Abstract

An interferometric method for measuring the distribution of refractive-index change in diffused channel waveguides is described. It is based on Young’s fringes generated by the interference between a point light source and its reflection from the surface of the waveguide substrate and requires the same experimental arrangement as that used for end-fire coupling. The technique allows a nondestructive measurement of the surface-index change and the lateral dependence of the index distribution if the depth diffusion constant and the diffusion time are known. When used in conjunction with successive removal of substrate layers, the method can in theory be used to measure both the depth and lateral dependencies. Experimentally measured surface-index changes and lateral dependencies of index change distributions in 5-, 9-, and 2 1-μm wide channel waveguides fabricated by diffusion of 195- and 390-Å thick Ti films into Z-cut LiNbO3 for 6 h at 1000°C are given. Maximum surface ordinary index changes were 4.2 × 10−3 and 8.5 × 10−3 for the two Ti thicknesses. Measured lateral dependencies agree with the theoretical sum of error function profiles calculated using a lateral diffusion coefficient of 1.0 × 10−12 cm2/sec.

© 1981 Optical Society of America

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References

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  1. M. Minakata, S. Saito, M. Shibata, J. Appl. Phys. 50, 3063 (1978).
    [CrossRef]
  2. M. Fukuma, J. Noda, Appl. Opt. 19, 591 (1980).
    [CrossRef] [PubMed]
  3. M. Fukuma, J. Noda, H. Iwasaki, J. Appl. Phys. 49, 3693 (1978).
    [CrossRef]
  4. W. K. Burns, P. H. Klein, E. J. West, L. E. Plew, J. Appl. Phys. 50, 6175 (1979).
    [CrossRef]
  5. D. Marcuse, Appl. Opt. 18, 9 (1979).
    [CrossRef] [PubMed]
  6. H. M. Presby, D. Marcuse, IEEE J. Quantum Electron. QE-16, 634 (1980).
    [CrossRef]
  7. M. J. Saunders, W. B. Gardner, Appl. Opt. 16, 2365 (1977).
    [CrossRef]
  8. C. A. Burrus, R. D. Standley, Appl. Opt. 13, 2365 (1974).
    [CrossRef] [PubMed]
  9. H. M. Presby, W. L. Brown, Appl. Phys. Lett. 24, 511 (1974).
    [CrossRef]
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  11. W. E. Martin, Appl. Opt. 13, 2112 (1974).
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  12. I. P. Kaminow, R. J. Carruthers, Appl. Phys. Lett. 22, 326 (1973).
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    [CrossRef]
  14. A. P. Webb et al., J. Phys. D 8, 1567 (1975).
    [CrossRef]
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  16. J. M. White, P. F. Heidrich, Appl. Opt. 15, 151 (1976).
    [CrossRef] [PubMed]
  17. A. R. Bayly, P. D. Townsend, J. Phys. D 6, 1115 (1973).
    [CrossRef]
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    [CrossRef]
  19. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970), pp. 260–262.
  20. J. Crank, Mathematics of Diffusion (Oxford U.P., New York.1970).
  21. L. Goldberg, “Application of Integrated Optics to Optical Signal Processing,” Dissertation, U. Calif. at San Diego (Dec.1979).
  22. J. R. Carruthers, I. P. Kaminow, L. W. Stulz, Appl. Opt. 13, 2333 (1974).
    [CrossRef] [PubMed]
  23. J. L. Jackel, V. Ramaswamy, S. C. Lyman, Appl. Phys. Lett. 7, 509 (1981).
    [CrossRef]

1981

J. L. Jackel, V. Ramaswamy, S. C. Lyman, Appl. Phys. Lett. 7, 509 (1981).
[CrossRef]

1980

H. M. Presby, D. Marcuse, IEEE J. Quantum Electron. QE-16, 634 (1980).
[CrossRef]

M. Fukuma, J. Noda, Appl. Opt. 19, 591 (1980).
[CrossRef] [PubMed]

1979

D. Marcuse, Appl. Opt. 18, 9 (1979).
[CrossRef] [PubMed]

W. K. Burns, P. H. Klein, E. J. West, L. E. Plew, J. Appl. Phys. 50, 6175 (1979).
[CrossRef]

1978

M. Minakata, S. Saito, M. Shibata, J. Appl. Phys. 50, 3063 (1978).
[CrossRef]

M. Fukuma, J. Noda, H. Iwasaki, J. Appl. Phys. 49, 3693 (1978).
[CrossRef]

J. Heibei, E. Voges, IEEE J. Quantum Electron. QE-14, 501 (1978).
[CrossRef]

1977

M. J. Saunders, W. B. Gardner, Appl. Opt. 16, 2365 (1977).
[CrossRef]

1976

1975

A. P. Webb et al., J. Phys. D 8, 1567 (1975).
[CrossRef]

1974

1973

I. P. Kaminow, R. J. Carruthers, Appl. Phys. Lett. 22, 326 (1973).
[CrossRef]

A. R. Bayly, P. D. Townsend, J. Phys. D 6, 1115 (1973).
[CrossRef]

Bayly, A. R.

A. R. Bayly, P. D. Townsend, J. Phys. D 6, 1115 (1973).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970), pp. 260–262.

Brown, W. L.

H. M. Presby, W. L. Brown, Appl. Phys. Lett. 24, 511 (1974).
[CrossRef]

Burns, W. K.

W. K. Burns, P. H. Klein, E. J. West, L. E. Plew, J. Appl. Phys. 50, 6175 (1979).
[CrossRef]

Burrus, C. A.

Carruthers, J. R.

Carruthers, R. J.

I. P. Kaminow, R. J. Carruthers, Appl. Phys. Lett. 22, 326 (1973).
[CrossRef]

Crank, J.

J. Crank, Mathematics of Diffusion (Oxford U.P., New York.1970).

French, W. G.

Fukuma, M.

M. Fukuma, J. Noda, Appl. Opt. 19, 591 (1980).
[CrossRef] [PubMed]

M. Fukuma, J. Noda, H. Iwasaki, J. Appl. Phys. 49, 3693 (1978).
[CrossRef]

Gardner, W. B.

M. J. Saunders, W. B. Gardner, Appl. Opt. 16, 2365 (1977).
[CrossRef]

Goldberg, L.

L. Goldberg, “Application of Integrated Optics to Optical Signal Processing,” Dissertation, U. Calif. at San Diego (Dec.1979).

Heibei, J.

J. Heibei, E. Voges, IEEE J. Quantum Electron. QE-14, 501 (1978).
[CrossRef]

Heidrich, P. F.

Iwasaki, H.

M. Fukuma, J. Noda, H. Iwasaki, J. Appl. Phys. 49, 3693 (1978).
[CrossRef]

Jackel, J. L.

J. L. Jackel, V. Ramaswamy, S. C. Lyman, Appl. Phys. Lett. 7, 509 (1981).
[CrossRef]

Kaminow, I. P.

Klein, P. H.

W. K. Burns, P. H. Klein, E. J. West, L. E. Plew, J. Appl. Phys. 50, 6175 (1979).
[CrossRef]

Lasay, P. D.

Lyman, S. C.

J. L. Jackel, V. Ramaswamy, S. C. Lyman, Appl. Phys. Lett. 7, 509 (1981).
[CrossRef]

Marcuse, D.

H. M. Presby, D. Marcuse, IEEE J. Quantum Electron. QE-16, 634 (1980).
[CrossRef]

D. Marcuse, Appl. Opt. 18, 9 (1979).
[CrossRef] [PubMed]

Martin, W. E.

Minakata, M.

M. Minakata, S. Saito, M. Shibata, J. Appl. Phys. 50, 3063 (1978).
[CrossRef]

Noda, J.

M. Fukuma, J. Noda, Appl. Opt. 19, 591 (1980).
[CrossRef] [PubMed]

M. Fukuma, J. Noda, H. Iwasaki, J. Appl. Phys. 49, 3693 (1978).
[CrossRef]

Plew, L. E.

W. K. Burns, P. H. Klein, E. J. West, L. E. Plew, J. Appl. Phys. 50, 6175 (1979).
[CrossRef]

Presby, H. M.

H. M. Presby, D. Marcuse, IEEE J. Quantum Electron. QE-16, 634 (1980).
[CrossRef]

H. M. Presby, W. L. Brown, Appl. Phys. Lett. 24, 511 (1974).
[CrossRef]

Ramaswamy, V.

J. L. Jackel, V. Ramaswamy, S. C. Lyman, Appl. Phys. Lett. 7, 509 (1981).
[CrossRef]

Saito, S.

M. Minakata, S. Saito, M. Shibata, J. Appl. Phys. 50, 3063 (1978).
[CrossRef]

Saunders, M. J.

M. J. Saunders, W. B. Gardner, Appl. Opt. 16, 2365 (1977).
[CrossRef]

Shibata, M.

M. Minakata, S. Saito, M. Shibata, J. Appl. Phys. 50, 3063 (1978).
[CrossRef]

Simpson, J. R.

Standley, R. D.

Stulz, L. W.

Tien, P. K.

P. K. Tien et al., Phys. Lett. 24, 503 (1974).

Townsend, P. D.

A. P. Webb, P. D. Townsend, J. Phys. D 9, 1343 (1976).
[CrossRef]

A. R. Bayly, P. D. Townsend, J. Phys. D 6, 1115 (1973).
[CrossRef]

Voges, E.

J. Heibei, E. Voges, IEEE J. Quantum Electron. QE-14, 501 (1978).
[CrossRef]

Webb, A. P.

A. P. Webb, P. D. Townsend, J. Phys. D 9, 1343 (1976).
[CrossRef]

A. P. Webb et al., J. Phys. D 8, 1567 (1975).
[CrossRef]

West, E. J.

W. K. Burns, P. H. Klein, E. J. West, L. E. Plew, J. Appl. Phys. 50, 6175 (1979).
[CrossRef]

White, J. M.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970), pp. 260–262.

Wonsiewicz, B. C.

Appl. Opt.

Appl. Phys. Lett.

J. L. Jackel, V. Ramaswamy, S. C. Lyman, Appl. Phys. Lett. 7, 509 (1981).
[CrossRef]

H. M. Presby, W. L. Brown, Appl. Phys. Lett. 24, 511 (1974).
[CrossRef]

I. P. Kaminow, R. J. Carruthers, Appl. Phys. Lett. 22, 326 (1973).
[CrossRef]

IEEE J. Quantum Electron.

J. Heibei, E. Voges, IEEE J. Quantum Electron. QE-14, 501 (1978).
[CrossRef]

H. M. Presby, D. Marcuse, IEEE J. Quantum Electron. QE-16, 634 (1980).
[CrossRef]

J. Appl. Phys.

M. Minakata, S. Saito, M. Shibata, J. Appl. Phys. 50, 3063 (1978).
[CrossRef]

M. Fukuma, J. Noda, H. Iwasaki, J. Appl. Phys. 49, 3693 (1978).
[CrossRef]

W. K. Burns, P. H. Klein, E. J. West, L. E. Plew, J. Appl. Phys. 50, 6175 (1979).
[CrossRef]

J. Phys. D

A. P. Webb et al., J. Phys. D 8, 1567 (1975).
[CrossRef]

A. R. Bayly, P. D. Townsend, J. Phys. D 6, 1115 (1973).
[CrossRef]

A. P. Webb, P. D. Townsend, J. Phys. D 9, 1343 (1976).
[CrossRef]

Phys. Lett.

P. K. Tien et al., Phys. Lett. 24, 503 (1974).

Other

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970), pp. 260–262.

J. Crank, Mathematics of Diffusion (Oxford U.P., New York.1970).

L. Goldberg, “Application of Integrated Optics to Optical Signal Processing,” Dissertation, U. Calif. at San Diego (Dec.1979).

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Figures (8)

Fig. 1
Fig. 1

Arrangement for generating Young’s fringes: (a) substrate with an embedded channel waveguide; (b) direct r1 and reflected rays r2 which produce an interference pattern described by intensity distribution I(y) at the observation plane z = 0.

Fig. 2
Fig. 2

Fringe shift fs caused by a rectangular channel waveguide: (a) fringe pattern produced by probing rays of the type r 2 which propagate through n2 + Δ region; (b) diagram used for calculating the difference between the optical path lengths of rays r2 and r 2 .

Fig. 3
Fig. 3

Ray paths through the rectangular r 2 and the diffused r 2 d channels. Refractive-index profiles are shown on the right, Δsn1, area under Δ(y) is assumed to be equal to tΔs. Reflected ray r2 outside of the channel is also shown.

Fig. 4
Fig. 4

Method used to determine the index depth profile of a diffused channel waveguide. Thin layers of thickness δ are successively removed from the waveguide surface. Index profile in the central plane of the waveguide (x = 0) is shown as a function of depth on the right.

Fig. 5
Fig. 5

End-on view of the channel waveguide and probing rays r 2 d . Lateral resolution of the lateral profile measurement is determined by ρ and κ. Point light source S and two fringes are shown.

Fig. 6
Fig. 6

Fringe patterns produced by diffused channel waveguides fabricated in LiNbO3 by (A) outdiffusion through SiO2 mask with a 10-μm gap (Y-cut) (E), (C), (D) diffusion of 5-, 9-, and 21-μm wide stripes of 390-Å thick Ti film (Z-cut). In all cases light (λ = 6328-Å) polarization is parallel to the substrate surface. Fringe spacings are 17 μm in (A) and 0.94 μm in others.

Fig. 7
Fig. 7

Measured and calculated ordinary refractive-index change at the waveguide surface as a function of lateral position. Ti-diffused channel waveguides fabricatd by 6-h 1000°C diffusion of 390 ± 40-Å thick Ti film in Z-cut LiNbO3. Theoretical curves assume 5-, 9-, 21-μm Ti stripe widths and lateral diffusion constant of 1.0 × 10−12 cm2/sec. Depth diffusion constant of 1.4 × 10−12 cm2/sec was used to calculate Δs(x) from the measured fringe shift fs(x). The 5-μm waveguide supported three TM type modes at λ = 6328 Å.

Fig. 8
Fig. 8

Ordinary refractive-index change at the waveguide surface as a function of position. Diffused Ti-film thickness was 195 ± 20 Å; other conditions are the same as in Fig. 7. The 5-μm waveguide supported two TM type modes.

Tables (1)

Tables Icon

Table I Values of Extraordinary Index Δs(x = 0) Calculated from the Measured Fringe Shift fs for different Values of yf and f. W = 8.2 μm, 1/α = 9.5 μma

Equations (39)

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l r 2 - l r 1 2 n 1 y f d W + λ 2 ,
f = λ W / ( 2 n 1 d ) .
f s f ( l - l ) λ ,
l - l = 2 t Δ cos θ 2 ,
cos θ 2 = cos θ 1 ( 1 + Δ n 1 tan 2 θ 1 ) ,
Δ n 1             2 t W             tan 2 θ 1 n 1 2 Δ .
n 2 ( y ) - n 1 = Δ ( y ) = Δ s exp ( - y α ) ,             y 0 ,
Δ ( y ) = Δ s exp ( - β 2 y 2 ) ,             y 0 ,
( l - l ) d e = 2 0 c Δ ( y ) cos θ ( y ) d y ,
1 cos θ ( y ) = { 1 - [ n 1 sin θ 1 n 1 + Δ ( y ) ] 2 } - 1 / 2 ,
1 cos θ ( y ) = 1 cos θ 1 [ 1 - Δ ( y ) n 1 tan 2 θ 1 ] .
( l - l ) d e = 2 Δ s α cos θ 1 ( 1 - Δ s 2 n 1 tan 2 θ 1 ) .
t e = 1 / α .
( l - l ) d g = π 2 β 2 Δ s cos θ 1 ( 1 - Δ s 2 n 1 tan 2 θ 1 ) ,
t g = π 2 β .
Δ s f s λ cos θ 1 2 f t g ( 1 + Δ s 2 n 1 tan 2 θ 1 ) ,
cos θ 1 y f + d W = y f W + λ 2 n 1 f .
Δ s Δ 0 1 - Δ 0 2 n 1 tan 2 θ 1 ,
Δ 0 = f s λ cos θ 1 2 f t g .
γ ( y ) = ( l - l ) y - ( l - l ) y + δ = 2 δ Δ ( y ) cos θ 2 ( y ) ,
cos θ 2 ( y ) cos θ 1 [ 1 + Δ ( y ) n 1 tan 2 θ 2 ] .
Δ ( y ) = Δ 0 ( y ) 1 - Δ 0 ( y ) n 1 tan 2 θ 1 ,
Δ 0 ( y ) = γ ( y ) 2 δ cos θ 1 .
Δ ( x , y ) = Δ ( x ) Δ ( y ) ,
Δ ( x ) = ½ [ erf ( w 4 D x τ + x 2 D x τ ) + erf ( w 4 D x τ - x 2 D x τ ) ] , Δ ( y ) = Δ s 0 exp - ( y 2 D y τ ) ,
l = n 1 ( y 1 + y 3 ) cos θ 1 + y 2 ( n 1 + Δ ) cos θ 2 ,
y 1 + y 3 = W - y 2 tan θ 2 tan θ 1 .
Δ n 1 .
l n 1 W sin θ 1 + 2 y 2 Δ cos θ 2 .
l = W n 1 sin ( θ 1 - β ) ,
β = ( h sin θ 1 ) / W .
h = y 2 cos θ 2 sin ( θ 1 - θ 2 ) .
l W n 1 sin θ 1 + n 1 y 2 ( cos θ 1 cos θ 2 - cos 2 θ 1 sin θ 2 sin θ 1 ) cos θ 2 ,
l W n 1 sin θ 1 + n 1 y 2 cos θ 2 [ cos 2 θ 1 ( 1 + 2 Δ n 1 tan 2 θ 1 ) 1 / 2 - ( 1 - Δ n 1 ) cos 2 θ 1 ] .
tan 2 θ 1 n 1 2 Δ .
l W n 1 sin θ 1 + y 2 Δ cos θ 2 .
l - l y 2 Δ cos θ 1 = 2 t Δ cos θ 2 ,
cos θ 2 ( 1 + Δ n 1 tan 2 θ 1 ) cos θ 1 .
Δ n 1 tan 2 θ 1 < 0.2.

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