Abstract

The relation between the ordinary and extraordinary index profiles of ion-exchanged glass waveguides is investigated on the basis of the stress-optic law and the Clausius–Mossotti relation. For K+ exchange and Ag+ exchange, the experimental results are consistent with our analysis. The values of the coefficient that relates the ordinary and extraordinary index profiles are presented.

© 1988 Optical Society of America

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References

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  1. T. G. Giallorenzi, E. J. West, R. Kirk, R. Ginther, R. A. Andrews, Appl. Opt. 12, 1240 (1973).
    [CrossRef] [PubMed]
  2. G. Stewart, C. A. Millar, P. J. R. Laybourn, C. D. W. Wilkinson, R. M. DeLaRue, IEEE J. Quantum Electron. QE-13, 192 (1977).
    [CrossRef]
  3. G. L. Yip, J. Albert, Opt. Lett. 10, 151 (1985).
    [CrossRef] [PubMed]
  4. K. Kishioka, M. Hashimoto, in National Convention Record (Institute of Electronics and Communication Engineers of Japan, Tokyo, 1983), Part 4, p. 163.
  5. P. C. Jaussaud, G. H. Chartier, J. Phys. D 10, 645 (1977).
    [CrossRef]
  6. A. Brandenburg, IEEE J. Lightwave Technol. LT-4, 1580 (1986).
    [CrossRef]
  7. J. W. Dally, W. F. Riley, Experimental Stress Analysis, 2nd ed. (McGraw-Hill, New York, 1978), p. 408.
  8. K. Tsutsumi, H. Hirai, Y. Yuba, Electron. Lett. 22, 1299 (1986).
    [CrossRef]
  9. C. Kittel, Introduction to Solid State Physics, 6th ed. (Wiley, New York, 1986), Chap. 13.
  10. A. K. Varshneya, R. J. Petti, J. Am. Ceram. Soc. 59, 42 (1976).
    [CrossRef]
  11. P. K. Tien, R. Ulrich, R. J. Martin, Appl. Phys. Lett. 14, 291 (1969).
    [CrossRef]
  12. J. M. White, P. F. Heidrich, Appl. Opt. 15, 151 (1976).
    [CrossRef] [PubMed]
  13. K. Tsutsumi, H. Hirai, Y. Yuba, in Technical Report on Optical and Quantum Electronics (Institute of Electronics and Communication Engineers of Japan, Tokyo, 1986), p. 9.

1986 (2)

A. Brandenburg, IEEE J. Lightwave Technol. LT-4, 1580 (1986).
[CrossRef]

K. Tsutsumi, H. Hirai, Y. Yuba, Electron. Lett. 22, 1299 (1986).
[CrossRef]

1985 (1)

1977 (2)

P. C. Jaussaud, G. H. Chartier, J. Phys. D 10, 645 (1977).
[CrossRef]

G. Stewart, C. A. Millar, P. J. R. Laybourn, C. D. W. Wilkinson, R. M. DeLaRue, IEEE J. Quantum Electron. QE-13, 192 (1977).
[CrossRef]

1976 (2)

A. K. Varshneya, R. J. Petti, J. Am. Ceram. Soc. 59, 42 (1976).
[CrossRef]

J. M. White, P. F. Heidrich, Appl. Opt. 15, 151 (1976).
[CrossRef] [PubMed]

1973 (1)

1969 (1)

P. K. Tien, R. Ulrich, R. J. Martin, Appl. Phys. Lett. 14, 291 (1969).
[CrossRef]

Albert, J.

Andrews, R. A.

Brandenburg, A.

A. Brandenburg, IEEE J. Lightwave Technol. LT-4, 1580 (1986).
[CrossRef]

Chartier, G. H.

P. C. Jaussaud, G. H. Chartier, J. Phys. D 10, 645 (1977).
[CrossRef]

Dally, J. W.

J. W. Dally, W. F. Riley, Experimental Stress Analysis, 2nd ed. (McGraw-Hill, New York, 1978), p. 408.

DeLaRue, R. M.

G. Stewart, C. A. Millar, P. J. R. Laybourn, C. D. W. Wilkinson, R. M. DeLaRue, IEEE J. Quantum Electron. QE-13, 192 (1977).
[CrossRef]

Giallorenzi, T. G.

Ginther, R.

Hashimoto, M.

K. Kishioka, M. Hashimoto, in National Convention Record (Institute of Electronics and Communication Engineers of Japan, Tokyo, 1983), Part 4, p. 163.

Heidrich, P. F.

Hirai, H.

K. Tsutsumi, H. Hirai, Y. Yuba, Electron. Lett. 22, 1299 (1986).
[CrossRef]

K. Tsutsumi, H. Hirai, Y. Yuba, in Technical Report on Optical and Quantum Electronics (Institute of Electronics and Communication Engineers of Japan, Tokyo, 1986), p. 9.

Jaussaud, P. C.

P. C. Jaussaud, G. H. Chartier, J. Phys. D 10, 645 (1977).
[CrossRef]

Kirk, R.

Kishioka, K.

K. Kishioka, M. Hashimoto, in National Convention Record (Institute of Electronics and Communication Engineers of Japan, Tokyo, 1983), Part 4, p. 163.

Kittel, C.

C. Kittel, Introduction to Solid State Physics, 6th ed. (Wiley, New York, 1986), Chap. 13.

Laybourn, P. J. R.

G. Stewart, C. A. Millar, P. J. R. Laybourn, C. D. W. Wilkinson, R. M. DeLaRue, IEEE J. Quantum Electron. QE-13, 192 (1977).
[CrossRef]

Martin, R. J.

P. K. Tien, R. Ulrich, R. J. Martin, Appl. Phys. Lett. 14, 291 (1969).
[CrossRef]

Millar, C. A.

G. Stewart, C. A. Millar, P. J. R. Laybourn, C. D. W. Wilkinson, R. M. DeLaRue, IEEE J. Quantum Electron. QE-13, 192 (1977).
[CrossRef]

Petti, R. J.

A. K. Varshneya, R. J. Petti, J. Am. Ceram. Soc. 59, 42 (1976).
[CrossRef]

Riley, W. F.

J. W. Dally, W. F. Riley, Experimental Stress Analysis, 2nd ed. (McGraw-Hill, New York, 1978), p. 408.

Stewart, G.

G. Stewart, C. A. Millar, P. J. R. Laybourn, C. D. W. Wilkinson, R. M. DeLaRue, IEEE J. Quantum Electron. QE-13, 192 (1977).
[CrossRef]

Tien, P. K.

P. K. Tien, R. Ulrich, R. J. Martin, Appl. Phys. Lett. 14, 291 (1969).
[CrossRef]

Tsutsumi, K.

K. Tsutsumi, H. Hirai, Y. Yuba, Electron. Lett. 22, 1299 (1986).
[CrossRef]

K. Tsutsumi, H. Hirai, Y. Yuba, in Technical Report on Optical and Quantum Electronics (Institute of Electronics and Communication Engineers of Japan, Tokyo, 1986), p. 9.

Ulrich, R.

P. K. Tien, R. Ulrich, R. J. Martin, Appl. Phys. Lett. 14, 291 (1969).
[CrossRef]

Varshneya, A. K.

A. K. Varshneya, R. J. Petti, J. Am. Ceram. Soc. 59, 42 (1976).
[CrossRef]

West, E. J.

White, J. M.

Wilkinson, C. D. W.

G. Stewart, C. A. Millar, P. J. R. Laybourn, C. D. W. Wilkinson, R. M. DeLaRue, IEEE J. Quantum Electron. QE-13, 192 (1977).
[CrossRef]

Yip, G. L.

Yuba, Y.

K. Tsutsumi, H. Hirai, Y. Yuba, Electron. Lett. 22, 1299 (1986).
[CrossRef]

K. Tsutsumi, H. Hirai, Y. Yuba, in Technical Report on Optical and Quantum Electronics (Institute of Electronics and Communication Engineers of Japan, Tokyo, 1986), p. 9.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

P. K. Tien, R. Ulrich, R. J. Martin, Appl. Phys. Lett. 14, 291 (1969).
[CrossRef]

Electron. Lett. (1)

K. Tsutsumi, H. Hirai, Y. Yuba, Electron. Lett. 22, 1299 (1986).
[CrossRef]

IEEE J. Lightwave Technol. (1)

A. Brandenburg, IEEE J. Lightwave Technol. LT-4, 1580 (1986).
[CrossRef]

IEEE J. Quantum Electron. (1)

G. Stewart, C. A. Millar, P. J. R. Laybourn, C. D. W. Wilkinson, R. M. DeLaRue, IEEE J. Quantum Electron. QE-13, 192 (1977).
[CrossRef]

J. Am. Ceram. Soc. (1)

A. K. Varshneya, R. J. Petti, J. Am. Ceram. Soc. 59, 42 (1976).
[CrossRef]

J. Phys. D (1)

P. C. Jaussaud, G. H. Chartier, J. Phys. D 10, 645 (1977).
[CrossRef]

Opt. Lett. (1)

Other (4)

K. Kishioka, M. Hashimoto, in National Convention Record (Institute of Electronics and Communication Engineers of Japan, Tokyo, 1983), Part 4, p. 163.

J. W. Dally, W. F. Riley, Experimental Stress Analysis, 2nd ed. (McGraw-Hill, New York, 1978), p. 408.

K. Tsutsumi, H. Hirai, Y. Yuba, in Technical Report on Optical and Quantum Electronics (Institute of Electronics and Communication Engineers of Japan, Tokyo, 1986), p. 9.

C. Kittel, Introduction to Solid State Physics, 6th ed. (Wiley, New York, 1986), Chap. 13.

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Figures (3)

Fig. 1
Fig. 1

Schematic drawing of the refractive-index profiles due to ion exchange of glass slabs. The profile by isotropic index increase is nu(x), and the ordinary and extraordinary profiles are no(x) and ne(x), respectively. The compressive stress [σ(x) < 0] and the negative coefficients C1 and C2 with |C2| > |C1| are assumed.

Fig. 2
Fig. 2

Index profiles of the glass waveguide formed by potassium-ion exchange at 440°C for 4 h. The substrate is a Matsunami soda-lime slide (nb = 1.5138). The surface indices nes and nos are 1.5226 and 1.5211, respectively.

Fig. 3
Fig. 3

Index profiles of the glass waveguide formed by silver-ion exchange at 225°C for 24 h. The substrate is a Starlux soda-lime slide (nb = 1.521). The surface indices nes and nos are 1.6194 and 1.6181, respectively.

Tables (1)

Tables Icon

Table 1 Values of the Coefficient KSO and the Extraordinary Index Increase at the Surface Δnes

Equations (10)

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n x n u = C 1 σ x + C 2 ( σ y + σ z ) , n y n u = C 1 σ y + C 2 ( σ z + σ x ) , n z n u = C 1 σ z + C 2 ( σ x + σ y ) ,
n e ( x ) n u ( x ) = 2 C 2 σ ( x ) , n o ( x ) n u ( x ) = ( C 1 + C 2 ) σ ( x ) ,
n o ( x ) n e ( x ) = ( C 1 C 2 ) σ ( x ) .
n u ( x ) = n b + Δ n ( x ) ,
n 2 1 n 2 + 1 = 1 3 0 i N i α i ,
Δ n ( x ) = ( n b 2 + 2 ) 2 18 0 n b Δ N D ( x ) Δ α ,
σ ( x ) Δ N D ( x )
σ ( x ) = p Δ n ( x ) ,
Δ n ( x ) = n e ( x ) n b 1 + 2 C 2 p = n o ( x ) n b 1 + ( C 1 + C 2 ) p .
n o ( x ) n e ( x ) = K SO [ n e ( x ) n b ] , K SO = ( C 1 C 2 ) p 1 + 2 C 2 p .

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