Abstract

Tapered transitions in the ion-exchanged glass waveguide are modeled to predict the index profile, propagation constant, and modal field along the taper. Results are in excellent agreement with the experimental data in Ag+–Na+ exchanged tapers fabricated by a two-step process in BK7 glass.

© 1990 Optical Society of America

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References

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  1. P. G. Suchoski, R. V. Ramaswamy, “Constant-Width Variable Index Transition for Efficient Ti:LiNbO3 Waveguide-Fiber Coupling,” IEEE/OSA J. Lightwave Technol. LT-5, 1246–1251 (1987).
    [CrossRef]
  2. P. G. Suchoski, R. V. Ramaswamy, “An Exact Numerical Technique for the Analysis of Step Discontinuities and Tapers in Optical Dielectric Waveguides,” J. Opt. Soc. Am. A 3, 194–203 (1986).
    [CrossRef]
  3. A. Mahapatra, J. M. Connors, “Thermal Tapering of Ion-Exchanged Channel Guides in Glass,” in Technical Digest, Conference on Integrated and Guided Wave Optics, Santa Fe, NM (1988), paper MF13.
  4. H. Zhenguang, R. Srivastava, R. V. Ramaswamy, “Low-Loss Small-Mode Passive Waveguides and Near-Adiabatic Tapers in BK7 Glass,” IEEE/OSA J. Lightwave Technol. LT-7, 1590–1596 (1989).
    [CrossRef]
  5. 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-Exchanged Waveguides; a Theoretical and Experimental Investigation,” Appl. Opt. 22, 1923–1928 (1983).
    [CrossRef] [PubMed]
  6. A. Brandenburg, “Stress in Ion-Exchanged Glass Waveguides,” IEEE/OSA J. Lightwave Technol. LT-4, 1580–1593 (1986).
    [CrossRef]
  7. H. C. Cheng, R. V. Ramaswamy, “Simulation of the Radiation Loss of Postbaked Ion-Exchanged Thermal Tapers by BPM,” in Technical Digest, MOC/GRIN, Tokyo (1989), paper B2.
  8. R. V. Ramaswamy, R. Srivastava, “Ion-Exchanged Glass Waveguides: A Review,” IEEE/OSA J. Lightwave Technol. LT-6, 984–1002 (1988).
    [CrossRef]
  9. H. M. Garfinkel, “Ion-Exchange Equilibria Between Glass and Molten Salts,” J. Phys. Chem. 72, 4175–4181(1968).
    [CrossRef]
  10. 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. QE-24, 780–786 (1988).
    [CrossRef]
  11. R. H. Doremus, “Exchange and Diffusion of Ions in Glass,” J. Phys. Chem. 68, 2212–2218 (1964).
    [CrossRef]
  12. R. Srivastava, H. Zhenguang, R. V. Ramaswamy, “Effect of Annealing on Diffused Channel Waveguides,” Appl. Opt. 29, 330–331 (1990).
    [CrossRef] [PubMed]
  13. J. Crank, The Mathematics of Diffusion (Clarendon, Oxford, 1956).
  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. R. G. Eguchi, E. A. Maunders, I. K. Naik, “Fabrication of Low-Loss Waveguides in BK7 by Ion-Exchange,” Proc. Soc. Photo-Opt. Instrum. Eng. 408, 21–26 (1983).
  16. R. V. Ramaswamy, S. I. Najafi, “Planar, Buried, Ion-Exchanged Glass Waveguides: Diffusion Characteristics,” IEEE J. Quantum Electron. QE-22, 883–891 (1986).
    [CrossRef]
  17. M. S. Stern, “Title,” IEE Proc. 135-J, 56 (1988).

1990

1989

H. Zhenguang, R. Srivastava, R. V. Ramaswamy, “Low-Loss Small-Mode Passive Waveguides and Near-Adiabatic Tapers in BK7 Glass,” IEEE/OSA J. Lightwave Technol. LT-7, 1590–1596 (1989).
[CrossRef]

1988

R. V. Ramaswamy, R. Srivastava, “Ion-Exchanged Glass Waveguides: A Review,” IEEE/OSA J. Lightwave Technol. LT-6, 984–1002 (1988).
[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. QE-24, 780–786 (1988).
[CrossRef]

M. S. Stern, “Title,” IEE Proc. 135-J, 56 (1988).

1987

P. G. Suchoski, R. V. Ramaswamy, “Constant-Width Variable Index Transition for Efficient Ti:LiNbO3 Waveguide-Fiber Coupling,” IEEE/OSA J. Lightwave Technol. LT-5, 1246–1251 (1987).
[CrossRef]

1986

P. G. Suchoski, R. V. Ramaswamy, “An Exact Numerical Technique for the Analysis of Step Discontinuities and Tapers in Optical Dielectric Waveguides,” J. Opt. Soc. Am. A 3, 194–203 (1986).
[CrossRef]

R. V. Ramaswamy, S. I. Najafi, “Planar, Buried, Ion-Exchanged Glass Waveguides: Diffusion Characteristics,” IEEE J. Quantum Electron. QE-22, 883–891 (1986).
[CrossRef]

A. Brandenburg, “Stress in Ion-Exchanged Glass Waveguides,” IEEE/OSA J. Lightwave Technol. LT-4, 1580–1593 (1986).
[CrossRef]

1983

1976

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).
[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. QE-24, 780–786 (1988).
[CrossRef]

Brandenburg, A.

A. Brandenburg, “Stress in Ion-Exchanged Glass Waveguides,” IEEE/OSA J. Lightwave Technol. LT-4, 1580–1593 (1986).
[CrossRef]

Cheng, H. C.

H. C. Cheng, R. V. Ramaswamy, “Simulation of the Radiation Loss of Postbaked Ion-Exchanged Thermal Tapers by BPM,” in Technical Digest, MOC/GRIN, Tokyo (1989), paper B2.

Chludzinski, P.

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. QE-24, 780–786 (1988).
[CrossRef]

Connors, J. M.

A. Mahapatra, J. M. Connors, “Thermal Tapering of Ion-Exchanged Channel Guides in Glass,” in Technical Digest, Conference on Integrated and Guided Wave Optics, Santa Fe, NM (1988), paper MF13.

Crank, J.

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

Doremus, R. H.

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

Eguchi, R. G.

R. G. Eguchi, E. A. Maunders, I. K. Naik, “Fabrication of Low-Loss Waveguides in BK7 by Ion-Exchange,” Proc. Soc. Photo-Opt. Instrum. Eng. 408, 21–26 (1983).

Garfinkel, H. M.

H. M. Garfinkel, “Ion-Exchange Equilibria Between Glass and Molten Salts,” J. Phys. Chem. 72, 4175–4181(1968).
[CrossRef]

Heidrich, P. F.

Mahapatra, A.

A. Mahapatra, J. M. Connors, “Thermal Tapering of Ion-Exchanged Channel Guides in Glass,” in Technical Digest, Conference on Integrated and Guided Wave Optics, Santa Fe, NM (1988), paper MF13.

Maunders, E. A.

R. G. Eguchi, E. A. Maunders, I. K. Naik, “Fabrication of Low-Loss Waveguides in BK7 by Ion-Exchange,” Proc. Soc. Photo-Opt. Instrum. Eng. 408, 21–26 (1983).

Naik, I. K.

R. G. Eguchi, E. A. Maunders, I. K. Naik, “Fabrication of Low-Loss Waveguides in BK7 by Ion-Exchange,” Proc. Soc. Photo-Opt. Instrum. Eng. 408, 21–26 (1983).

Najafi, S. I.

R. V. Ramaswamy, S. I. Najafi, “Planar, Buried, Ion-Exchanged Glass Waveguides: Diffusion Characteristics,” IEEE J. Quantum Electron. QE-22, 883–891 (1986).
[CrossRef]

Ramaswamy, R. V.

R. Srivastava, H. Zhenguang, R. V. Ramaswamy, “Effect of Annealing on Diffused Channel Waveguides,” Appl. Opt. 29, 330–331 (1990).
[CrossRef] [PubMed]

H. Zhenguang, R. Srivastava, R. V. Ramaswamy, “Low-Loss Small-Mode Passive Waveguides and Near-Adiabatic Tapers in BK7 Glass,” IEEE/OSA J. Lightwave Technol. LT-7, 1590–1596 (1989).
[CrossRef]

R. V. Ramaswamy, R. Srivastava, “Ion-Exchanged Glass Waveguides: A Review,” IEEE/OSA J. Lightwave Technol. LT-6, 984–1002 (1988).
[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. QE-24, 780–786 (1988).
[CrossRef]

P. G. Suchoski, R. V. Ramaswamy, “Constant-Width Variable Index Transition for Efficient Ti:LiNbO3 Waveguide-Fiber Coupling,” IEEE/OSA J. Lightwave Technol. LT-5, 1246–1251 (1987).
[CrossRef]

P. G. Suchoski, R. V. Ramaswamy, “An Exact Numerical Technique for the Analysis of Step Discontinuities and Tapers in Optical Dielectric Waveguides,” J. Opt. Soc. Am. A 3, 194–203 (1986).
[CrossRef]

R. V. Ramaswamy, S. I. Najafi, “Planar, Buried, Ion-Exchanged Glass Waveguides: Diffusion Characteristics,” IEEE J. Quantum Electron. QE-22, 883–891 (1986).
[CrossRef]

H. C. Cheng, R. V. Ramaswamy, “Simulation of the Radiation Loss of Postbaked Ion-Exchanged Thermal Tapers by BPM,” in Technical Digest, MOC/GRIN, Tokyo (1989), paper B2.

Srivastava, R.

R. Srivastava, H. Zhenguang, R. V. Ramaswamy, “Effect of Annealing on Diffused Channel Waveguides,” Appl. Opt. 29, 330–331 (1990).
[CrossRef] [PubMed]

H. Zhenguang, R. Srivastava, R. V. Ramaswamy, “Low-Loss Small-Mode Passive Waveguides and Near-Adiabatic Tapers in BK7 Glass,” IEEE/OSA J. Lightwave Technol. LT-7, 1590–1596 (1989).
[CrossRef]

R. V. Ramaswamy, R. Srivastava, “Ion-Exchanged Glass Waveguides: A Review,” IEEE/OSA J. Lightwave Technol. LT-6, 984–1002 (1988).
[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. QE-24, 780–786 (1988).
[CrossRef]

Stern, M. S.

M. S. Stern, “Title,” IEE Proc. 135-J, 56 (1988).

Suchoski, P. G.

P. G. Suchoski, R. V. Ramaswamy, “Constant-Width Variable Index Transition for Efficient Ti:LiNbO3 Waveguide-Fiber Coupling,” IEEE/OSA J. Lightwave Technol. LT-5, 1246–1251 (1987).
[CrossRef]

P. G. Suchoski, R. V. Ramaswamy, “An Exact Numerical Technique for the Analysis of Step Discontinuities and Tapers in Optical Dielectric Waveguides,” J. Opt. Soc. Am. A 3, 194–203 (1986).
[CrossRef]

Walker, R. G.

White, J. M.

Wilkinson, C. D. W.

Wilkinson, J. A. H.

Zhenguang, H.

R. Srivastava, H. Zhenguang, R. V. Ramaswamy, “Effect of Annealing on Diffused Channel Waveguides,” Appl. Opt. 29, 330–331 (1990).
[CrossRef] [PubMed]

H. Zhenguang, R. Srivastava, R. V. Ramaswamy, “Low-Loss Small-Mode Passive Waveguides and Near-Adiabatic Tapers in BK7 Glass,” IEEE/OSA J. Lightwave Technol. LT-7, 1590–1596 (1989).
[CrossRef]

Appl. Opt.

IEE Proc.

M. S. Stern, “Title,” IEE Proc. 135-J, 56 (1988).

IEEE J. Quantum Electron.

R. V. Ramaswamy, S. I. Najafi, “Planar, Buried, Ion-Exchanged Glass Waveguides: Diffusion Characteristics,” IEEE J. Quantum Electron. QE-22, 883–891 (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. QE-24, 780–786 (1988).
[CrossRef]

IEEE/OSA J. Lightwave Technol.

R. V. Ramaswamy, R. Srivastava, “Ion-Exchanged Glass Waveguides: A Review,” IEEE/OSA J. Lightwave Technol. LT-6, 984–1002 (1988).
[CrossRef]

A. Brandenburg, “Stress in Ion-Exchanged Glass Waveguides,” IEEE/OSA J. Lightwave Technol. LT-4, 1580–1593 (1986).
[CrossRef]

P. G. Suchoski, R. V. Ramaswamy, “Constant-Width Variable Index Transition for Efficient Ti:LiNbO3 Waveguide-Fiber Coupling,” IEEE/OSA J. Lightwave Technol. LT-5, 1246–1251 (1987).
[CrossRef]

H. Zhenguang, R. Srivastava, R. V. Ramaswamy, “Low-Loss Small-Mode Passive Waveguides and Near-Adiabatic Tapers in BK7 Glass,” IEEE/OSA J. Lightwave Technol. LT-7, 1590–1596 (1989).
[CrossRef]

J. Opt. Soc. Am. A

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).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng.

R. G. Eguchi, E. A. Maunders, I. K. Naik, “Fabrication of Low-Loss Waveguides in BK7 by Ion-Exchange,” Proc. Soc. Photo-Opt. Instrum. Eng. 408, 21–26 (1983).

Other

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

A. Mahapatra, J. M. Connors, “Thermal Tapering of Ion-Exchanged Channel Guides in Glass,” in Technical Digest, Conference on Integrated and Guided Wave Optics, Santa Fe, NM (1988), paper MF13.

H. C. Cheng, R. V. Ramaswamy, “Simulation of the Radiation Loss of Postbaked Ion-Exchanged Thermal Tapers by BPM,” in Technical Digest, MOC/GRIN, Tokyo (1989), paper B2.

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Figures (13)

Fig. 1
Fig. 1

Fabrication of (a) a straight channel waveguide using a single step binary ion exchange and (b) a tapered guide by postbaking a straight channel (a) under a thermal gradient.

Fig. 2
Fig. 2

Flow chart of the modeling of planar, channel, and tapered waveguides that includes the simulation and correlation with experimental results.

Fig. 3
Fig. 3

Index profiles of a multimode planar waveguide reconstructed by an inverse WKB method (cross-points) from the prism–coupler measurement and solved by FDM (solid line). The fabrication condition is described in the text.

Fig. 4
Fig. 4

Calculated self-diffusion coefficient DAg (μm2/min) of silver ion in BK7 as a function of temperature.

Fig. 5
Fig. 5

1/e width (dy, dashed line) and 1/e depth (dx, solid line) of the index profile vs the mask opening from 2 to 6 μm. The open squares with the error bars are measured values using an electron microprobe.

Fig. 6
Fig. 6

Lateral diffusion (dyWM, dashed line) and normalized depth (dx/dp, solid line) as functions of the mask opening WM, where dp is the 1/e diffusion depth of the surface-planar waveguide fabricated in the same condition.

Fig. 7
Fig. 7

1/e widths of the mode fields in the horizontal direction (Wh, dashed line) and the vertical direction (Wv, solid line). The open squares are data points obtained by the near field measurement.

Fig. 8
Fig. 8

Calculated depths of index profile dx as functions of diffusion time. Curves show dx for the planar waveguide and the channel waveguides for WM = 3 and 8 μm fabricated in the same condition. The arrows show the single mode regions for the channel waveguides.

Fig. 9
Fig. 9

Width dy and depth dx of the index profile for the tapered waveguide vs the postbaking temperature. The squares show the data measured by the electron microprobe, and the solid lines are calculated values.

Fig. 10
Fig. 10

Calculated surface index ns vs postbaking temperature. The closed circle on the y-axis shows the calculated data point prior to the postbaking. The same symbols are used for the values before postbaking in Figs. 1113.

Fig. 11
Fig. 11

Normalized frequency V defined in the text vs the postbaking temperature for the tapered waveguide.

Fig. 12
Fig. 12

Normalized mode index b vs the postbaking temperature.

Fig. 13
Fig. 13

Widths of the mode fields as functions of the postbaking temperature. The solid lines show the simulation results. The open squares denote the data obtained by near field measurement.

Equations (6)

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

N A t = x ( m D A 1 - α N A N A x ) + y ( m D A 1 - α N A N A y ) ,
α = 1 - μ A μ B ,
m = ( ln a A ) ( ln C A ) ,
D A = D A 0 exp ( - Δ H R T ) ,
2 F x 2 + 2 F y 2 + [ k 0 2 n 2 ( x , y ) - β 2 ] F = 0 ,
N A x | x = 0 = 0.

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