–Na+ Ion-Exchange Equilibrium on the Index Profile of Single-Mode Glass Waveguides,” Tech. Dig. GRIN ’87, Reno, Nev. Paper ThB4-1.

J. Crank, Mathematics of Diffusion (Oxford, U.P., London, 1956).

E. Rodriguez, R. V. Ramaswamy, R. Srivastava, U. Florida; unpublished.

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Figures (7)

Fig. 1
Fig. 1

Comparison of the index profile as given by Eq. (17) (dotted curve) and by Eq. (11) (solid curve): T = 30 min, D ˜ = 0 . 15 μ m 2 / min for each curve. For curve 2, μ = 5.0 μm2/Vmin, E = 45 V/mm.

Fig. 2
Fig. 2

Schematic of the experimental and theoretical procedure.

Fig. 3
Fig. 3

A comparison of the index profile results using various techniques. +, AAS; ×, SEM; ○, Inv WKB; *, Electron Microprobe; – – fitted ERFC to the measured mode indices using finite difference method. W 0 = 2 D ˜ t.

Fig. 4
Fig. 4

Fitting of mode indices by the inverse WKB method: ×, mode indices surface guides without an external field; ○, data with an external field. Curve 1 is a fitted complementary error function profile with D ˜ = 0 . 15 μ m 2 / min and t1 = 120 min. Curve 2 represents Eq. (11) with D ˜ = 0 . 04 μ m 2 / min, μ = 5.0 μm2/min, E1 = 45 V/min, and t1 = 30 min. Silver melt concentration in both cases is NAg = 4 × 10−4.

Fig. 5
Fig. 5

Evolution of the index profile with second-step diffusion time.

Fig. 6
Fig. 6

Variation of the peak-index change with second-step diffusion time.

Fig. 7
Fig. 7

Variation of the index peak position xpeak and the 1/e index width W with the second-step parameters. Curves 1, 2, and 3 correspond to E2 = 10, 40, and 70 V/mm, respectively. The data points are from Ref. 2.

Tables (2)

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Table I Chemical Composition of a Fisher Brand Glass Slide

Equations (20)

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

C ¯ A t = μ A E · C ¯ A ( 1 1 α C ¯ A ) + n 1 α C ¯ A D ¯ A 2 C ¯ A ,
α = 1 μ A μ B ,
n = ln a ¯ A ln C ¯ A .
N ¯ A t = x ( n D ¯ A 1 α N ¯ A N ¯ A x ) + y ( n D ¯ A 1 α N ¯ A N ¯ A y ) .
N ¯ A t = x ( D ˜ N ¯ A x ) ,
D ˜ = n D ¯ A 1 α N ¯ A = n D ¯ A D ¯ B D ¯ A N ¯ A + D ¯ B N ¯ B .
N ¯ A t = n D ¯ A 2 N ¯ A x 2
N ¯ A ( x , t ) = N ¯ 0 erfc ( x / W 0 ) ,
W 0 = 2 n D ˜ A t ,
¯ N A t = n D ¯ A 2 N ¯ A x 2 μ E N ¯ A x ,
N ¯ A = 1 2 N ¯ 0 { erfc ( x r ) + exp ( 4 r x ) erfc ( x + r ) } ,
N ¯ A ( x , r ) N ¯ 0 2 { erfc ( x r ) } , r > 2 . 5 .
C ¯ t = D ˜ 2 C ¯ x 2 μ E C ¯ x
C ¯ 0 ( x ) = Σ i C ¯ i ( x i ) δ ( x x i ) .
C ¯ ( x , t ) = i C ¯ i ( x i ) 4 π D t exp [ ( x x i μ E t ) 2 4 D t ] .
C ¯ ( x , t ) = C ¯ 0 ( x ) 4 π D t exp [ ( x x μ E t ) 2 4 D t ] d x .
C ¯ ( x , t i ) = C ¯ 0 ( x ) 4 π D t exp [ ( x x μ E Δ t ) 2 4 D Δ t ] ( d x ) i i integrals .
C ¯ ( u ) = 0 C ¯ 1 ( u τ ) π exp [ ( u u ) 2 ] d u .
u x μ E 2 t 2 2 D t 2 , u = x 2 D t 2 , τ = t 2 / t 1 ,
C ¯ 1 ( u τ ) = C ¯ 0 ( 0 ) erfc ( τ u ) , s

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