Abstract

A systematic study of thermal silver ion exchange used for the fabrication of optical channel waveguides is reported in a single-alkali glass. The diffusion equilibrium and diffusion dynamics are experimentally studied, and the concentration-dependent diffusion coefficients are determined. The relationship between the fabrication conditions, i.e., time, temperature, and melt concentration, and the induced waveguide refractive index profile is established. It is demonstrated that the diffusion equation can be solved, without use of any free parameters, to predict the refractive index profiles of both planar and channel waveguides. A 1.6  cm diameter integrated optic ring resonator, with a propagation loss of 0.1dB/cm, is fabricated in a glass by thermal silver ion exchange. The induced refractive index profile is related to the optical characteristics of the functional device.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  11. H. Wakabayashi, "The relationship between kinetic and thermodynamic properties in mixed alkali glass," J. Non-Cryst. Solids 203, 274-279 (1996).
    [CrossRef]
  12. G. Stewart, C. A. Millar, P. J. R. Laybourn, C. D. W. Wilkinson, and R. M. DelaRue, "Planar optical waveguides formed by silver ion migration in glass," IEEE J. Quantum Electron. QE-13, 192-200 (1977).
    [CrossRef]
  13. G. Stewart and P. J. R. Laybourn, "Fabrication of ion-exchanged optical waveguide from diluted silver nitrate melts," IEEE J. Quantum Electron. QE-14, 930-934 (1978).
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  14. H.-J. Lilienhof, E. Voges, D. Ritter, and B. Pantschew, "Field-induced index profiles of multimode ion-exchanged strip waveguides," IEEE J. Quantum Electron. QE-18, 1877-1883 (1982).
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  30. B. Pantchev and Z. Nikolov, "Characterization of refractive index profiles in silver-sodium ion-exchanged glass waveguides for homogeneous refracting waveguide structures," IEEE J. Quantum Electron. 29, 2459-2465 (1993).
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    [CrossRef]
  32. A. Lupascu, A. Kevorkian, T. Boudet, F. Saint-Andre, D. Persegol, and M. Levy, "Modeling ion exchange in glass with concentration-dependent diffusion coefficients and mobilities," Opt. Eng. 35, 1603-1610 (1996).
    [CrossRef]
  33. A. Lupascu, A. Kevorkian, C. P. Cristescu, and I. M. Popescu, "Local electric fields in optical glasses during field-assisted ionic exchanges," in Proc. SPIE 4068, 26-32 (2000).
    [CrossRef]
  34. J.-E. Broquin, "Ion exchanged integrated devices," in Proc. SPIE 4277, 105-117 (2001).
    [CrossRef]
  35. P. Y. Choo, J. A. Frantz, J. T. A. Carriere, D. L. Mathine, R. K. Kostuk, and N. Peyghambarian, "Measurement and modeling of ion-exchange parameters for IOG-10 glass," Opt. Eng. 42, 2812-2816 (2003).
    [CrossRef]
  36. A. Bradenburg, "Stress in ion-exchanged glass waveguides," J. Lightwave Technol. LT-4, 1580-1593 (1986).
  37. C. De Bernardi, S. Morasca, D. Scarano, A. Camera, and M. Morra, "Compositional and stress-optical effects in glass waveguides: comparison between K-Na and Ag-Na ion exchange," J. Non-Cryst. Solids 119, 195-204 (1990).
    [CrossRef]
  38. R. Araujo, "Colorless glasses containing, ion-exchanged sliver," Appl. Opt. 31, 5221-5224 (1992).
  39. C. Kaps and W. Fliegel, "Sodium/silver ion exchange between a non-bridging oxygen-free boroaluminosilicate glass and nitrate melts," Glastech. Ber. 64, 199-204 (1991).
  40. R. W. Laity, "Fused salt concentration cells with transference. Activity coefficients in the system silver nitrate-sodium nitrate," J. Am. Chem. Soc. 79, 1849-1851 (1957).
    [CrossRef]
  41. R. Goring and M. Rothhardt, "Application of the refracted near-field technique to multimode planar and channel waveguides in glass," J. Opt. Commun. 7, 82-85 (1986).
  42. J. Crank, The Mathematics of Diffusion (Clarendon, 1976), Chap. 7.
  43. W. Beier and G. H. Frischat, "Transport mechanisms in alkali silicate glasses," J. Non-Cryst. Solids 73, 113-133 (1985).
    [CrossRef]
  44. S. A. Poling and S. N. Houde-Walter, "Structural factors in silver-induced relaxation in aluminosilicate glasses," J. Non-Cryst. Solids 293-295, 430-439 (2001).
    [CrossRef]
  45. R. Terai, H. Wakabayashi, and H. Yamanaka, "Haven ratio in mixed alkali glass," J. Non-Cryst. Solids 103, 137-142 (1988).
    [CrossRef]
  46. H. Wakabayashi, "The relationship between kinetic and thermodynamic properties in mixed alkali glass," J. Non-Cryst. Solids 203, 274-279 (1996).
    [CrossRef]
  47. D. E. Day, "Mixed alkali glasses—their properties and uses," J. Non-Cryst. Solids 21, 343-372 (1976).
    [CrossRef]
  48. G. Chartier, P. Collier, A. Guez, P. Jaussaud, and Y. Won, "Graded-index surface or buried waveguides by ion exchange in glass," Appl. Opt. 19, 1092-1095 (1980).
  49. G. Li and K. A. Winick, "Integrated optical ring resonators fabricated by silver ion exchange in glass," in Conference on Lasers & Electro-Optics (Optical Society of America, 2004), paper CWA63.
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  51. T. Tamir, ed., Guided-Wave Optoelectronics (Springer-Verlag, 1988), Chap. 2.

2003

P. Y. Choo, J. A. Frantz, J. T. A. Carriere, D. L. Mathine, R. K. Kostuk, and N. Peyghambarian, "Measurement and modeling of ion-exchange parameters for IOG-10 glass," Opt. Eng. 42, 2812-2816 (2003).
[CrossRef]

2001

J.-E. Broquin, "Ion exchanged integrated devices," in Proc. SPIE 4277, 105-117 (2001).
[CrossRef]

S. A. Poling and S. N. Houde-Walter, "Structural factors in silver-induced relaxation in aluminosilicate glasses," J. Non-Cryst. Solids 293-295, 430-439 (2001).
[CrossRef]

2000

A. Lupascu, A. Kevorkian, C. P. Cristescu, and I. M. Popescu, "Local electric fields in optical glasses during field-assisted ionic exchanges," in Proc. SPIE 4068, 26-32 (2000).
[CrossRef]

1997

B. Messerschmidt, C. H. Hsieh, B. L. McIntyre, and S. N. Houde-Walter, "Ionic mobility in an ion exchanged silver-sodium boroaluminosilicate glass for micro-optics applications," J. Non-Cryst. Solids 217, 264-271 (1997).
[CrossRef]

1996

H. Wakabayashi, "The relationship between kinetic and thermodynamic properties in mixed alkali glass," J. Non-Cryst. Solids 203, 274-279 (1996).
[CrossRef]

A. Lupascu, A. Kevorkian, T. Boudet, F. Saint-Andre, D. Persegol, and M. Levy, "Modeling ion exchange in glass with concentration-dependent diffusion coefficients and mobilities," Opt. Eng. 35, 1603-1610 (1996).
[CrossRef]

H. Wakabayashi, "The relationship between kinetic and thermodynamic properties in mixed alkali glass," J. Non-Cryst. Solids 203, 274-279 (1996).
[CrossRef]

1995

D. G. Ashworth, R. Oven, and M. C. Page, "The influence of the pseudo-mixed-alkali effect on the field-assisted diffusion of silver ions into glass for optical waveguides," J. Phys. D 28, 657-664 (1995).
[CrossRef]

1993

I. G. Voitrnko, V. P. Reko, L. I. Sotskaya, and A. V. Tomov, "Mode interference pattern in ion-exchanged channel waveguides," in Proc. SPIE 1932, 2-13 (1993).
[CrossRef]

B. Pantchev and Z. Nikolov, "Characterization of refractive index profiles in silver-sodium ion-exchanged glass waveguides for homogeneous refracting waveguide structures," IEEE J. Quantum Electron. 29, 2459-2465 (1993).
[CrossRef]

1992

1991

M. C. Page, R. Oven, and D. G. Ashworth, "Scaling rules for glass based planar optical waveguides made by field assisted ion diffusion," Electron. Lett. 27, 2073-2076 (1991).

T. Poszner, G. Schreiter, and R. Muller, "Stripe waveguides with matched refractive index profiles fabricated by ion exchange in glass," J. Appl. Phys. 70, 1966-1974 (1991).
[CrossRef]

C. Kaps and W. Fliegel, "Sodium/silver ion exchange between a non-bridging oxygen-free boroaluminosilicate glass and nitrate melts," Glastech. Ber. 64, 199-204 (1991).

1990

C. De Bernardi, S. Morasca, D. Scarano, A. Camera, and M. Morra, "Compositional and stress-optical effects in glass waveguides: comparison between K-Na and Ag-Na ion exchange," J. Non-Cryst. Solids 119, 195-204 (1990).
[CrossRef]

H. C. Cheng and R. Ramaswamy, "Simulation of tapered transitions in ion-exchanged channel waveguides," Appl. Opt. 29, 1150-1156 (1990).

J. Albert and J. W. Y. Lit, "Full modeling of field-assisted ion exchange for graded index buried channel optical waveguides," Appl. Opt. 29, 2798-2804 (1990).

1989

L. Robeta, "Integrated optical components in substrate glasses," Glastech Ber. 62, 285-297 (1989).

1988

R. Terai, H. Wakabayashi, and H. Yamanaka, "Haven ratio in mixed alkali glass," J. Non-Cryst. Solids 103, 137-142 (1988).
[CrossRef]

R. V. Ramaswamy, R. Srivastava, P. Chludzinski, and J. T. Anderson, "Influence of Ag+-Na+ ion-exchange equilibrium on waveguide index profiles," IEEE J. Quantum Electron. 24, 780-785 (1988).
[CrossRef]

S. Honkanen and A. Tervonen, "Experimental analysis of Ag+-Na+ exchange in glass with Ag film ion sources for planar optical waveguide fabrication," J. Appl. Phys. 63, 634-639 (1988).
[CrossRef]

R. V. Ramaswamy and R. Srivastava, "Recent advances in ion-exchanged optical waveguides and components," J. Mod. Opt. 35, 1049-1067 (1988).

R. V. Ramaswamy and R. Srivastava, "Ion-exchanged glass waveguides: a review," J. Lightwave Technol. 6, 984-1001 (1988).
[CrossRef]

R. V. Ramaswamy, H. C. Cheng, and R. Srivastava, "Process optimization of buried Ag+-Na+ ion-exchange waveguides: theory and experiment," Appl. Opt. 27, 1814-1819 (1988).

1986

R. Lagu and R. Ramaswamy, "Process and waveguide parameter relationships for planar silver ion-exchanged glass waveguides," J. Lightwave Technol. LT-4, 176-181 (1986).

R. V. Ramaswamy and S. I. Najafi, "Planar, buried, ion-exchanged glass waveguides: diffusion characteristics," IEEE J. Quantum Electron. QE-22, 883-891 (1986).
[CrossRef]

R. Goring and M. Rothhardt, "Application of the refracted near-field technique to multimode planar and channel waveguides in glass," J. Opt. Commun. 7, 82-85 (1986).

A. Bradenburg, "Stress in ion-exchanged glass waveguides," J. Lightwave Technol. LT-4, 1580-1593 (1986).

1985

W. Beier and G. H. Frischat, "Transport mechanisms in alkali silicate glasses," J. Non-Cryst. Solids 73, 113-133 (1985).
[CrossRef]

T. Findakly, "Glass waveguides by ion exchange: a review," Opt. Eng. 24, 244-250 (1985).

1983

1982

H.-J. Lilienhof, E. Voges, D. Ritter, and B. Pantschew, "Field-induced index profiles of multimode ion-exchanged strip waveguides," IEEE J. Quantum Electron. QE-18, 1877-1883 (1982).
[CrossRef]

1980

1978

G. Stewart and P. J. R. Laybourn, "Fabrication of ion-exchanged optical waveguide from diluted silver nitrate melts," IEEE J. Quantum Electron. QE-14, 930-934 (1978).
[CrossRef]

1977

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

1976

D. E. Day, "Mixed alkali glasses—their properties and uses," J. Non-Cryst. Solids 21, 343-372 (1976).
[CrossRef]

1972

T. Izawa and H. Nakagome, "Silver ion-exchanged glass waveguides," Appl. Phys. Lett. 21, 584-586 (1972).
[CrossRef]

1968

H. M. Garfinkel, "Ion-exchange equilibria between glass and molten salts," J. Phys. Chem. 72, 4175-4181 (1968).
[CrossRef]

1964

R. H. Doremus, "Exchange and diffusion of ions in glass," J. Phys. Chem. 68, 2212-2218 (1964).

1957

R. W. Laity, "Fused salt concentration cells with transference. Activity coefficients in the system silver nitrate-sodium nitrate," J. Am. Chem. Soc. 79, 1849-1851 (1957).
[CrossRef]

Albert, J.

Anderson, J. T.

R. V. Ramaswamy, R. Srivastava, P. Chludzinski, and J. T. Anderson, "Influence of Ag+-Na+ ion-exchange equilibrium on waveguide index profiles," IEEE J. Quantum Electron. 24, 780-785 (1988).
[CrossRef]

Araujo, R.

Ashworth, D. G.

D. G. Ashworth, R. Oven, and M. C. Page, "The influence of the pseudo-mixed-alkali effect on the field-assisted diffusion of silver ions into glass for optical waveguides," J. Phys. D 28, 657-664 (1995).
[CrossRef]

M. C. Page, R. Oven, and D. G. Ashworth, "Scaling rules for glass based planar optical waveguides made by field assisted ion diffusion," Electron. Lett. 27, 2073-2076 (1991).

Beier, W.

W. Beier and G. H. Frischat, "Transport mechanisms in alkali silicate glasses," J. Non-Cryst. Solids 73, 113-133 (1985).
[CrossRef]

Boudet, T.

A. Lupascu, A. Kevorkian, T. Boudet, F. Saint-Andre, D. Persegol, and M. Levy, "Modeling ion exchange in glass with concentration-dependent diffusion coefficients and mobilities," Opt. Eng. 35, 1603-1610 (1996).
[CrossRef]

Bradenburg, A.

A. Bradenburg, "Stress in ion-exchanged glass waveguides," J. Lightwave Technol. LT-4, 1580-1593 (1986).

Broquin, J.-E.

J.-E. Broquin, "Ion exchanged integrated devices," in Proc. SPIE 4277, 105-117 (2001).
[CrossRef]

Camera, A.

C. De Bernardi, S. Morasca, D. Scarano, A. Camera, and M. Morra, "Compositional and stress-optical effects in glass waveguides: comparison between K-Na and Ag-Na ion exchange," J. Non-Cryst. Solids 119, 195-204 (1990).
[CrossRef]

Carriere, J. T. A.

P. Y. Choo, J. A. Frantz, J. T. A. Carriere, D. L. Mathine, R. K. Kostuk, and N. Peyghambarian, "Measurement and modeling of ion-exchange parameters for IOG-10 glass," Opt. Eng. 42, 2812-2816 (2003).
[CrossRef]

Chartier, G.

Cheng, H. C.

Chludzinski, P.

R. V. Ramaswamy, R. Srivastava, P. Chludzinski, and J. T. Anderson, "Influence of Ag+-Na+ ion-exchange equilibrium on waveguide index profiles," IEEE J. Quantum Electron. 24, 780-785 (1988).
[CrossRef]

Choo, P. Y.

P. Y. Choo, J. A. Frantz, J. T. A. Carriere, D. L. Mathine, R. K. Kostuk, and N. Peyghambarian, "Measurement and modeling of ion-exchange parameters for IOG-10 glass," Opt. Eng. 42, 2812-2816 (2003).
[CrossRef]

Collier, P.

Coutaz, J.-L.

Crank, J.

J. Crank, The Mathematics of Diffusion (Clarendon, 1976), Chap. 7.

Cristescu, C. P.

A. Lupascu, A. Kevorkian, C. P. Cristescu, and I. M. Popescu, "Local electric fields in optical glasses during field-assisted ionic exchanges," in Proc. SPIE 4068, 26-32 (2000).
[CrossRef]

Day, D. E.

D. E. Day, "Mixed alkali glasses—their properties and uses," J. Non-Cryst. Solids 21, 343-372 (1976).
[CrossRef]

De Bernardi, C.

C. De Bernardi, S. Morasca, D. Scarano, A. Camera, and M. Morra, "Compositional and stress-optical effects in glass waveguides: comparison between K-Na and Ag-Na ion exchange," J. Non-Cryst. Solids 119, 195-204 (1990).
[CrossRef]

DelaRue, R. M.

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

Djanta, G.

Doremus, R. H.

R. H. Doremus, "Exchange and diffusion of ions in glass," J. Phys. Chem. 68, 2212-2218 (1964).

R. H. Doremus, Glass Science, 2nd ed. (Wiley, 1994), Chap. 15.

Fabricius, N.

L. Robeta, N. Fabricius, and H. Öeste, "Single mode integrated optical waveguides by ion-exchange in glass," in Proceedings of EFOC/LAN 87 (Information Gatekeepers, 1987), pp. 99-103.

N. Fabricius, H. Öeste, H.-J. Guttmann, H. Quast, and L. Ross, "BGG 31: a new glass for multimode waveguide fabrication," in Proceedings of EFOC/LAN 88 (Information Gatekeepers, 1988), pp. 59-62.

Findakly, T.

T. Findakly, "Glass waveguides by ion exchange: a review," Opt. Eng. 24, 244-250 (1985).

Fliegel, W.

C. Kaps and W. Fliegel, "Sodium/silver ion exchange between a non-bridging oxygen-free boroaluminosilicate glass and nitrate melts," Glastech. Ber. 64, 199-204 (1991).

Frantz, J. A.

P. Y. Choo, J. A. Frantz, J. T. A. Carriere, D. L. Mathine, R. K. Kostuk, and N. Peyghambarian, "Measurement and modeling of ion-exchange parameters for IOG-10 glass," Opt. Eng. 42, 2812-2816 (2003).
[CrossRef]

Frischat, G. H.

W. Beier and G. H. Frischat, "Transport mechanisms in alkali silicate glasses," J. Non-Cryst. Solids 73, 113-133 (1985).
[CrossRef]

Garfinkel, H. M.

H. M. Garfinkel, "Ion-exchange equilibria between glass and molten salts," J. Phys. Chem. 72, 4175-4181 (1968).
[CrossRef]

Goring, R.

R. Goring and M. Rothhardt, "Application of the refracted near-field technique to multimode planar and channel waveguides in glass," J. Opt. Commun. 7, 82-85 (1986).

Guez, A.

Guttmann, H.-J.

N. Fabricius, H. Öeste, H.-J. Guttmann, H. Quast, and L. Ross, "BGG 31: a new glass for multimode waveguide fabrication," in Proceedings of EFOC/LAN 88 (Information Gatekeepers, 1988), pp. 59-62.

Honkanen, S.

S. Honkanen and A. Tervonen, "Experimental analysis of Ag+-Na+ exchange in glass with Ag film ion sources for planar optical waveguide fabrication," J. Appl. Phys. 63, 634-639 (1988).
[CrossRef]

Houde-Walter, S. N.

S. A. Poling and S. N. Houde-Walter, "Structural factors in silver-induced relaxation in aluminosilicate glasses," J. Non-Cryst. Solids 293-295, 430-439 (2001).
[CrossRef]

B. Messerschmidt, C. H. Hsieh, B. L. McIntyre, and S. N. Houde-Walter, "Ionic mobility in an ion exchanged silver-sodium boroaluminosilicate glass for micro-optics applications," J. Non-Cryst. Solids 217, 264-271 (1997).
[CrossRef]

Hsieh, C. H.

B. Messerschmidt, C. H. Hsieh, B. L. McIntyre, and S. N. Houde-Walter, "Ionic mobility in an ion exchanged silver-sodium boroaluminosilicate glass for micro-optics applications," J. Non-Cryst. Solids 217, 264-271 (1997).
[CrossRef]

Izawa, T.

T. Izawa and H. Nakagome, "Silver ion-exchanged glass waveguides," Appl. Phys. Lett. 21, 584-586 (1972).
[CrossRef]

Jaussaud, P.

Johansson, J.

Kaps, C.

C. Kaps and W. Fliegel, "Sodium/silver ion exchange between a non-bridging oxygen-free boroaluminosilicate glass and nitrate melts," Glastech. Ber. 64, 199-204 (1991).

Kevorkian, A.

A. Lupascu, A. Kevorkian, C. P. Cristescu, and I. M. Popescu, "Local electric fields in optical glasses during field-assisted ionic exchanges," in Proc. SPIE 4068, 26-32 (2000).
[CrossRef]

A. Lupascu, A. Kevorkian, T. Boudet, F. Saint-Andre, D. Persegol, and M. Levy, "Modeling ion exchange in glass with concentration-dependent diffusion coefficients and mobilities," Opt. Eng. 35, 1603-1610 (1996).
[CrossRef]

Kostuk, R. K.

P. Y. Choo, J. A. Frantz, J. T. A. Carriere, D. L. Mathine, R. K. Kostuk, and N. Peyghambarian, "Measurement and modeling of ion-exchange parameters for IOG-10 glass," Opt. Eng. 42, 2812-2816 (2003).
[CrossRef]

Lagu, R.

R. Lagu and R. Ramaswamy, "Process and waveguide parameter relationships for planar silver ion-exchanged glass waveguides," J. Lightwave Technol. LT-4, 176-181 (1986).

Laity, R. W.

R. W. Laity, "Fused salt concentration cells with transference. Activity coefficients in the system silver nitrate-sodium nitrate," J. Am. Chem. Soc. 79, 1849-1851 (1957).
[CrossRef]

Laybourn, P. J. R.

G. Stewart and P. J. R. Laybourn, "Fabrication of ion-exchanged optical waveguide from diluted silver nitrate melts," IEEE J. Quantum Electron. QE-14, 930-934 (1978).
[CrossRef]

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

Levy, M.

A. Lupascu, A. Kevorkian, T. Boudet, F. Saint-Andre, D. Persegol, and M. Levy, "Modeling ion exchange in glass with concentration-dependent diffusion coefficients and mobilities," Opt. Eng. 35, 1603-1610 (1996).
[CrossRef]

Li, G.

G. Li and K. A. Winick, "Integrated optical ring resonators fabricated by silver ion exchange in glass," in Conference on Lasers & Electro-Optics (Optical Society of America, 2004), paper CWA63.

Lilienhof, H.-J.

H.-J. Lilienhof, E. Voges, D. Ritter, and B. Pantschew, "Field-induced index profiles of multimode ion-exchanged strip waveguides," IEEE J. Quantum Electron. QE-18, 1877-1883 (1982).
[CrossRef]

Lit, J. W. Y.

Lupascu, A.

A. Lupascu, A. Kevorkian, C. P. Cristescu, and I. M. Popescu, "Local electric fields in optical glasses during field-assisted ionic exchanges," in Proc. SPIE 4068, 26-32 (2000).
[CrossRef]

A. Lupascu, A. Kevorkian, T. Boudet, F. Saint-Andre, D. Persegol, and M. Levy, "Modeling ion exchange in glass with concentration-dependent diffusion coefficients and mobilities," Opt. Eng. 35, 1603-1610 (1996).
[CrossRef]

Mathine, D. L.

P. Y. Choo, J. A. Frantz, J. T. A. Carriere, D. L. Mathine, R. K. Kostuk, and N. Peyghambarian, "Measurement and modeling of ion-exchange parameters for IOG-10 glass," Opt. Eng. 42, 2812-2816 (2003).
[CrossRef]

McIntyre, B. L.

B. Messerschmidt, C. H. Hsieh, B. L. McIntyre, and S. N. Houde-Walter, "Ionic mobility in an ion exchanged silver-sodium boroaluminosilicate glass for micro-optics applications," J. Non-Cryst. Solids 217, 264-271 (1997).
[CrossRef]

Messerschmidt, B.

B. Messerschmidt, C. H. Hsieh, B. L. McIntyre, and S. N. Houde-Walter, "Ionic mobility in an ion exchanged silver-sodium boroaluminosilicate glass for micro-optics applications," J. Non-Cryst. Solids 217, 264-271 (1997).
[CrossRef]

Millar, C. A.

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

Morasca, S.

C. De Bernardi, S. Morasca, D. Scarano, A. Camera, and M. Morra, "Compositional and stress-optical effects in glass waveguides: comparison between K-Na and Ag-Na ion exchange," J. Non-Cryst. Solids 119, 195-204 (1990).
[CrossRef]

Morra, M.

C. De Bernardi, S. Morasca, D. Scarano, A. Camera, and M. Morra, "Compositional and stress-optical effects in glass waveguides: comparison between K-Na and Ag-Na ion exchange," J. Non-Cryst. Solids 119, 195-204 (1990).
[CrossRef]

Muller, R.

T. Poszner, G. Schreiter, and R. Muller, "Stripe waveguides with matched refractive index profiles fabricated by ion exchange in glass," J. Appl. Phys. 70, 1966-1974 (1991).
[CrossRef]

Najafi, S. I.

R. V. Ramaswamy and S. I. Najafi, "Planar, buried, ion-exchanged glass waveguides: diffusion characteristics," IEEE J. Quantum Electron. QE-22, 883-891 (1986).
[CrossRef]

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

Nakagome, H.

T. Izawa and H. Nakagome, "Silver ion-exchanged glass waveguides," Appl. Phys. Lett. 21, 584-586 (1972).
[CrossRef]

Nikolov, Z.

B. Pantchev and Z. Nikolov, "Characterization of refractive index profiles in silver-sodium ion-exchanged glass waveguides for homogeneous refracting waveguide structures," IEEE J. Quantum Electron. 29, 2459-2465 (1993).
[CrossRef]

Öeste, H.

N. Fabricius, H. Öeste, H.-J. Guttmann, H. Quast, and L. Ross, "BGG 31: a new glass for multimode waveguide fabrication," in Proceedings of EFOC/LAN 88 (Information Gatekeepers, 1988), pp. 59-62.

L. Robeta, N. Fabricius, and H. Öeste, "Single mode integrated optical waveguides by ion-exchange in glass," in Proceedings of EFOC/LAN 87 (Information Gatekeepers, 1987), pp. 99-103.

Okamoto, K.

K. Okamoto, Fundamentals of Optical Waveguides (Academic, 2000), Chap. 4.

Oven, R.

D. G. Ashworth, R. Oven, and M. C. Page, "The influence of the pseudo-mixed-alkali effect on the field-assisted diffusion of silver ions into glass for optical waveguides," J. Phys. D 28, 657-664 (1995).
[CrossRef]

M. C. Page, R. Oven, and D. G. Ashworth, "Scaling rules for glass based planar optical waveguides made by field assisted ion diffusion," Electron. Lett. 27, 2073-2076 (1991).

Page, M. C.

D. G. Ashworth, R. Oven, and M. C. Page, "The influence of the pseudo-mixed-alkali effect on the field-assisted diffusion of silver ions into glass for optical waveguides," J. Phys. D 28, 657-664 (1995).
[CrossRef]

M. C. Page, R. Oven, and D. G. Ashworth, "Scaling rules for glass based planar optical waveguides made by field assisted ion diffusion," Electron. Lett. 27, 2073-2076 (1991).

Pantchev, B.

B. Pantchev and Z. Nikolov, "Characterization of refractive index profiles in silver-sodium ion-exchanged glass waveguides for homogeneous refracting waveguide structures," IEEE J. Quantum Electron. 29, 2459-2465 (1993).
[CrossRef]

Pantschew, B.

H.-J. Lilienhof, E. Voges, D. Ritter, and B. Pantschew, "Field-induced index profiles of multimode ion-exchanged strip waveguides," IEEE J. Quantum Electron. QE-18, 1877-1883 (1982).
[CrossRef]

Persegol, D.

A. Lupascu, A. Kevorkian, T. Boudet, F. Saint-Andre, D. Persegol, and M. Levy, "Modeling ion exchange in glass with concentration-dependent diffusion coefficients and mobilities," Opt. Eng. 35, 1603-1610 (1996).
[CrossRef]

Peyghambarian, N.

P. Y. Choo, J. A. Frantz, J. T. A. Carriere, D. L. Mathine, R. K. Kostuk, and N. Peyghambarian, "Measurement and modeling of ion-exchange parameters for IOG-10 glass," Opt. Eng. 42, 2812-2816 (2003).
[CrossRef]

Poling, S. A.

S. A. Poling and S. N. Houde-Walter, "Structural factors in silver-induced relaxation in aluminosilicate glasses," J. Non-Cryst. Solids 293-295, 430-439 (2001).
[CrossRef]

Popescu, I. M.

A. Lupascu, A. Kevorkian, C. P. Cristescu, and I. M. Popescu, "Local electric fields in optical glasses during field-assisted ionic exchanges," in Proc. SPIE 4068, 26-32 (2000).
[CrossRef]

Poszner, T.

T. Poszner, G. Schreiter, and R. Muller, "Stripe waveguides with matched refractive index profiles fabricated by ion exchange in glass," J. Appl. Phys. 70, 1966-1974 (1991).
[CrossRef]

Quast, H.

N. Fabricius, H. Öeste, H.-J. Guttmann, H. Quast, and L. Ross, "BGG 31: a new glass for multimode waveguide fabrication," in Proceedings of EFOC/LAN 88 (Information Gatekeepers, 1988), pp. 59-62.

Ramaswamy, R.

H. C. Cheng and R. Ramaswamy, "Simulation of tapered transitions in ion-exchanged channel waveguides," Appl. Opt. 29, 1150-1156 (1990).

R. Lagu and R. Ramaswamy, "Process and waveguide parameter relationships for planar silver ion-exchanged glass waveguides," J. Lightwave Technol. LT-4, 176-181 (1986).

Ramaswamy, R. V.

R. V. Ramaswamy, H. C. Cheng, and R. Srivastava, "Process optimization of buried Ag+-Na+ ion-exchange waveguides: theory and experiment," Appl. Opt. 27, 1814-1819 (1988).

R. V. Ramaswamy and R. Srivastava, "Ion-exchanged glass waveguides: a review," J. Lightwave Technol. 6, 984-1001 (1988).
[CrossRef]

R. V. Ramaswamy and R. Srivastava, "Recent advances in ion-exchanged optical waveguides and components," J. Mod. Opt. 35, 1049-1067 (1988).

R. V. Ramaswamy, R. Srivastava, P. Chludzinski, and J. T. Anderson, "Influence of Ag+-Na+ ion-exchange equilibrium on waveguide index profiles," IEEE J. Quantum Electron. 24, 780-785 (1988).
[CrossRef]

R. V. Ramaswamy and S. I. Najafi, "Planar, buried, ion-exchanged glass waveguides: diffusion characteristics," IEEE J. Quantum Electron. QE-22, 883-891 (1986).
[CrossRef]

Reko, V. P.

I. G. Voitrnko, V. P. Reko, L. I. Sotskaya, and A. V. Tomov, "Mode interference pattern in ion-exchanged channel waveguides," in Proc. SPIE 1932, 2-13 (1993).
[CrossRef]

Ritter, D.

H.-J. Lilienhof, E. Voges, D. Ritter, and B. Pantschew, "Field-induced index profiles of multimode ion-exchanged strip waveguides," IEEE J. Quantum Electron. QE-18, 1877-1883 (1982).
[CrossRef]

Robeta, L.

L. Robeta, "Integrated optical components in substrate glasses," Glastech Ber. 62, 285-297 (1989).

L. Robeta, N. Fabricius, and H. Öeste, "Single mode integrated optical waveguides by ion-exchange in glass," in Proceedings of EFOC/LAN 87 (Information Gatekeepers, 1987), pp. 99-103.

Ross, L.

N. Fabricius, H. Öeste, H.-J. Guttmann, H. Quast, and L. Ross, "BGG 31: a new glass for multimode waveguide fabrication," in Proceedings of EFOC/LAN 88 (Information Gatekeepers, 1988), pp. 59-62.

Rothhardt, M.

R. Goring and M. Rothhardt, "Application of the refracted near-field technique to multimode planar and channel waveguides in glass," J. Opt. Commun. 7, 82-85 (1986).

Saint-Andre, F.

A. Lupascu, A. Kevorkian, T. Boudet, F. Saint-Andre, D. Persegol, and M. Levy, "Modeling ion exchange in glass with concentration-dependent diffusion coefficients and mobilities," Opt. Eng. 35, 1603-1610 (1996).
[CrossRef]

Scarano, D.

C. De Bernardi, S. Morasca, D. Scarano, A. Camera, and M. Morra, "Compositional and stress-optical effects in glass waveguides: comparison between K-Na and Ag-Na ion exchange," J. Non-Cryst. Solids 119, 195-204 (1990).
[CrossRef]

Schreiter, G.

T. Poszner, G. Schreiter, and R. Muller, "Stripe waveguides with matched refractive index profiles fabricated by ion exchange in glass," J. Appl. Phys. 70, 1966-1974 (1991).
[CrossRef]

Shewmon, P.

P. Shewmon, Diffusion in Solids, 2nd ed. (The Minerals, Metals and Materials Society, 1989).

Sotskaya, L. I.

I. G. Voitrnko, V. P. Reko, L. I. Sotskaya, and A. V. Tomov, "Mode interference pattern in ion-exchanged channel waveguides," in Proc. SPIE 1932, 2-13 (1993).
[CrossRef]

Srivastava, R.

R. V. Ramaswamy, R. Srivastava, P. Chludzinski, and J. T. Anderson, "Influence of Ag+-Na+ ion-exchange equilibrium on waveguide index profiles," IEEE J. Quantum Electron. 24, 780-785 (1988).
[CrossRef]

R. V. Ramaswamy and R. Srivastava, "Recent advances in ion-exchanged optical waveguides and components," J. Mod. Opt. 35, 1049-1067 (1988).

R. V. Ramaswamy and R. Srivastava, "Ion-exchanged glass waveguides: a review," J. Lightwave Technol. 6, 984-1001 (1988).
[CrossRef]

R. V. Ramaswamy, H. C. Cheng, and R. Srivastava, "Process optimization of buried Ag+-Na+ ion-exchange waveguides: theory and experiment," Appl. Opt. 27, 1814-1819 (1988).

Stewart, G.

G. Stewart and P. J. R. Laybourn, "Fabrication of ion-exchanged optical waveguide from diluted silver nitrate melts," IEEE J. Quantum Electron. QE-14, 930-934 (1978).
[CrossRef]

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

Tamir, T.

T. Tamir, ed., Guided-Wave Optoelectronics (Springer-Verlag, 1988), Chap. 2.

Terai, R.

R. Terai, H. Wakabayashi, and H. Yamanaka, "Haven ratio in mixed alkali glass," J. Non-Cryst. Solids 103, 137-142 (1988).
[CrossRef]

Tervonen, A.

S. Honkanen and A. Tervonen, "Experimental analysis of Ag+-Na+ exchange in glass with Ag film ion sources for planar optical waveguide fabrication," J. Appl. Phys. 63, 634-639 (1988).
[CrossRef]

Tomov, A. V.

I. G. Voitrnko, V. P. Reko, L. I. Sotskaya, and A. V. Tomov, "Mode interference pattern in ion-exchanged channel waveguides," in Proc. SPIE 1932, 2-13 (1993).
[CrossRef]

Voges, E.

H.-J. Lilienhof, E. Voges, D. Ritter, and B. Pantschew, "Field-induced index profiles of multimode ion-exchanged strip waveguides," IEEE J. Quantum Electron. QE-18, 1877-1883 (1982).
[CrossRef]

Voitrnko, I. G.

I. G. Voitrnko, V. P. Reko, L. I. Sotskaya, and A. V. Tomov, "Mode interference pattern in ion-exchanged channel waveguides," in Proc. SPIE 1932, 2-13 (1993).
[CrossRef]

Wakabayashi, H.

H. Wakabayashi, "The relationship between kinetic and thermodynamic properties in mixed alkali glass," J. Non-Cryst. Solids 203, 274-279 (1996).
[CrossRef]

H. Wakabayashi, "The relationship between kinetic and thermodynamic properties in mixed alkali glass," J. Non-Cryst. Solids 203, 274-279 (1996).
[CrossRef]

R. Terai, H. Wakabayashi, and H. Yamanaka, "Haven ratio in mixed alkali glass," J. Non-Cryst. Solids 103, 137-142 (1988).
[CrossRef]

Walker, R. G.

Wilkinson, C. D. W.

R. G. Walker, C. D. W. Wilkinson, and J. A. H. Wilkinson, "Integrated optical waveguiding structures made by silver ion-exchange in glass. 1: The propagation characteristics of stripe ion-exchanged waveguides: a theoretical and experimental investigation," Appl. Opt. 22, 1923-1928 (1983).

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

Wilkinson, J. A. H.

Winick, K. A.

G. Li and K. A. Winick, "Integrated optical ring resonators fabricated by silver ion exchange in glass," in Conference on Lasers & Electro-Optics (Optical Society of America, 2004), paper CWA63.

Won, Y.

Yamanaka, H.

R. Terai, H. Wakabayashi, and H. Yamanaka, "Haven ratio in mixed alkali glass," J. Non-Cryst. Solids 103, 137-142 (1988).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

T. Izawa and H. Nakagome, "Silver ion-exchanged glass waveguides," Appl. Phys. Lett. 21, 584-586 (1972).
[CrossRef]

Electron. Lett.

M. C. Page, R. Oven, and D. G. Ashworth, "Scaling rules for glass based planar optical waveguides made by field assisted ion diffusion," Electron. Lett. 27, 2073-2076 (1991).

Glastech Ber.

L. Robeta, "Integrated optical components in substrate glasses," Glastech Ber. 62, 285-297 (1989).

Glastech. Ber.

C. Kaps and W. Fliegel, "Sodium/silver ion exchange between a non-bridging oxygen-free boroaluminosilicate glass and nitrate melts," Glastech. Ber. 64, 199-204 (1991).

IEEE J. Quantum Electron.

R. V. Ramaswamy, R. Srivastava, P. Chludzinski, and J. T. Anderson, "Influence of Ag+-Na+ ion-exchange equilibrium on waveguide index profiles," IEEE J. Quantum Electron. 24, 780-785 (1988).
[CrossRef]

B. Pantchev and Z. Nikolov, "Characterization of refractive index profiles in silver-sodium ion-exchanged glass waveguides for homogeneous refracting waveguide structures," IEEE J. Quantum Electron. 29, 2459-2465 (1993).
[CrossRef]

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

G. Stewart and P. J. R. Laybourn, "Fabrication of ion-exchanged optical waveguide from diluted silver nitrate melts," IEEE J. Quantum Electron. QE-14, 930-934 (1978).
[CrossRef]

H.-J. Lilienhof, E. Voges, D. Ritter, and B. Pantschew, "Field-induced index profiles of multimode ion-exchanged strip waveguides," IEEE J. Quantum Electron. QE-18, 1877-1883 (1982).
[CrossRef]

R. V. Ramaswamy and S. I. Najafi, "Planar, buried, ion-exchanged glass waveguides: diffusion characteristics," IEEE J. Quantum Electron. QE-22, 883-891 (1986).
[CrossRef]

J. Am. Chem. Soc.

R. W. Laity, "Fused salt concentration cells with transference. Activity coefficients in the system silver nitrate-sodium nitrate," J. Am. Chem. Soc. 79, 1849-1851 (1957).
[CrossRef]

J. Appl. Phys.

S. Honkanen and A. Tervonen, "Experimental analysis of Ag+-Na+ exchange in glass with Ag film ion sources for planar optical waveguide fabrication," J. Appl. Phys. 63, 634-639 (1988).
[CrossRef]

T. Poszner, G. Schreiter, and R. Muller, "Stripe waveguides with matched refractive index profiles fabricated by ion exchange in glass," J. Appl. Phys. 70, 1966-1974 (1991).
[CrossRef]

J. Lightwave Technol.

A. Bradenburg, "Stress in ion-exchanged glass waveguides," J. Lightwave Technol. LT-4, 1580-1593 (1986).

R. Lagu and R. Ramaswamy, "Process and waveguide parameter relationships for planar silver ion-exchanged glass waveguides," J. Lightwave Technol. LT-4, 176-181 (1986).

R. V. Ramaswamy and R. Srivastava, "Ion-exchanged glass waveguides: a review," J. Lightwave Technol. 6, 984-1001 (1988).
[CrossRef]

J. Mod. Opt.

R. V. Ramaswamy and R. Srivastava, "Recent advances in ion-exchanged optical waveguides and components," J. Mod. Opt. 35, 1049-1067 (1988).

J. Non-Cryst. Solids

B. Messerschmidt, C. H. Hsieh, B. L. McIntyre, and S. N. Houde-Walter, "Ionic mobility in an ion exchanged silver-sodium boroaluminosilicate glass for micro-optics applications," J. Non-Cryst. Solids 217, 264-271 (1997).
[CrossRef]

H. Wakabayashi, "The relationship between kinetic and thermodynamic properties in mixed alkali glass," J. Non-Cryst. Solids 203, 274-279 (1996).
[CrossRef]

W. Beier and G. H. Frischat, "Transport mechanisms in alkali silicate glasses," J. Non-Cryst. Solids 73, 113-133 (1985).
[CrossRef]

S. A. Poling and S. N. Houde-Walter, "Structural factors in silver-induced relaxation in aluminosilicate glasses," J. Non-Cryst. Solids 293-295, 430-439 (2001).
[CrossRef]

R. Terai, H. Wakabayashi, and H. Yamanaka, "Haven ratio in mixed alkali glass," J. Non-Cryst. Solids 103, 137-142 (1988).
[CrossRef]

H. Wakabayashi, "The relationship between kinetic and thermodynamic properties in mixed alkali glass," J. Non-Cryst. Solids 203, 274-279 (1996).
[CrossRef]

D. E. Day, "Mixed alkali glasses—their properties and uses," J. Non-Cryst. Solids 21, 343-372 (1976).
[CrossRef]

C. De Bernardi, S. Morasca, D. Scarano, A. Camera, and M. Morra, "Compositional and stress-optical effects in glass waveguides: comparison between K-Na and Ag-Na ion exchange," J. Non-Cryst. Solids 119, 195-204 (1990).
[CrossRef]

J. Opt. Commun.

R. Goring and M. Rothhardt, "Application of the refracted near-field technique to multimode planar and channel waveguides in glass," J. Opt. Commun. 7, 82-85 (1986).

J. Phys. Chem.

H. M. Garfinkel, "Ion-exchange equilibria between glass and molten salts," J. Phys. Chem. 72, 4175-4181 (1968).
[CrossRef]

R. H. Doremus, "Exchange and diffusion of ions in glass," J. Phys. Chem. 68, 2212-2218 (1964).

J. Phys. D

D. G. Ashworth, R. Oven, and M. C. Page, "The influence of the pseudo-mixed-alkali effect on the field-assisted diffusion of silver ions into glass for optical waveguides," J. Phys. D 28, 657-664 (1995).
[CrossRef]

Opt. Eng.

A. Lupascu, A. Kevorkian, T. Boudet, F. Saint-Andre, D. Persegol, and M. Levy, "Modeling ion exchange in glass with concentration-dependent diffusion coefficients and mobilities," Opt. Eng. 35, 1603-1610 (1996).
[CrossRef]

T. Findakly, "Glass waveguides by ion exchange: a review," Opt. Eng. 24, 244-250 (1985).

P. Y. Choo, J. A. Frantz, J. T. A. Carriere, D. L. Mathine, R. K. Kostuk, and N. Peyghambarian, "Measurement and modeling of ion-exchange parameters for IOG-10 glass," Opt. Eng. 42, 2812-2816 (2003).
[CrossRef]

Proc. SPIE

A. Lupascu, A. Kevorkian, C. P. Cristescu, and I. M. Popescu, "Local electric fields in optical glasses during field-assisted ionic exchanges," in Proc. SPIE 4068, 26-32 (2000).
[CrossRef]

J.-E. Broquin, "Ion exchanged integrated devices," in Proc. SPIE 4277, 105-117 (2001).
[CrossRef]

I. G. Voitrnko, V. P. Reko, L. I. Sotskaya, and A. V. Tomov, "Mode interference pattern in ion-exchanged channel waveguides," in Proc. SPIE 1932, 2-13 (1993).
[CrossRef]

Other

N. Fabricius, H. Öeste, H.-J. Guttmann, H. Quast, and L. Ross, "BGG 31: a new glass for multimode waveguide fabrication," in Proceedings of EFOC/LAN 88 (Information Gatekeepers, 1988), pp. 59-62.

J. Crank, The Mathematics of Diffusion (Clarendon, 1976), Chap. 7.

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

P. Shewmon, Diffusion in Solids, 2nd ed. (The Minerals, Metals and Materials Society, 1989).

R. H. Doremus, Glass Science, 2nd ed. (Wiley, 1994), Chap. 15.

L. Robeta, N. Fabricius, and H. Öeste, "Single mode integrated optical waveguides by ion-exchange in glass," in Proceedings of EFOC/LAN 87 (Information Gatekeepers, 1987), pp. 99-103.

G. Li and K. A. Winick, "Integrated optical ring resonators fabricated by silver ion exchange in glass," in Conference on Lasers & Electro-Optics (Optical Society of America, 2004), paper CWA63.

K. Okamoto, Fundamentals of Optical Waveguides (Academic, 2000), Chap. 4.

T. Tamir, ed., Guided-Wave Optoelectronics (Springer-Verlag, 1988), Chap. 2.

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Figures (17)

Fig. 1
Fig. 1

XPS-measured oxygen spectrum of IEG. Gaussian fits give the BO and NBO contents.

Fig. 2
Fig. 2

Ion exchange equilibrium study at 320 °C in IEG.

Fig. 3
Fig. 3

Surface index change in IEG at 658 nm versus mole fraction of AgNO3 in the melt at 320 °C.

Fig. 4
Fig. 4

Linear dependence of surface index change (Δn surf) at 658 nm with the silver concentration at the glass surface [c Ag(0)].

Fig. 5
Fig. 5

Measured Ag+ and Δn diffusion profiles in IEG obtained by the EDX, BSE, and RNF methods for a 9 h exchange at 320 °C using a 10 mol.% silver nitrate melt.

Fig. 6
Fig. 6

Interdiffusion coefficient in IEG at 320 °C derived from a curve-fit RNF profile using the Boltzmann–Matano relation.

Fig. 7
Fig. 7

Na-22 diffusion profile in IEG glass sample 3 with 85% of the Na in the virgin glass replaced by Ag. The diffusion was performed at 320 °C for 60 min.

Fig. 8
Fig. 8

Effective indices of planar waveguide fabricated in 1 mol.% AgNO3 at 320 °C for 4 h comparison of the prism coupler measured data with FDM-calculated data at 1.55 μm with α = 0.847.

Fig. 9
Fig. 9

Dispersion of IEG substrate and ion-exchanged planar waveguide fabricated at 320 °C for 4 h using 1 mol.% AgNO3.

Fig. 10
Fig. 10

Comparison of the modeled diffusion profile with the experimental results for planar waveguides.

Fig. 11
Fig. 11

Comparison of the computed diffusion profile with measured results for channel waveguides fabricated under different conditions. The inner contours in each of the two graphs correspond to Δn = 0.9Δn surf, while each succeeding contour line represents an additional change of the refractive index in decrements of 0.1Δn surf.

Fig. 12
Fig. 12

Illustration of the ring resonators: (a) single-arm ring resonator, (b) dual-arm ring resonator.

Fig. 13
Fig. 13

Photograph of a dual-arm ring resonator illuminated at 632.8 nm.

Fig. 14
Fig. 14

Measured spectral response of ring resonators with a 1.6 cm diameter: (a) single-arm ring resonator with center-to-center coupler spacing of 10.5 μm, (b) dual-arm ring resonator with center-to-center coupler spacing of 11.5 μm.

Fig. 15
Fig. 15

RNF measurement of the channel waveguide index profile for a minimum loss device.

Fig. 16
Fig. 16

Comparison of the measured and CMT-predicted coupling ratios.

Fig. 17
Fig. 17

Comparison of mode field profiles for (a) the waveguide shown in Fig. 15 and (b) a standard SMF-28 optical fiber.

Tables (4)

Tables Icon

Table 1 Glass Composition

Tables Icon

Table 2 X-Ray Photoelectron Spectroscopy Results for Nonbridging Oxygen Analysis

Tables Icon

Table 3 Silver and Sodium Tracer Diffusion Coefficient at 320 °C

Tables Icon

Table 4 Waveguide Annealing Results for 1.6 cm Diameter Ring with a Coupler Waveguide Spacing of 10.5 μm

Equations (44)

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

ln ( m Ag m Na ) E R T ( 1 2 m Na ) = n ln ( c Ag c Na ) ln K ,
C Ag t = · ( D ˜ C Ag ) ,
C Na = C 0 C Ag ,
c Ag C Ag C 0 , c Na C Na C 0 .
{ c Ag = c Ag ( x = 0 ) , x = 0 , t > 0 c Ag = 0 , x > 0 , t = 0 .
η x t ,
η 2 d c Ag d η = d d η ( D ˜ d c Ag d η ) ,
{ c Ag = c Ag ( x = 0 ) , η = 0 c Ag = 0 , η = .
D ˜ ( c Ag ) = 1 2 t f d x ( c Ag ) d c Ag | c Ag = c Ag 0 c Ag x ( c Ag ) d c Ag
ε i = ε i     ( 0 ) + R T ln ( γ i C 0 c i V i ) ,
ν ¯ i = a i ε i ,
J ¯ i = C 0 c i ν ¯ i = a i R T C 0 ( c i ) ξ i ,
ξ i 1 + d ln γ i d ln c i .
J ¯ i = D i * ξ i C 0 c i + e E ¯ int u i C 0 c i ,
D i * a i R T .
J ¯ Ag + J ¯ Na = 0 ,
c Ag + c Na = 1 ,
E ¯ int = ( D Ag * ξ Ag D Na * ξ Na ) e ( μ Ag c Ag + μ Na c Na ) c Ag .
d ( C 0 c i ) d t = · J ¯ i
d c Ag d t = ( D Ag * ξ Ag c Ag ) + [ μ Ag   c Ag ( D Na * ξ Na D Ag * ξ Ag μ Ag c Ag + μ Na c Na ) c Ag ] .
D i * = k T e    μ i .
D i * = H i k T e μ i ,
ξ Ag = ξ Na .
H Ag = H Na ,
d c Ag d t = ( D ˜ c Ag ) ,
D ˜ = D Ag * D Na * D Ag * c Ag + D Na * c Na ( 1 + d   ln   γ Ag d   ln   c Ag ) .
c i ( x , t ) = c 0     ( i ) π D i * t exp ( x 2 4 D i * t ) ,
c i 0   as   t , for    x > 0 ,
c i   as   t 0 , for    x = 0 ,
0 c i ( x , t ) d x = c 0   ( i ) , for all t .
Δ n ( x ) = α ( λ ) c Ag ( x ) ,
c Ag = c surf a t x = 0 for all t ,
c Ag = 0  for  x > 0 at t = 0 ,
c Ag ( x , t ) = c surf   erfc ( x / 2 D ˜ t ) ,
erfc ( z ) 2 π z exp ( - t 2 ) d t .
c Ag = c surf a t     x = 0 , | y | w , t 0 ,
c Ag = 0  for    x > 0 , t = 0, and all y ,
c Ag x | x = 0 = 0 for | y | > w , t 0 ,
T r ( ϕ ) I out I in = | ( 1 Γ ) 1 / 2 y x exp ( j ϕ ) 1 x y exp ( j ϕ ) | 2 ,
x ( 1 Γ ) 1 / 2 exp ( α L / 2 ) = exp { [ α ln ( 1 Γ ) L ] L 2 } ,
y 1 K c ,
ϕ = 2 π λ N eff L ,
F 2 π Δϕ FWHM = π cos 1 ( 2 x y 1 + x 2 y 2 ) ,
D p T max T min T max = 4 x y ( 1 + x 2 y 2 x 2 y 2 ) ( 1 x y ) 2 ( x + y ) 2 ,

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