Abstract

Coupling characteristics for designing a LiNbO3 directional coupler fabricated by Ti diffusion have been investigated with a modified WKB method. The present analysis is verified by comparing the refractive-index change in the Ti-diffused LiNbCO3 waveguide derived from direct measurement and coupling length calculation. Coupling length variations due to refractive-index change, diffusion length waveguide spacing, and wavelength are described. Tolerances in coupling length mismatch and propagation constant differences affecting cross talk of the directional coupler are discussed.

© 1981 Optical Society of America

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  1. R. C. Alferness, R. V. Schmidt, E. H. Turner, Appl. Opt. 18, 4012 (1979).
    [Crossref] [PubMed]
  2. T. Suhara, Y. Handa, H. Nishihara, J. Koyama, J. Opt. Soc. Am. 69, 807 (1979).
    [Crossref]
  3. T. Taniuchi, M. Kudo, Y. Mushiaki, Trans. IECE Jpn. J61-C, 256 (1978).
  4. E. A. Marcatili, Bell Syst. Tech. J. 48, 2071 (1969).
  5. G. B. Hocker, W. K. Burns, Appl. Opt. 16, 113 (1977).
    [Crossref] [PubMed]
  6. M. Fukuma, J. Noda, H. Iwasaki, J. Appl. Phys. 49, 3693 (1978).
    [Crossref]
  7. J. Noda, M. Fukuma, Appl. Opt. 19, 2897 (1980).
    [Crossref] [PubMed]
  8. O. Mikami, J. Noda, M. Fukuma, Trans. IECE Jpn. E61, 1441 (1978).
  9. J. Noda, M. Fukuma, J. Appl. Phys. 51, 1379 (1980).
    [Crossref]
  10. Y. Suematsu, K. Kishino, Radio Sci. 12, 587 (1977).
    [Crossref]
  11. D. F. Nelson, R. M. Mikulyak, J. Appl. Phys. 45, 3688 (1974).
    [Crossref]
  12. R. C. Alferness, R. V. Schmidt, Appl. Phys. Lett. 33, 161 (1978).
    [Crossref]
  13. O. Mikami, J. Noda, Appl. Phys. Lett. 33, 856 (1978).
    [Crossref]
  14. M. Fukuma, J. Noda, Appl. Opt. 19, 591 (1980).
    [Crossref] [PubMed]
  15. J. Noda, N. Uchida, S. Saito, T. Saku, M. Minakata, Appl. Phys. Lett. 27, 19 (1975).
    [Crossref]
  16. S. Miyazawa, J. Appl. Phys. 50, 4599 (1979).
    [Crossref]
  17. V. Ramaswamy, M. D. Divino, R. D. Standly, Appl. Phys. Lett. 32, 644 (1978).
    [Crossref]
  18. O. Mikami, J. Noda, S. Zembutsi, S. Fukunishi, Appl. Phys. Lett. 31, 376 (1977).
    [Crossref]

1980 (3)

1979 (3)

1978 (6)

T. Taniuchi, M. Kudo, Y. Mushiaki, Trans. IECE Jpn. J61-C, 256 (1978).

O. Mikami, J. Noda, M. Fukuma, Trans. IECE Jpn. E61, 1441 (1978).

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

V. Ramaswamy, M. D. Divino, R. D. Standly, Appl. Phys. Lett. 32, 644 (1978).
[Crossref]

R. C. Alferness, R. V. Schmidt, Appl. Phys. Lett. 33, 161 (1978).
[Crossref]

O. Mikami, J. Noda, Appl. Phys. Lett. 33, 856 (1978).
[Crossref]

1977 (3)

Y. Suematsu, K. Kishino, Radio Sci. 12, 587 (1977).
[Crossref]

O. Mikami, J. Noda, S. Zembutsi, S. Fukunishi, Appl. Phys. Lett. 31, 376 (1977).
[Crossref]

G. B. Hocker, W. K. Burns, Appl. Opt. 16, 113 (1977).
[Crossref] [PubMed]

1975 (1)

J. Noda, N. Uchida, S. Saito, T. Saku, M. Minakata, Appl. Phys. Lett. 27, 19 (1975).
[Crossref]

1974 (1)

D. F. Nelson, R. M. Mikulyak, J. Appl. Phys. 45, 3688 (1974).
[Crossref]

1969 (1)

E. A. Marcatili, Bell Syst. Tech. J. 48, 2071 (1969).

Alferness, R. C.

Burns, W. K.

Divino, M. D.

V. Ramaswamy, M. D. Divino, R. D. Standly, Appl. Phys. Lett. 32, 644 (1978).
[Crossref]

Fukuma, M.

J. Noda, M. Fukuma, J. Appl. Phys. 51, 1379 (1980).
[Crossref]

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

J. Noda, M. Fukuma, Appl. Opt. 19, 2897 (1980).
[Crossref] [PubMed]

O. Mikami, J. Noda, M. Fukuma, Trans. IECE Jpn. E61, 1441 (1978).

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

Fukunishi, S.

O. Mikami, J. Noda, S. Zembutsi, S. Fukunishi, Appl. Phys. Lett. 31, 376 (1977).
[Crossref]

Handa, Y.

Hocker, G. B.

Iwasaki, H.

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

Kishino, K.

Y. Suematsu, K. Kishino, Radio Sci. 12, 587 (1977).
[Crossref]

Koyama, J.

Kudo, M.

T. Taniuchi, M. Kudo, Y. Mushiaki, Trans. IECE Jpn. J61-C, 256 (1978).

Marcatili, E. A.

E. A. Marcatili, Bell Syst. Tech. J. 48, 2071 (1969).

Mikami, O.

O. Mikami, J. Noda, M. Fukuma, Trans. IECE Jpn. E61, 1441 (1978).

O. Mikami, J. Noda, Appl. Phys. Lett. 33, 856 (1978).
[Crossref]

O. Mikami, J. Noda, S. Zembutsi, S. Fukunishi, Appl. Phys. Lett. 31, 376 (1977).
[Crossref]

Mikulyak, R. M.

D. F. Nelson, R. M. Mikulyak, J. Appl. Phys. 45, 3688 (1974).
[Crossref]

Minakata, M.

J. Noda, N. Uchida, S. Saito, T. Saku, M. Minakata, Appl. Phys. Lett. 27, 19 (1975).
[Crossref]

Miyazawa, S.

S. Miyazawa, J. Appl. Phys. 50, 4599 (1979).
[Crossref]

Mushiaki, Y.

T. Taniuchi, M. Kudo, Y. Mushiaki, Trans. IECE Jpn. J61-C, 256 (1978).

Nelson, D. F.

D. F. Nelson, R. M. Mikulyak, J. Appl. Phys. 45, 3688 (1974).
[Crossref]

Nishihara, H.

Noda, J.

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

J. Noda, M. Fukuma, Appl. Opt. 19, 2897 (1980).
[Crossref] [PubMed]

J. Noda, M. Fukuma, J. Appl. Phys. 51, 1379 (1980).
[Crossref]

O. Mikami, J. Noda, M. Fukuma, Trans. IECE Jpn. E61, 1441 (1978).

O. Mikami, J. Noda, Appl. Phys. Lett. 33, 856 (1978).
[Crossref]

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

O. Mikami, J. Noda, S. Zembutsi, S. Fukunishi, Appl. Phys. Lett. 31, 376 (1977).
[Crossref]

J. Noda, N. Uchida, S. Saito, T. Saku, M. Minakata, Appl. Phys. Lett. 27, 19 (1975).
[Crossref]

Ramaswamy, V.

V. Ramaswamy, M. D. Divino, R. D. Standly, Appl. Phys. Lett. 32, 644 (1978).
[Crossref]

Saito, S.

J. Noda, N. Uchida, S. Saito, T. Saku, M. Minakata, Appl. Phys. Lett. 27, 19 (1975).
[Crossref]

Saku, T.

J. Noda, N. Uchida, S. Saito, T. Saku, M. Minakata, Appl. Phys. Lett. 27, 19 (1975).
[Crossref]

Schmidt, R. V.

Standly, R. D.

V. Ramaswamy, M. D. Divino, R. D. Standly, Appl. Phys. Lett. 32, 644 (1978).
[Crossref]

Suematsu, Y.

Y. Suematsu, K. Kishino, Radio Sci. 12, 587 (1977).
[Crossref]

Suhara, T.

Taniuchi, T.

T. Taniuchi, M. Kudo, Y. Mushiaki, Trans. IECE Jpn. J61-C, 256 (1978).

Turner, E. H.

Uchida, N.

J. Noda, N. Uchida, S. Saito, T. Saku, M. Minakata, Appl. Phys. Lett. 27, 19 (1975).
[Crossref]

Zembutsi, S.

O. Mikami, J. Noda, S. Zembutsi, S. Fukunishi, Appl. Phys. Lett. 31, 376 (1977).
[Crossref]

Appl. Opt. (4)

Appl. Phys. Lett. (5)

J. Noda, N. Uchida, S. Saito, T. Saku, M. Minakata, Appl. Phys. Lett. 27, 19 (1975).
[Crossref]

V. Ramaswamy, M. D. Divino, R. D. Standly, Appl. Phys. Lett. 32, 644 (1978).
[Crossref]

O. Mikami, J. Noda, S. Zembutsi, S. Fukunishi, Appl. Phys. Lett. 31, 376 (1977).
[Crossref]

R. C. Alferness, R. V. Schmidt, Appl. Phys. Lett. 33, 161 (1978).
[Crossref]

O. Mikami, J. Noda, Appl. Phys. Lett. 33, 856 (1978).
[Crossref]

Bell Syst. Tech. J. (1)

E. A. Marcatili, Bell Syst. Tech. J. 48, 2071 (1969).

J. Appl. Phys. (4)

D. F. Nelson, R. M. Mikulyak, J. Appl. Phys. 45, 3688 (1974).
[Crossref]

S. Miyazawa, J. Appl. Phys. 50, 4599 (1979).
[Crossref]

J. Noda, M. Fukuma, J. Appl. Phys. 51, 1379 (1980).
[Crossref]

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

J. Opt. Soc. Am. (1)

Radio Sci. (1)

Y. Suematsu, K. Kishino, Radio Sci. 12, 587 (1977).
[Crossref]

Trans. IECE Jpn. (2)

O. Mikami, J. Noda, M. Fukuma, Trans. IECE Jpn. E61, 1441 (1978).

T. Taniuchi, M. Kudo, Y. Mushiaki, Trans. IECE Jpn. J61-C, 256 (1978).

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Figures (12)

Fig. 1
Fig. 1

Turning and tunneling points in the directional coupler with a graded-index profile.

Fig. 2
Fig. 2

Ti-diffused profile in the directional coupler along the substrate surface. Ti stripes are 8 μm wide, 500 Å thick, separated by 12-μm gaps.

Fig. 3
Fig. 3

Dependence of even- and odd-mode normalized propagation constants nx even, nx odd on waveguide spacing h.

Fig. 4
Fig. 4

Relation between coupling length L0 and waveguide spacing h, taking refractive-index change Δn as the parameter.

Fig. 5
Fig. 5

Relation between coupling length L0 and refractive-index change Δn, taking waveguide spacing h as the parameter.

Fig. 6
Fig. 6

Relation between coupling length L0 and diffusion distance dx, taking waveguide h as the parameter.

Fig. 7
Fig. 7

Wavelength dependence on coupling length.

Fig. 8
Fig. 8

Coupled light intensity variation with Al film removed length.

Fig. 9
Fig. 9

Coupled light intensity variation with waveguide spacing.

Fig. 10
Fig. 10

Relation between coupled length and waveguide spacing.

Fig. 11
Fig. 11

Optimum refractive-index change and diffusion distance at constant coupling length L0 = 15 mm at 1.153-μm wavelength.

Fig. 12
Fig. 12

Normalized propagation constant difference (a) and coupling length mismatch (b) vs coupling length at each cross talk.

Tables (1)

Tables Icon

Table I Waveguide Parameter Tolerances at 20-dB Cross Talk

Equations (15)

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n z 2 = n x 2 + n y 2 n t 2 ,
L 0 = λ / 2 ( n z even n z odd ) ,
L 0 λ / 2 ( n x even n x odd ) .
n ( x , y ) = n s + Δ ng ( y ) [ f ( x ) + f ( x h ) ] ,
k x 2 x 1 [ n 2 ( x ) n x 2 ] 1 / 2 dx = ( m + ½ ) π + ϕ ,
ϕ = 1 x 2 h / 2 x 2 h / 2 tan 1 [ tanh coth ( γ x ) ] dx ,
γ = k [ n x 2 n 2 ( x 2 ) ] 1 / 2 ,
f ( x ) = 1 2 [ erf ( w x d x ) + erf ( w + x d x ) ] / erf ( w d x ) ,
Δ n ( x ) = 0.0045 { exp [ ( x / 5.3 ) 2 ] + exp [ ( x + 12 ) 2 / 5.3 2 ] } .
L 0 = ah b ,
n 2 = K λ 2 / ( λ 2 λ 0 2 ) + 1 .
P 1 / ( P 1 + P 2 ) = sin 2 ( π L / 2 L 0 ) ,
1 / ( 1 + S ) = 1 T + 1 sin 2 [ T + 1 π ( L 0 + Δ L ) 2 L 0 ] ,
S = 10 χ / 10 ,
T = ( 2 Δ n L 0 / λ ) 2 + 1 .

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