Abstract

Planar glass waveguides fabricated by diffusion of silver ions in soda-lime–silicate glass substrates have been characterized by measuring the wavelength dependence of propagation constants of the guided modes. The results are in good agreement with theoretical prediction obtained by an accurate WKB analysis using a complementary error function for the index profile. Cutoff wavelengths of higher-order modes are larger than were predicted by the analysis and are a result of higher attenuation encountered close to the cutoff.

© 1986 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 (1985).
    [CrossRef]
  2. S. I. Najafi, R. V. Ramaswamy, R. K. Lagu, “An Improved Method for Fabricating Ion-Exchange Waveguides Through Electrolytic Release of Silver Ions,” IEEE/OSA J. Lightwave Technol. LT-3, 763 (1985).
    [CrossRef]
  3. S. I. Najafi, R. V. Ramaswamy, “Ag+-Exchanged Graded-Index Glass Waveguides: Diffusion and Modal Characterization,” paper presented at the Gradient-Index Optical Imaging Systems Conference, Palermo, Italy (Sept.1985).
  4. S. I. Najafi, R. V. Ramaswamy, “Diffusion and Modal Characterization of Ag+-Na+ Exchanged Channel Waveguides,” paper presented at the Integrated and Guided Wave Optics Conference, Atlanta (Feb. 1986).
  5. R. K. Lagu, R. V. Ramaswamy, “Process and Waveguide Parameter Relationships for the Design of Planar Silver Ion-Diffused Glass Waveguides,” IEEE/OSA J. Lightwave Technol. LT-4, 176 (1986).
    [CrossRef]
  6. R. V. Ramaswamy, S. I. Najafi, “Planar, Buried, Ion-Exchanged Glass Waveguides: Diffusion Characteristics,” IEEE J. Quantum Electron., to be published in special issue on Integrated Optics, June1986.
    [CrossRef]
  7. R. Srivastava, C. K. Kao, R. V. Ramaswamy, “An Accurate WKB Analysis of Planar Optical Waveguides,” IEEE/OSA J. Lightwave Technology, in press.
  8. G. L. Yip, J. Albert, “Characterization of Planar Optical Waveguides by K+-Ion Exchange in Glass,” Opt. Lett. 10, 151 (1985).
    [CrossRef] [PubMed]
  9. R. V. Ramaswamy, R. K. Lagu, “Numerical Field Solution for an Arbitrary Asymmetrical Grade-Index Planar Waveguide,” IEEE/OSA J. Lightwave Technol. LT-1, 408 (1983).
    [CrossRef]
  10. W. T. Anderson, T. A. Lenahan, “Length Dependence of the Effective Cutoff Wavelength in Single-Mode Fibers,” IEEE/OSA J. Lightwave Technol. LT-2, 238 (1984).
    [CrossRef]
  11. D. L. Franzen, “Determining the Effective Cutoff Wavelength of Single-Mode Fiber: an Interlaboratory Comparison,” IEEE/OSA J. Lightwave Technol. LT-3, 128 (1985).
    [CrossRef]
  12. K. Thyagarajan, A. Enard, P. Kayoun, D. Papillon, M. Popuchon, “Measurement of Guided Mode Cutoff Wavelengths in Ti:LiNbO3 Channel Waveguides,” in Proceedings, Third European Conference, ECIO '85, Berlin, H. P. Nolting, R. Ulrich, Eds. (Springer-Verlag, New York, 1985), pp. 236–239.

1986 (1)

R. K. Lagu, R. V. Ramaswamy, “Process and Waveguide Parameter Relationships for the Design of Planar Silver Ion-Diffused Glass Waveguides,” IEEE/OSA J. Lightwave Technol. LT-4, 176 (1986).
[CrossRef]

1985 (4)

T. Findakly, “Glass Waveguides by Ion Exchange: A Review,” Opt. Eng. 24, 244 (1985).
[CrossRef]

S. I. Najafi, R. V. Ramaswamy, R. K. Lagu, “An Improved Method for Fabricating Ion-Exchange Waveguides Through Electrolytic Release of Silver Ions,” IEEE/OSA J. Lightwave Technol. LT-3, 763 (1985).
[CrossRef]

D. L. Franzen, “Determining the Effective Cutoff Wavelength of Single-Mode Fiber: an Interlaboratory Comparison,” IEEE/OSA J. Lightwave Technol. LT-3, 128 (1985).
[CrossRef]

G. L. Yip, J. Albert, “Characterization of Planar Optical Waveguides by K+-Ion Exchange in Glass,” Opt. Lett. 10, 151 (1985).
[CrossRef] [PubMed]

1984 (1)

W. T. Anderson, T. A. Lenahan, “Length Dependence of the Effective Cutoff Wavelength in Single-Mode Fibers,” IEEE/OSA J. Lightwave Technol. LT-2, 238 (1984).
[CrossRef]

1983 (1)

R. V. Ramaswamy, R. K. Lagu, “Numerical Field Solution for an Arbitrary Asymmetrical Grade-Index Planar Waveguide,” IEEE/OSA J. Lightwave Technol. LT-1, 408 (1983).
[CrossRef]

Albert, J.

Anderson, W. T.

W. T. Anderson, T. A. Lenahan, “Length Dependence of the Effective Cutoff Wavelength in Single-Mode Fibers,” IEEE/OSA J. Lightwave Technol. LT-2, 238 (1984).
[CrossRef]

Enard, A.

K. Thyagarajan, A. Enard, P. Kayoun, D. Papillon, M. Popuchon, “Measurement of Guided Mode Cutoff Wavelengths in Ti:LiNbO3 Channel Waveguides,” in Proceedings, Third European Conference, ECIO '85, Berlin, H. P. Nolting, R. Ulrich, Eds. (Springer-Verlag, New York, 1985), pp. 236–239.

Findakly, T.

T. Findakly, “Glass Waveguides by Ion Exchange: A Review,” Opt. Eng. 24, 244 (1985).
[CrossRef]

Franzen, D. L.

D. L. Franzen, “Determining the Effective Cutoff Wavelength of Single-Mode Fiber: an Interlaboratory Comparison,” IEEE/OSA J. Lightwave Technol. LT-3, 128 (1985).
[CrossRef]

Kao, C. K.

R. Srivastava, C. K. Kao, R. V. Ramaswamy, “An Accurate WKB Analysis of Planar Optical Waveguides,” IEEE/OSA J. Lightwave Technology, in press.

Kayoun, P.

K. Thyagarajan, A. Enard, P. Kayoun, D. Papillon, M. Popuchon, “Measurement of Guided Mode Cutoff Wavelengths in Ti:LiNbO3 Channel Waveguides,” in Proceedings, Third European Conference, ECIO '85, Berlin, H. P. Nolting, R. Ulrich, Eds. (Springer-Verlag, New York, 1985), pp. 236–239.

Lagu, R. K.

R. K. Lagu, R. V. Ramaswamy, “Process and Waveguide Parameter Relationships for the Design of Planar Silver Ion-Diffused Glass Waveguides,” IEEE/OSA J. Lightwave Technol. LT-4, 176 (1986).
[CrossRef]

S. I. Najafi, R. V. Ramaswamy, R. K. Lagu, “An Improved Method for Fabricating Ion-Exchange Waveguides Through Electrolytic Release of Silver Ions,” IEEE/OSA J. Lightwave Technol. LT-3, 763 (1985).
[CrossRef]

R. V. Ramaswamy, R. K. Lagu, “Numerical Field Solution for an Arbitrary Asymmetrical Grade-Index Planar Waveguide,” IEEE/OSA J. Lightwave Technol. LT-1, 408 (1983).
[CrossRef]

Lenahan, T. A.

W. T. Anderson, T. A. Lenahan, “Length Dependence of the Effective Cutoff Wavelength in Single-Mode Fibers,” IEEE/OSA J. Lightwave Technol. LT-2, 238 (1984).
[CrossRef]

Najafi, S. I.

S. I. Najafi, R. V. Ramaswamy, R. K. Lagu, “An Improved Method for Fabricating Ion-Exchange Waveguides Through Electrolytic Release of Silver Ions,” IEEE/OSA J. Lightwave Technol. LT-3, 763 (1985).
[CrossRef]

S. I. Najafi, R. V. Ramaswamy, “Diffusion and Modal Characterization of Ag+-Na+ Exchanged Channel Waveguides,” paper presented at the Integrated and Guided Wave Optics Conference, Atlanta (Feb. 1986).

S. I. Najafi, R. V. Ramaswamy, “Ag+-Exchanged Graded-Index Glass Waveguides: Diffusion and Modal Characterization,” paper presented at the Gradient-Index Optical Imaging Systems Conference, Palermo, Italy (Sept.1985).

R. V. Ramaswamy, S. I. Najafi, “Planar, Buried, Ion-Exchanged Glass Waveguides: Diffusion Characteristics,” IEEE J. Quantum Electron., to be published in special issue on Integrated Optics, June1986.
[CrossRef]

Papillon, D.

K. Thyagarajan, A. Enard, P. Kayoun, D. Papillon, M. Popuchon, “Measurement of Guided Mode Cutoff Wavelengths in Ti:LiNbO3 Channel Waveguides,” in Proceedings, Third European Conference, ECIO '85, Berlin, H. P. Nolting, R. Ulrich, Eds. (Springer-Verlag, New York, 1985), pp. 236–239.

Popuchon, M.

K. Thyagarajan, A. Enard, P. Kayoun, D. Papillon, M. Popuchon, “Measurement of Guided Mode Cutoff Wavelengths in Ti:LiNbO3 Channel Waveguides,” in Proceedings, Third European Conference, ECIO '85, Berlin, H. P. Nolting, R. Ulrich, Eds. (Springer-Verlag, New York, 1985), pp. 236–239.

Ramaswamy, R. V.

R. K. Lagu, R. V. Ramaswamy, “Process and Waveguide Parameter Relationships for the Design of Planar Silver Ion-Diffused Glass Waveguides,” IEEE/OSA J. Lightwave Technol. LT-4, 176 (1986).
[CrossRef]

S. I. Najafi, R. V. Ramaswamy, R. K. Lagu, “An Improved Method for Fabricating Ion-Exchange Waveguides Through Electrolytic Release of Silver Ions,” IEEE/OSA J. Lightwave Technol. LT-3, 763 (1985).
[CrossRef]

R. V. Ramaswamy, R. K. Lagu, “Numerical Field Solution for an Arbitrary Asymmetrical Grade-Index Planar Waveguide,” IEEE/OSA J. Lightwave Technol. LT-1, 408 (1983).
[CrossRef]

S. I. Najafi, R. V. Ramaswamy, “Diffusion and Modal Characterization of Ag+-Na+ Exchanged Channel Waveguides,” paper presented at the Integrated and Guided Wave Optics Conference, Atlanta (Feb. 1986).

R. Srivastava, C. K. Kao, R. V. Ramaswamy, “An Accurate WKB Analysis of Planar Optical Waveguides,” IEEE/OSA J. Lightwave Technology, in press.

R. V. Ramaswamy, S. I. Najafi, “Planar, Buried, Ion-Exchanged Glass Waveguides: Diffusion Characteristics,” IEEE J. Quantum Electron., to be published in special issue on Integrated Optics, June1986.
[CrossRef]

S. I. Najafi, R. V. Ramaswamy, “Ag+-Exchanged Graded-Index Glass Waveguides: Diffusion and Modal Characterization,” paper presented at the Gradient-Index Optical Imaging Systems Conference, Palermo, Italy (Sept.1985).

Srivastava, R.

R. Srivastava, C. K. Kao, R. V. Ramaswamy, “An Accurate WKB Analysis of Planar Optical Waveguides,” IEEE/OSA J. Lightwave Technology, in press.

Thyagarajan, K.

K. Thyagarajan, A. Enard, P. Kayoun, D. Papillon, M. Popuchon, “Measurement of Guided Mode Cutoff Wavelengths in Ti:LiNbO3 Channel Waveguides,” in Proceedings, Third European Conference, ECIO '85, Berlin, H. P. Nolting, R. Ulrich, Eds. (Springer-Verlag, New York, 1985), pp. 236–239.

Yip, G. L.

IEEE/OSA J. Lightwave Technol. (5)

S. I. Najafi, R. V. Ramaswamy, R. K. Lagu, “An Improved Method for Fabricating Ion-Exchange Waveguides Through Electrolytic Release of Silver Ions,” IEEE/OSA J. Lightwave Technol. LT-3, 763 (1985).
[CrossRef]

R. K. Lagu, R. V. Ramaswamy, “Process and Waveguide Parameter Relationships for the Design of Planar Silver Ion-Diffused Glass Waveguides,” IEEE/OSA J. Lightwave Technol. LT-4, 176 (1986).
[CrossRef]

R. V. Ramaswamy, R. K. Lagu, “Numerical Field Solution for an Arbitrary Asymmetrical Grade-Index Planar Waveguide,” IEEE/OSA J. Lightwave Technol. LT-1, 408 (1983).
[CrossRef]

W. T. Anderson, T. A. Lenahan, “Length Dependence of the Effective Cutoff Wavelength in Single-Mode Fibers,” IEEE/OSA J. Lightwave Technol. LT-2, 238 (1984).
[CrossRef]

D. L. Franzen, “Determining the Effective Cutoff Wavelength of Single-Mode Fiber: an Interlaboratory Comparison,” IEEE/OSA J. Lightwave Technol. LT-3, 128 (1985).
[CrossRef]

Opt. Eng. (1)

T. Findakly, “Glass Waveguides by Ion Exchange: A Review,” Opt. Eng. 24, 244 (1985).
[CrossRef]

Opt. Lett. (1)

Other (5)

K. Thyagarajan, A. Enard, P. Kayoun, D. Papillon, M. Popuchon, “Measurement of Guided Mode Cutoff Wavelengths in Ti:LiNbO3 Channel Waveguides,” in Proceedings, Third European Conference, ECIO '85, Berlin, H. P. Nolting, R. Ulrich, Eds. (Springer-Verlag, New York, 1985), pp. 236–239.

R. V. Ramaswamy, S. I. Najafi, “Planar, Buried, Ion-Exchanged Glass Waveguides: Diffusion Characteristics,” IEEE J. Quantum Electron., to be published in special issue on Integrated Optics, June1986.
[CrossRef]

R. Srivastava, C. K. Kao, R. V. Ramaswamy, “An Accurate WKB Analysis of Planar Optical Waveguides,” IEEE/OSA J. Lightwave Technology, in press.

S. I. Najafi, R. V. Ramaswamy, “Ag+-Exchanged Graded-Index Glass Waveguides: Diffusion and Modal Characterization,” paper presented at the Gradient-Index Optical Imaging Systems Conference, Palermo, Italy (Sept.1985).

S. I. Najafi, R. V. Ramaswamy, “Diffusion and Modal Characterization of Ag+-Na+ Exchanged Channel Waveguides,” paper presented at the Integrated and Guided Wave Optics Conference, Atlanta (Feb. 1986).

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Figures (5)

Fig. 1
Fig. 1

SEM photograph of two waveguides epoxied face to face. The dip between the two waveguides is due to the epoxy.

Fig. 2
Fig. 2

Schematics for measurement of wavelength dependence of the mode index.

Fig. 3
Fig. 3

bV characteristics for the complementary error function profile. The points are the experimental values giving the closest agreement to theory.

Fig. 4
Fig. 4

bV curves for the exponential profile and the experimental data.

Fig. 5
Fig. 5

bV curves for the Gaussian profile. Points show the experimental data.

Equations (14)

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C t = D 2 C x 2 ,
C ( x , t ) = C 0 erfc ( X W 0 ) ,
W 0 = 2 D t ,
erfc ( z ) = 2 π z exp ( α 2 ) d α .
C ( W 0 , t ) = 0.157 C 0 .
n ( x ) = Δ n erfc ( x W 0 ) + n b ,
W 0 Schott W 0 Fisher 1.1
Δ n Schott Δ n Fisher 4.2 .
d 2 E y d x 2 + [ k 0 2 n 2 ( x ) β 2 ] E y = 0
V 0 x t [ f ( x ) b ] 1 / 2 d x = ( m + 3 4 ) π ,
V = k 0 d 2 n b Δ n
b = ( N 2 n b 2 ) / ( 2 n b Δ n ) N n b Δ n .
f ( x ) = n ( x ) n b Δ n .
N = n p sin [ A + sin 1 ( sin i n p ) ] ,

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