Abstract

Double-ion-exchanged glass waveguides are made first by a potassium-ion exchange followed by a silver-ion exchange. The inverse WKB method is used to determine the index profile. It is shown that a combination of a truncated quadratic function and a complementary error function represents the refractive index best. A direct WKB method is employed to find the maximum index change and the diffusion coefficient of the second exchange process. The concentration of silver, potassium, and sodium ions are measured by an x-ray photoelectron spectroscopy technique. The results agree well with the index profile when a quadratic function is used.

© 1994 Optical Society of America

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References

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  1. T. Izawa, H. Nakagome, “Optical waveguides formed by electrically induced migration of ions in glass plates,” Appl. Phys. Lett. 21, 584–586 (1972).
    [CrossRef]
  2. S. I. Najafi, ed., Introduction to Glass Integrated Optics (Artech, Boston, Mass., 1992).
  3. M. J. Li, S. Honkanen, W. J. Wang, R. Leonelli, J. Albert, S. I. Najafi, “Potassium and silver ion-exchanged dual-core glass waveguides with gratings,” Appl. Phys. Lett. 58, 2607–2609 (1991).
    [CrossRef]
  4. W. J. Wang, S. Honkanen, S. I. Najafi, A. Tervonen, “Loss characteristics of potassium and silver double-ion-exchanged glass waveguides,” J. Appl. Phys. 74, 1529–1533 (1993).
    [CrossRef]
  5. H. Helmers, O. G. Helleso, P. Benech, R. Rimet, “Single mode potassium and silver ion-exchanged glass waveguides with low losses and high index increase,” Appl. Phys. Lett. 61, 2759–2760 (1992).
    [CrossRef]
  6. J. M. White, P. F. Heidrich, “Optical waveguide refractive index profiles determined from measurement of mode indices: a simple analysis,” Appl. Opt. 15, 151–155 (1976).
    [CrossRef] [PubMed]
  7. J. E. Gortych, D. G. Hall, “Fabrication of planar optical waveguides by K+-ion exchange in BK7 and Pyrex glass,” IEEE J. Quantum Electron. QE-22, 892–895 (1986).
    [CrossRef]
  8. G. Stewart, C. A. Millar, P. J. R. Laybourn, C. D. W. Wilkinson, R. M. DeLaRue, “Planar optical waveguides formed by silver-ion migration in glass,” IEEE J. Quantum Electron. QE-13, 192–200 (1977).
    [CrossRef]
  9. G. B. Hocker, W. K. Burns, “Modes in diffused optical waveguides of arbitrary index profile,” IEEE J. Quantum Electron. QE-11, 270–276 (1975).
    [CrossRef]
  10. A. M. Cohen, J. F. Cutts, R. Fielder, D. E. Jones, J. Ribbans, E. Stuart, Numerical Analysis (McGraw-Hill, London, 1973), pp. 276–280.
  11. S. Honkanen, A. Tervonen, M. McCourt, “Control of birefringence in ion-exchanged glass waveguides,” Appl. Opt. 26, 4710–4711 (1987).
    [CrossRef] [PubMed]

1993 (1)

W. J. Wang, S. Honkanen, S. I. Najafi, A. Tervonen, “Loss characteristics of potassium and silver double-ion-exchanged glass waveguides,” J. Appl. Phys. 74, 1529–1533 (1993).
[CrossRef]

1992 (1)

H. Helmers, O. G. Helleso, P. Benech, R. Rimet, “Single mode potassium and silver ion-exchanged glass waveguides with low losses and high index increase,” Appl. Phys. Lett. 61, 2759–2760 (1992).
[CrossRef]

1991 (1)

M. J. Li, S. Honkanen, W. J. Wang, R. Leonelli, J. Albert, S. I. Najafi, “Potassium and silver ion-exchanged dual-core glass waveguides with gratings,” Appl. Phys. Lett. 58, 2607–2609 (1991).
[CrossRef]

1987 (1)

1986 (1)

J. E. Gortych, D. G. Hall, “Fabrication of planar optical waveguides by K+-ion exchange in BK7 and Pyrex glass,” IEEE J. Quantum Electron. QE-22, 892–895 (1986).
[CrossRef]

1977 (1)

G. Stewart, C. A. Millar, P. J. R. Laybourn, C. D. W. Wilkinson, R. M. DeLaRue, “Planar optical waveguides formed by silver-ion migration in glass,” IEEE J. Quantum Electron. QE-13, 192–200 (1977).
[CrossRef]

1976 (1)

1975 (1)

G. B. Hocker, W. K. Burns, “Modes in diffused optical waveguides of arbitrary index profile,” IEEE J. Quantum Electron. QE-11, 270–276 (1975).
[CrossRef]

1972 (1)

T. Izawa, H. Nakagome, “Optical waveguides formed by electrically induced migration of ions in glass plates,” Appl. Phys. Lett. 21, 584–586 (1972).
[CrossRef]

Albert, J.

M. J. Li, S. Honkanen, W. J. Wang, R. Leonelli, J. Albert, S. I. Najafi, “Potassium and silver ion-exchanged dual-core glass waveguides with gratings,” Appl. Phys. Lett. 58, 2607–2609 (1991).
[CrossRef]

Benech, P.

H. Helmers, O. G. Helleso, P. Benech, R. Rimet, “Single mode potassium and silver ion-exchanged glass waveguides with low losses and high index increase,” Appl. Phys. Lett. 61, 2759–2760 (1992).
[CrossRef]

Burns, W. K.

G. B. Hocker, W. K. Burns, “Modes in diffused optical waveguides of arbitrary index profile,” IEEE J. Quantum Electron. QE-11, 270–276 (1975).
[CrossRef]

Cohen, A. M.

A. M. Cohen, J. F. Cutts, R. Fielder, D. E. Jones, J. Ribbans, E. Stuart, Numerical Analysis (McGraw-Hill, London, 1973), pp. 276–280.

Cutts, J. F.

A. M. Cohen, J. F. Cutts, R. Fielder, D. E. Jones, J. Ribbans, E. Stuart, Numerical Analysis (McGraw-Hill, London, 1973), pp. 276–280.

DeLaRue, R. M.

G. Stewart, C. A. Millar, P. J. R. Laybourn, C. D. W. Wilkinson, R. M. DeLaRue, “Planar optical waveguides formed by silver-ion migration in glass,” IEEE J. Quantum Electron. QE-13, 192–200 (1977).
[CrossRef]

Fielder, R.

A. M. Cohen, J. F. Cutts, R. Fielder, D. E. Jones, J. Ribbans, E. Stuart, Numerical Analysis (McGraw-Hill, London, 1973), pp. 276–280.

Gortych, J. E.

J. E. Gortych, D. G. Hall, “Fabrication of planar optical waveguides by K+-ion exchange in BK7 and Pyrex glass,” IEEE J. Quantum Electron. QE-22, 892–895 (1986).
[CrossRef]

Hall, D. G.

J. E. Gortych, D. G. Hall, “Fabrication of planar optical waveguides by K+-ion exchange in BK7 and Pyrex glass,” IEEE J. Quantum Electron. QE-22, 892–895 (1986).
[CrossRef]

Heidrich, P. F.

Helleso, O. G.

H. Helmers, O. G. Helleso, P. Benech, R. Rimet, “Single mode potassium and silver ion-exchanged glass waveguides with low losses and high index increase,” Appl. Phys. Lett. 61, 2759–2760 (1992).
[CrossRef]

Helmers, H.

H. Helmers, O. G. Helleso, P. Benech, R. Rimet, “Single mode potassium and silver ion-exchanged glass waveguides with low losses and high index increase,” Appl. Phys. Lett. 61, 2759–2760 (1992).
[CrossRef]

Hocker, G. B.

G. B. Hocker, W. K. Burns, “Modes in diffused optical waveguides of arbitrary index profile,” IEEE J. Quantum Electron. QE-11, 270–276 (1975).
[CrossRef]

Honkanen, S.

W. J. Wang, S. Honkanen, S. I. Najafi, A. Tervonen, “Loss characteristics of potassium and silver double-ion-exchanged glass waveguides,” J. Appl. Phys. 74, 1529–1533 (1993).
[CrossRef]

M. J. Li, S. Honkanen, W. J. Wang, R. Leonelli, J. Albert, S. I. Najafi, “Potassium and silver ion-exchanged dual-core glass waveguides with gratings,” Appl. Phys. Lett. 58, 2607–2609 (1991).
[CrossRef]

S. Honkanen, A. Tervonen, M. McCourt, “Control of birefringence in ion-exchanged glass waveguides,” Appl. Opt. 26, 4710–4711 (1987).
[CrossRef] [PubMed]

Izawa, T.

T. Izawa, H. Nakagome, “Optical waveguides formed by electrically induced migration of ions in glass plates,” Appl. Phys. Lett. 21, 584–586 (1972).
[CrossRef]

Jones, D. E.

A. M. Cohen, J. F. Cutts, R. Fielder, D. E. Jones, J. Ribbans, E. Stuart, Numerical Analysis (McGraw-Hill, London, 1973), pp. 276–280.

Laybourn, P. J. R.

G. Stewart, C. A. Millar, P. J. R. Laybourn, C. D. W. Wilkinson, R. M. DeLaRue, “Planar optical waveguides formed by silver-ion migration in glass,” IEEE J. Quantum Electron. QE-13, 192–200 (1977).
[CrossRef]

Leonelli, R.

M. J. Li, S. Honkanen, W. J. Wang, R. Leonelli, J. Albert, S. I. Najafi, “Potassium and silver ion-exchanged dual-core glass waveguides with gratings,” Appl. Phys. Lett. 58, 2607–2609 (1991).
[CrossRef]

Li, M. J.

M. J. Li, S. Honkanen, W. J. Wang, R. Leonelli, J. Albert, S. I. Najafi, “Potassium and silver ion-exchanged dual-core glass waveguides with gratings,” Appl. Phys. Lett. 58, 2607–2609 (1991).
[CrossRef]

McCourt, M.

Millar, C. A.

G. Stewart, C. A. Millar, P. J. R. Laybourn, C. D. W. Wilkinson, R. M. DeLaRue, “Planar optical waveguides formed by silver-ion migration in glass,” IEEE J. Quantum Electron. QE-13, 192–200 (1977).
[CrossRef]

Najafi, S. I.

W. J. Wang, S. Honkanen, S. I. Najafi, A. Tervonen, “Loss characteristics of potassium and silver double-ion-exchanged glass waveguides,” J. Appl. Phys. 74, 1529–1533 (1993).
[CrossRef]

M. J. Li, S. Honkanen, W. J. Wang, R. Leonelli, J. Albert, S. I. Najafi, “Potassium and silver ion-exchanged dual-core glass waveguides with gratings,” Appl. Phys. Lett. 58, 2607–2609 (1991).
[CrossRef]

Nakagome, H.

T. Izawa, H. Nakagome, “Optical waveguides formed by electrically induced migration of ions in glass plates,” Appl. Phys. Lett. 21, 584–586 (1972).
[CrossRef]

Ribbans, J.

A. M. Cohen, J. F. Cutts, R. Fielder, D. E. Jones, J. Ribbans, E. Stuart, Numerical Analysis (McGraw-Hill, London, 1973), pp. 276–280.

Rimet, R.

H. Helmers, O. G. Helleso, P. Benech, R. Rimet, “Single mode potassium and silver ion-exchanged glass waveguides with low losses and high index increase,” Appl. Phys. Lett. 61, 2759–2760 (1992).
[CrossRef]

Stewart, G.

G. Stewart, C. A. Millar, P. J. R. Laybourn, C. D. W. Wilkinson, R. M. DeLaRue, “Planar optical waveguides formed by silver-ion migration in glass,” IEEE J. Quantum Electron. QE-13, 192–200 (1977).
[CrossRef]

Stuart, E.

A. M. Cohen, J. F. Cutts, R. Fielder, D. E. Jones, J. Ribbans, E. Stuart, Numerical Analysis (McGraw-Hill, London, 1973), pp. 276–280.

Tervonen, A.

W. J. Wang, S. Honkanen, S. I. Najafi, A. Tervonen, “Loss characteristics of potassium and silver double-ion-exchanged glass waveguides,” J. Appl. Phys. 74, 1529–1533 (1993).
[CrossRef]

S. Honkanen, A. Tervonen, M. McCourt, “Control of birefringence in ion-exchanged glass waveguides,” Appl. Opt. 26, 4710–4711 (1987).
[CrossRef] [PubMed]

Wang, W. J.

W. J. Wang, S. Honkanen, S. I. Najafi, A. Tervonen, “Loss characteristics of potassium and silver double-ion-exchanged glass waveguides,” J. Appl. Phys. 74, 1529–1533 (1993).
[CrossRef]

M. J. Li, S. Honkanen, W. J. Wang, R. Leonelli, J. Albert, S. I. Najafi, “Potassium and silver ion-exchanged dual-core glass waveguides with gratings,” Appl. Phys. Lett. 58, 2607–2609 (1991).
[CrossRef]

White, J. M.

Wilkinson, C. D. W.

G. Stewart, C. A. Millar, P. J. R. Laybourn, C. D. W. Wilkinson, R. M. DeLaRue, “Planar optical waveguides formed by silver-ion migration in glass,” IEEE J. Quantum Electron. QE-13, 192–200 (1977).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (3)

T. Izawa, H. Nakagome, “Optical waveguides formed by electrically induced migration of ions in glass plates,” Appl. Phys. Lett. 21, 584–586 (1972).
[CrossRef]

M. J. Li, S. Honkanen, W. J. Wang, R. Leonelli, J. Albert, S. I. Najafi, “Potassium and silver ion-exchanged dual-core glass waveguides with gratings,” Appl. Phys. Lett. 58, 2607–2609 (1991).
[CrossRef]

H. Helmers, O. G. Helleso, P. Benech, R. Rimet, “Single mode potassium and silver ion-exchanged glass waveguides with low losses and high index increase,” Appl. Phys. Lett. 61, 2759–2760 (1992).
[CrossRef]

IEEE J. Quantum Electron. (3)

J. E. Gortych, D. G. Hall, “Fabrication of planar optical waveguides by K+-ion exchange in BK7 and Pyrex glass,” IEEE J. Quantum Electron. QE-22, 892–895 (1986).
[CrossRef]

G. Stewart, C. A. Millar, P. J. R. Laybourn, C. D. W. Wilkinson, R. M. DeLaRue, “Planar optical waveguides formed by silver-ion migration in glass,” IEEE J. Quantum Electron. QE-13, 192–200 (1977).
[CrossRef]

G. B. Hocker, W. K. Burns, “Modes in diffused optical waveguides of arbitrary index profile,” IEEE J. Quantum Electron. QE-11, 270–276 (1975).
[CrossRef]

J. Appl. Phys. (1)

W. J. Wang, S. Honkanen, S. I. Najafi, A. Tervonen, “Loss characteristics of potassium and silver double-ion-exchanged glass waveguides,” J. Appl. Phys. 74, 1529–1533 (1993).
[CrossRef]

Other (2)

S. I. Najafi, ed., Introduction to Glass Integrated Optics (Artech, Boston, Mass., 1992).

A. M. Cohen, J. F. Cutts, R. Fielder, D. E. Jones, J. Ribbans, E. Stuart, Numerical Analysis (McGraw-Hill, London, 1973), pp. 276–280.

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Figures (7)

Fig. 1
Fig. 1

Index profile for K- and Ag-double-ion-exchanged waveguides. Ion-exchange temperatures: 400 °C (K+) and 300 °C (Ag+). K+ exchange time 15 h, Ag+ exchange time is given in the figures. ●, experimental measurement; —, fit obtained with a truncated second-order polynomial.

Fig. 2
Fig. 2

Fits of different trial functions to experimental data for K- and Ag-double-ion-exchanged waveguides. Exchange time is 15 h for both K+ and Ag+. Exchange temperatures: 400 °C (K+) and 300 °C (Ag+).

Fig. 3
Fig. 3

Variations of Ag region depths with the square root of time.

Fig. 4
Fig. 4

Variations of effective indices with Ag-ion-exchange time. λ = 0.6328 μm. The exchange time for the K ion is 15 h. (Top) TE modes, (bottom) TM modes.

Fig. 5
Fig. 5

Variations of effective indices for fundamental TE and TM modes as a function of Ag-ion-exchange time. K-ion-exchange time for all the waveguides is 1 h. Ion-exchange temperatures: 400 °C (K+) and 3000 °(Ag+).

Fig. 6
Fig. 6

Calculated intensity profile for the fundamental mode. λ = 1.3 μm.

Fig. 7
Fig. 7

Variations of K, Ag, and Na concentrations as functions of depth in a K- and Ag-double-ion-exchanged waveguide. K+ and Ag+ exchange times are both 15 h. Ion-exchange temperatures: 400 °C (K+) and 300 °C (Ag+).

Equations (14)

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Δ n = 0.0073 , D = 1.98 μ m 2 / h .
Δ n = 0.0093 , D = 1.73 μ m 2 / h .
n ( x ) = Δ n Ag f ( x / d Ag ) + Δ n K erfc ( x / d K ) + n b ,
erfc ( x / d Ag ) ,
exp ( - x 2 / d Ag 2 ) ,
exp ( - x 4 / d Ag 4 ) ,
erfc ( x 2 / d Ag 2 ) ,
{ 1 - ( x / d Ag ) - b ( x / d Ag ) 2 for x d Ag < ( 1 + 4 b ) 1 / 2 - 1 2 b 0 for x d Ag > ( 1 + 4 b ) 1 / 2 - 1 2 b .
k 0 0 x t m [ n 2 ( x ) - N m 2 ] 1 / 2 d x = ( 4 m + 1 4 ) π + arctg [ ( N m 2 - n c 2 n s 2 - N m 2 ) n s p ] 1 / 2 , P = { 0 for TE 2 for TM ,
sum = m = 0 K ( N m measured - N m calculated ] 2 .
Δ n Ag = 0.067 ± 0.002 , D Ag = 1.59 ± 0.09 μ m 2 / h .
Δ n Ag = 0.066 ± 0.002 , D Ag = 1.59 ± 0.09 μ m 2 / h .
C Ag = A [ 1 - ( x / d Ag ) - 1.67 ( x / d Ag ) 2 ] ,
C K = B erfc ( x / d K ) - C [ 1 - ( x / d Ag ) - 1.7 ( x / d Ag ) 2 ] .

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