Abstract

We present the study of multimode glass waveguides fabricated by a silver-ion electromigration process followed by a diffusion process. The study is concerned mainly with the diffusion process, which occurs by variation of the diffusion time. The obtained guides are analyzed by the prism-coupling technique, which determines their effective refractive indices that are treated by the inverse WKB method, assumed to be proportional to the silver ions’ concentration profiles, for which a Gaussian model is attributed. Diffusion coefficients then are determined from these Gaussian profiles experimentally by both methods. These diffusion coefficients show a concentration dependence related to the variation of the diffusion time. A mathematical model representing the best fit to this dependence is also presented. Finally, our results are compared with other research results, with which we find good agreement.

© 2002 Optical Society of America

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References

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  1. T. Findakly, “Glass waveguides by ion exchange: a review,” Opt. Eng. 24, 244–250 (1985).
    [CrossRef]
  2. R. Srivastava, R. V. Ramaswamy, “Ion-exchanged waveguides: current status,” Integrated Optical Circuits, K.-K. Wong, ed., Proc. SPIE1583, 2–13 (1991) and references therein.
    [CrossRef]
  3. G. Stewart, C. A. Millar, P. J. R. Layboum, 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]
  4. S. I. Najafi, P. G. Suchoski, R. V. Ramaswamy, “Silver film-diffused glass waveguides: diffusion process and optical properties,” IEEE J. Quantum Electron. QE-22, 2213–2218 (1986).
    [CrossRef]
  5. T. Findakly, E. Garmire, “Reduction and control of optical waveguide losses in glass,” App. Phys. Lett. 37, 855–856 (1980).
    [CrossRef]
  6. J. Viljanen, M. Leppihalme, “Fabrication of optical strip waveguides with nearly circular cross section by silver ion migration technique,” J. App. Phys. 51, 3563–3565 (1980).
    [CrossRef]
  7. J. E. Samuels, D. T. Moore, “Gradient-index profile control from mixed molten salt baths,” Appl. Opt. 29, 4042–4050 (1990).
    [CrossRef] [PubMed]
  8. G. Chartier, P. Collier, A. Guez, P. Jaussaud, Y. Won, “Graded-index surface or buried waveguides by ion exchange in glass,” App. Opt. 19, 1092–1095 (1980).
    [CrossRef]
  9. M. Oikawa, K. Iga, M. Morinaga, T. Usui, T. Chiba, “Distributed-index formation process in a planar microlens,” App. Opt. 23, 1787–1789 (1984).
    [CrossRef]
  10. A. Tervonen, P. Pöyhönen, S. Honkanen, M. Tahkokorpi, S. Tammela, “Examination of two-step fabrication methods for single-mode fiber compatible ion-exchanged glass waveguides,” Appl. Opt. 30, 338–343 (1991) and references therein.
    [CrossRef] [PubMed]
  11. A. Belkhir, “A comparative study of silver diffusion in a glass substrate for optical waveguide applications,” IEEE J. Quantum Electron. 35, 306–311 (1999).
    [CrossRef]
  12. J. Albert, G. L. Yip, “Refractive-index profiles of planar waveguides made by ion-exchange in glass,” Appl. Opt. 24, 3692–3693 (1985).
    [CrossRef] [PubMed]
  13. P. K. Tien, R. Ulrich, “Theory of prism-film coupler and thin-film light guides,” J. Opt. Soc. Am. 60, 1325–1337 (1970).
    [CrossRef]
  14. 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]
  15. J. J. Crank, The Mathematics of Diffusion (Clarendon, Oxford, England, 1956).
  16. R. H. Doremus, “Exchange and diffusion of ions in glass,” J. Phys. Chem. 68, 2212–2218 (1964).
    [CrossRef]
  17. F. Helfferich, M. S. Plesset, “Ion exchange kinetics. A nonlinear diffusion problem,” J. Chem. Phys. 28, 418–424 (1958).
    [CrossRef]
  18. L. Tsonev, I. Savatinova, “Investigation of refractive-index profiles of ion-exchanged planar waveguides in glass,” J. Mod. Opt. 35, 919–924 (1988).
    [CrossRef]
  19. S. I. Najafi, R. V. Ramaswamy, “Ag+-diffused graded-index glass waveguides: diffusion and model characterization,” in Proceedings of the Graded-Index Optical Imaging Systems Conference (n.p., Palermo, Italy, 1985), pp. 142–145.
  20. S. I. Najafi, R. V. Ramaswamy, “Diffusion and model characterization Ag+-Na+ exchanged channel waveguides,” in Digest of Meeting on Integrated and Guided-Wave Optics (Optical Society of America, Washington, D.C., 1986), pp. 60–61.

1999 (1)

A. Belkhir, “A comparative study of silver diffusion in a glass substrate for optical waveguide applications,” IEEE J. Quantum Electron. 35, 306–311 (1999).
[CrossRef]

1991 (1)

1990 (1)

1988 (1)

L. Tsonev, I. Savatinova, “Investigation of refractive-index profiles of ion-exchanged planar waveguides in glass,” J. Mod. Opt. 35, 919–924 (1988).
[CrossRef]

1986 (1)

S. I. Najafi, P. G. Suchoski, R. V. Ramaswamy, “Silver film-diffused glass waveguides: diffusion process and optical properties,” IEEE J. Quantum Electron. QE-22, 2213–2218 (1986).
[CrossRef]

1985 (2)

1984 (1)

M. Oikawa, K. Iga, M. Morinaga, T. Usui, T. Chiba, “Distributed-index formation process in a planar microlens,” App. Opt. 23, 1787–1789 (1984).
[CrossRef]

1980 (3)

T. Findakly, E. Garmire, “Reduction and control of optical waveguide losses in glass,” App. Phys. Lett. 37, 855–856 (1980).
[CrossRef]

J. Viljanen, M. Leppihalme, “Fabrication of optical strip waveguides with nearly circular cross section by silver ion migration technique,” J. App. Phys. 51, 3563–3565 (1980).
[CrossRef]

G. Chartier, P. Collier, A. Guez, P. Jaussaud, Y. Won, “Graded-index surface or buried waveguides by ion exchange in glass,” App. Opt. 19, 1092–1095 (1980).
[CrossRef]

1977 (1)

G. Stewart, C. A. Millar, P. J. R. Layboum, 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)

1970 (1)

1964 (1)

R. H. Doremus, “Exchange and diffusion of ions in glass,” J. Phys. Chem. 68, 2212–2218 (1964).
[CrossRef]

1958 (1)

F. Helfferich, M. S. Plesset, “Ion exchange kinetics. A nonlinear diffusion problem,” J. Chem. Phys. 28, 418–424 (1958).
[CrossRef]

Albert, J.

Belkhir, A.

A. Belkhir, “A comparative study of silver diffusion in a glass substrate for optical waveguide applications,” IEEE J. Quantum Electron. 35, 306–311 (1999).
[CrossRef]

Chartier, G.

G. Chartier, P. Collier, A. Guez, P. Jaussaud, Y. Won, “Graded-index surface or buried waveguides by ion exchange in glass,” App. Opt. 19, 1092–1095 (1980).
[CrossRef]

Chiba, T.

M. Oikawa, K. Iga, M. Morinaga, T. Usui, T. Chiba, “Distributed-index formation process in a planar microlens,” App. Opt. 23, 1787–1789 (1984).
[CrossRef]

Collier, P.

G. Chartier, P. Collier, A. Guez, P. Jaussaud, Y. Won, “Graded-index surface or buried waveguides by ion exchange in glass,” App. Opt. 19, 1092–1095 (1980).
[CrossRef]

Crank, J. J.

J. J. Crank, The Mathematics of Diffusion (Clarendon, Oxford, England, 1956).

DeLaRue, R. M.

G. Stewart, C. A. Millar, P. J. R. Layboum, 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]

Doremus, R. H.

R. H. Doremus, “Exchange and diffusion of ions in glass,” J. Phys. Chem. 68, 2212–2218 (1964).
[CrossRef]

Findakly, T.

T. Findakly, “Glass waveguides by ion exchange: a review,” Opt. Eng. 24, 244–250 (1985).
[CrossRef]

T. Findakly, E. Garmire, “Reduction and control of optical waveguide losses in glass,” App. Phys. Lett. 37, 855–856 (1980).
[CrossRef]

Garmire, E.

T. Findakly, E. Garmire, “Reduction and control of optical waveguide losses in glass,” App. Phys. Lett. 37, 855–856 (1980).
[CrossRef]

Guez, A.

G. Chartier, P. Collier, A. Guez, P. Jaussaud, Y. Won, “Graded-index surface or buried waveguides by ion exchange in glass,” App. Opt. 19, 1092–1095 (1980).
[CrossRef]

Heidrich, P. F.

Helfferich, F.

F. Helfferich, M. S. Plesset, “Ion exchange kinetics. A nonlinear diffusion problem,” J. Chem. Phys. 28, 418–424 (1958).
[CrossRef]

Honkanen, S.

Iga, K.

M. Oikawa, K. Iga, M. Morinaga, T. Usui, T. Chiba, “Distributed-index formation process in a planar microlens,” App. Opt. 23, 1787–1789 (1984).
[CrossRef]

Jaussaud, P.

G. Chartier, P. Collier, A. Guez, P. Jaussaud, Y. Won, “Graded-index surface or buried waveguides by ion exchange in glass,” App. Opt. 19, 1092–1095 (1980).
[CrossRef]

Layboum, P. J. R.

G. Stewart, C. A. Millar, P. J. R. Layboum, 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]

Leppihalme, M.

J. Viljanen, M. Leppihalme, “Fabrication of optical strip waveguides with nearly circular cross section by silver ion migration technique,” J. App. Phys. 51, 3563–3565 (1980).
[CrossRef]

Millar, C. A.

G. Stewart, C. A. Millar, P. J. R. Layboum, 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]

Moore, D. T.

Morinaga, M.

M. Oikawa, K. Iga, M. Morinaga, T. Usui, T. Chiba, “Distributed-index formation process in a planar microlens,” App. Opt. 23, 1787–1789 (1984).
[CrossRef]

Najafi, S. I.

S. I. Najafi, P. G. Suchoski, R. V. Ramaswamy, “Silver film-diffused glass waveguides: diffusion process and optical properties,” IEEE J. Quantum Electron. QE-22, 2213–2218 (1986).
[CrossRef]

S. I. Najafi, R. V. Ramaswamy, “Ag+-diffused graded-index glass waveguides: diffusion and model characterization,” in Proceedings of the Graded-Index Optical Imaging Systems Conference (n.p., Palermo, Italy, 1985), pp. 142–145.

S. I. Najafi, R. V. Ramaswamy, “Diffusion and model characterization Ag+-Na+ exchanged channel waveguides,” in Digest of Meeting on Integrated and Guided-Wave Optics (Optical Society of America, Washington, D.C., 1986), pp. 60–61.

Oikawa, M.

M. Oikawa, K. Iga, M. Morinaga, T. Usui, T. Chiba, “Distributed-index formation process in a planar microlens,” App. Opt. 23, 1787–1789 (1984).
[CrossRef]

Plesset, M. S.

F. Helfferich, M. S. Plesset, “Ion exchange kinetics. A nonlinear diffusion problem,” J. Chem. Phys. 28, 418–424 (1958).
[CrossRef]

Pöyhönen, P.

Ramaswamy, R. V.

S. I. Najafi, P. G. Suchoski, R. V. Ramaswamy, “Silver film-diffused glass waveguides: diffusion process and optical properties,” IEEE J. Quantum Electron. QE-22, 2213–2218 (1986).
[CrossRef]

R. Srivastava, R. V. Ramaswamy, “Ion-exchanged waveguides: current status,” Integrated Optical Circuits, K.-K. Wong, ed., Proc. SPIE1583, 2–13 (1991) and references therein.
[CrossRef]

S. I. Najafi, R. V. Ramaswamy, “Ag+-diffused graded-index glass waveguides: diffusion and model characterization,” in Proceedings of the Graded-Index Optical Imaging Systems Conference (n.p., Palermo, Italy, 1985), pp. 142–145.

S. I. Najafi, R. V. Ramaswamy, “Diffusion and model characterization Ag+-Na+ exchanged channel waveguides,” in Digest of Meeting on Integrated and Guided-Wave Optics (Optical Society of America, Washington, D.C., 1986), pp. 60–61.

Samuels, J. E.

Savatinova, I.

L. Tsonev, I. Savatinova, “Investigation of refractive-index profiles of ion-exchanged planar waveguides in glass,” J. Mod. Opt. 35, 919–924 (1988).
[CrossRef]

Srivastava, R.

R. Srivastava, R. V. Ramaswamy, “Ion-exchanged waveguides: current status,” Integrated Optical Circuits, K.-K. Wong, ed., Proc. SPIE1583, 2–13 (1991) and references therein.
[CrossRef]

Stewart, G.

G. Stewart, C. A. Millar, P. J. R. Layboum, 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]

Suchoski, P. G.

S. I. Najafi, P. G. Suchoski, R. V. Ramaswamy, “Silver film-diffused glass waveguides: diffusion process and optical properties,” IEEE J. Quantum Electron. QE-22, 2213–2218 (1986).
[CrossRef]

Tahkokorpi, M.

Tammela, S.

Tervonen, A.

Tien, P. K.

Tsonev, L.

L. Tsonev, I. Savatinova, “Investigation of refractive-index profiles of ion-exchanged planar waveguides in glass,” J. Mod. Opt. 35, 919–924 (1988).
[CrossRef]

Ulrich, R.

Usui, T.

M. Oikawa, K. Iga, M. Morinaga, T. Usui, T. Chiba, “Distributed-index formation process in a planar microlens,” App. Opt. 23, 1787–1789 (1984).
[CrossRef]

Viljanen, J.

J. Viljanen, M. Leppihalme, “Fabrication of optical strip waveguides with nearly circular cross section by silver ion migration technique,” J. App. Phys. 51, 3563–3565 (1980).
[CrossRef]

White, J. M.

Wilkinson, C. D. W.

G. Stewart, C. A. Millar, P. J. R. Layboum, 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]

Won, Y.

G. Chartier, P. Collier, A. Guez, P. Jaussaud, Y. Won, “Graded-index surface or buried waveguides by ion exchange in glass,” App. Opt. 19, 1092–1095 (1980).
[CrossRef]

Yip, G. L.

App. Opt. (2)

G. Chartier, P. Collier, A. Guez, P. Jaussaud, Y. Won, “Graded-index surface or buried waveguides by ion exchange in glass,” App. Opt. 19, 1092–1095 (1980).
[CrossRef]

M. Oikawa, K. Iga, M. Morinaga, T. Usui, T. Chiba, “Distributed-index formation process in a planar microlens,” App. Opt. 23, 1787–1789 (1984).
[CrossRef]

App. Phys. Lett. (1)

T. Findakly, E. Garmire, “Reduction and control of optical waveguide losses in glass,” App. Phys. Lett. 37, 855–856 (1980).
[CrossRef]

Appl. Opt. (4)

IEEE J. Quantum Electron. (3)

A. Belkhir, “A comparative study of silver diffusion in a glass substrate for optical waveguide applications,” IEEE J. Quantum Electron. 35, 306–311 (1999).
[CrossRef]

G. Stewart, C. A. Millar, P. J. R. Layboum, 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]

S. I. Najafi, P. G. Suchoski, R. V. Ramaswamy, “Silver film-diffused glass waveguides: diffusion process and optical properties,” IEEE J. Quantum Electron. QE-22, 2213–2218 (1986).
[CrossRef]

J. App. Phys. (1)

J. Viljanen, M. Leppihalme, “Fabrication of optical strip waveguides with nearly circular cross section by silver ion migration technique,” J. App. Phys. 51, 3563–3565 (1980).
[CrossRef]

J. Chem. Phys. (1)

F. Helfferich, M. S. Plesset, “Ion exchange kinetics. A nonlinear diffusion problem,” J. Chem. Phys. 28, 418–424 (1958).
[CrossRef]

J. Mod. Opt. (1)

L. Tsonev, I. Savatinova, “Investigation of refractive-index profiles of ion-exchanged planar waveguides in glass,” J. Mod. Opt. 35, 919–924 (1988).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. Chem. (1)

R. H. Doremus, “Exchange and diffusion of ions in glass,” J. Phys. Chem. 68, 2212–2218 (1964).
[CrossRef]

Opt. Eng. (1)

T. Findakly, “Glass waveguides by ion exchange: a review,” Opt. Eng. 24, 244–250 (1985).
[CrossRef]

Other (4)

R. Srivastava, R. V. Ramaswamy, “Ion-exchanged waveguides: current status,” Integrated Optical Circuits, K.-K. Wong, ed., Proc. SPIE1583, 2–13 (1991) and references therein.
[CrossRef]

J. J. Crank, The Mathematics of Diffusion (Clarendon, Oxford, England, 1956).

S. I. Najafi, R. V. Ramaswamy, “Ag+-diffused graded-index glass waveguides: diffusion and model characterization,” in Proceedings of the Graded-Index Optical Imaging Systems Conference (n.p., Palermo, Italy, 1985), pp. 142–145.

S. I. Najafi, R. V. Ramaswamy, “Diffusion and model characterization Ag+-Na+ exchanged channel waveguides,” in Digest of Meeting on Integrated and Guided-Wave Optics (Optical Society of America, Washington, D.C., 1986), pp. 60–61.

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Figures (5)

Fig. 1
Fig. 1

Making the optical waveguide during the electromigration process at T = 254 °C. Thickness of silver film d f = 0.54 µm, U = 100 V, i = 560 µA/cm2.

Fig. 2
Fig. 2

Refractive-index profiles after the diffusion process (annealing) at T = 370 °C. Diffusion times: profile A, 1 h; profile B, 2 h; profile C, 4 h; profile D, 6 h.

Fig. 3
Fig. 3

Refractive-index profiles in the diffusion process (annealing) at T = 370 °C. Diffusion times: profile E, 19 min; profile F, 8 h. Profile I, initial guide in the electromigration process at T = 254 °C, from Ref. 11.

Fig. 4
Fig. 4

Surface effective index n es versus diffusion time t (in seconds). Dashed curve, the best-fitting function written as n(0, t) = 1.525 + 1.47/(t + 444.89)1/2.

Fig. 5
Fig. 5

Diffusion coefficient D versus the normalized concentration C in the diffusion process at T = 370 °C, thickness of silver film d f = 0.54 µm, U = 100 V, i = 560 µA/cm2. Dashed curve, the best-fitting function: 0.506 + 0.085 exp(3.63 C).

Tables (1)

Tables Icon

Table 1 Characteristics of the Obtained Optical Waveguides and the Relevant Fabrication Parametersa

Equations (12)

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

C1t=D1xC0C0-1-MC1C1x.
1-M=1-D1D2=α, C1C0=C1C1+C2=C,
Ct=xD11-αCCx.
Ct=xDCCx,
DC=D11-αC,
Cx, t=0=C0 δx,
Cx, t=0 for x t0.
Cx, t=QπDt1/2exp-x24Dt,
C0, t=QπDt1/2.
D=xe2/4t1,
Q=0 Cx, tdx  0 Δnx, tdx=const.
C=C0, tCmax0, t=Δn0, tΔnmax0, t=ΔnesΔnmax

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