Abstract

A large-angle Bragg deflector has been demonstrated, utilizing the photoinduced refractive-index change in an As-Se-S-Ge amorphous film loaded on a Ti-diffused LiNbO3 waveguide. Modal analysis shows that optical fields and effective indices in a LiNbO3 wavelength are affected strongly through the index change in the amorphous overlayer. Coupling coefficient and interaction length of the deflector are derived analytically by the coupled wave theory. Interaction length becomes short rapidly with increasing the refractive-index change of the grating or the loaded film thickness. An almost 40° deflection has been achieved experimentally with a 0.7-μm grating pitch and 1-mm interaction length.

© 1980 Optical Society of America

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References

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  1. I. P. Kaminow, IEEE Trans. Microwave Theory Tech. MTT-23, 57 (1975).
    [CrossRef]
  2. Y. K. Lee, S. Wang, Appl. Opt. 15, 1565 (1976).
    [CrossRef] [PubMed]
  3. L. T. Nguyen, C. S. Tsai, Appl. Opt. 16, 1297 (1977).
    [CrossRef] [PubMed]
  4. H. Kotani, M. Kubota, M. Kawabe, S. Namba, K. Masuda, in Technical Digest of International Conference on Integrated Optics and Optical Fiber Communication (Tokyo, 1977), paper A11-1, p. 169.
  5. S. Zembutsu, S. Fukunishi, Appl. Opt. 18, 393 (1979).
    [CrossRef] [PubMed]
  6. J. P. deNeufville, Optical Properties of Solids: New Developments (North-Holland, Amsterdam, 1976), Chap. 9.
  7. K. Tanaka, H. Hamanaka, S. Iizima, in Proceedings, 7th International Conference on Amorphous and Liquid Semiconductors (1977), p. 787.
  8. O. Mikami, J. Noda, S. Zembutsu, S. Fukunishi, Appl. Phys. Lett. 31, 376 (1977).
    [CrossRef]
  9. J. Noda, S. Zembutsu, S. Fukunishi, N. Uchida, Appl. Opt. 17, 1953 (1978).
    [CrossRef] [PubMed]
  10. E. M. Conwell, Appl. Phys. Lett. 23, 328 (1973).
    [CrossRef]
  11. D. F. Nelson, R. M. Mikulyak, J. Appl. Phys. 45, 3688 (1974).
    [CrossRef]
  12. H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
  13. A. Yariv, IEEE J. Quantum Electron. QE-9, 919 (1973).
    [CrossRef]

1979

1978

1977

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

L. T. Nguyen, C. S. Tsai, Appl. Opt. 16, 1297 (1977).
[CrossRef] [PubMed]

1976

1975

I. P. Kaminow, IEEE Trans. Microwave Theory Tech. MTT-23, 57 (1975).
[CrossRef]

1974

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

1973

E. M. Conwell, Appl. Phys. Lett. 23, 328 (1973).
[CrossRef]

A. Yariv, IEEE J. Quantum Electron. QE-9, 919 (1973).
[CrossRef]

1969

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Conwell, E. M.

E. M. Conwell, Appl. Phys. Lett. 23, 328 (1973).
[CrossRef]

deNeufville, J. P.

J. P. deNeufville, Optical Properties of Solids: New Developments (North-Holland, Amsterdam, 1976), Chap. 9.

Fukunishi, S.

Hamanaka, H.

K. Tanaka, H. Hamanaka, S. Iizima, in Proceedings, 7th International Conference on Amorphous and Liquid Semiconductors (1977), p. 787.

Iizima, S.

K. Tanaka, H. Hamanaka, S. Iizima, in Proceedings, 7th International Conference on Amorphous and Liquid Semiconductors (1977), p. 787.

Kaminow, I. P.

I. P. Kaminow, IEEE Trans. Microwave Theory Tech. MTT-23, 57 (1975).
[CrossRef]

Kawabe, M.

H. Kotani, M. Kubota, M. Kawabe, S. Namba, K. Masuda, in Technical Digest of International Conference on Integrated Optics and Optical Fiber Communication (Tokyo, 1977), paper A11-1, p. 169.

Kogelnik, H.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Kotani, H.

H. Kotani, M. Kubota, M. Kawabe, S. Namba, K. Masuda, in Technical Digest of International Conference on Integrated Optics and Optical Fiber Communication (Tokyo, 1977), paper A11-1, p. 169.

Kubota, M.

H. Kotani, M. Kubota, M. Kawabe, S. Namba, K. Masuda, in Technical Digest of International Conference on Integrated Optics and Optical Fiber Communication (Tokyo, 1977), paper A11-1, p. 169.

Lee, Y. K.

Masuda, K.

H. Kotani, M. Kubota, M. Kawabe, S. Namba, K. Masuda, in Technical Digest of International Conference on Integrated Optics and Optical Fiber Communication (Tokyo, 1977), paper A11-1, p. 169.

Mikami, O.

O. Mikami, J. Noda, S. Zembutsu, 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]

Namba, S.

H. Kotani, M. Kubota, M. Kawabe, S. Namba, K. Masuda, in Technical Digest of International Conference on Integrated Optics and Optical Fiber Communication (Tokyo, 1977), paper A11-1, p. 169.

Nelson, D. F.

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

Nguyen, L. T.

Noda, J.

J. Noda, S. Zembutsu, S. Fukunishi, N. Uchida, Appl. Opt. 17, 1953 (1978).
[CrossRef] [PubMed]

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

Tanaka, K.

K. Tanaka, H. Hamanaka, S. Iizima, in Proceedings, 7th International Conference on Amorphous and Liquid Semiconductors (1977), p. 787.

Tsai, C. S.

Uchida, N.

Wang, S.

Yariv, A.

A. Yariv, IEEE J. Quantum Electron. QE-9, 919 (1973).
[CrossRef]

Zembutsu, S.

Appl. Opt.

Appl. Phys. Lett.

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

E. M. Conwell, Appl. Phys. Lett. 23, 328 (1973).
[CrossRef]

Bell Syst. Tech. J.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

IEEE J. Quantum Electron.

A. Yariv, IEEE J. Quantum Electron. QE-9, 919 (1973).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

I. P. Kaminow, IEEE Trans. Microwave Theory Tech. MTT-23, 57 (1975).
[CrossRef]

J. Appl. Phys.

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

Other

H. Kotani, M. Kubota, M. Kawabe, S. Namba, K. Masuda, in Technical Digest of International Conference on Integrated Optics and Optical Fiber Communication (Tokyo, 1977), paper A11-1, p. 169.

J. P. deNeufville, Optical Properties of Solids: New Developments (North-Holland, Amsterdam, 1976), Chap. 9.

K. Tanaka, H. Hamanaka, S. Iizima, in Proceedings, 7th International Conference on Amorphous and Liquid Semiconductors (1977), p. 787.

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Figures (11)

Fig. 1
Fig. 1

Refractive-index profile of a graded-index LiNbO3 waveguide loaded with a chalcogenide amorphous film.

Fig. 2
Fig. 2

Variation of the TE0 mode field distribution along the x direction, taking loaded-film thickness t as a parameter.

Fig. 3
Fig. 3

Optical energy distribution for the TE0 mode accumulated in the waveguide along the x direction. Parameters are the same as in Fig. 2.

Fig. 4
Fig. 4

Effective index change vs loaded-film index increment, taking loaded-film thickness as a parameter.

Fig. 5
Fig. 5

Schematic Bragg deflection by a grating fabricated in an amorphous loaded film.

Fig. 6
Fig. 6

Dependence of the minimum interaction length on a grating index change for the TE0 mode in (a) and for the TM0 mode in (b), taking loaded-film thickness t as a parameter.

Fig. 7
Fig. 7

Bragg-angle dependence on grating period for the TE0 mode (solid line) and for the TM0 mode (dotted line).

Fig. 8
Fig. 8

Relation between deflection efficiency and angular deviation from the Bragg angle for the TE0 mode. Solid line curves are for Δn = 0.02, and dotted line curves are for Δn = 0.01. a, b, and c correspond to Λ = 1.0, 0.7, and 0.5 μm, respectively.

Fig. 9
Fig. 9

Relation between deflection efficiency and wavelength deviation for the TE0 mode in Δn = 0.01 and t = 4100 Å. a, b, and c are the same as in Fig. 8.

Fig. 10
Fig. 10

Experimental setup for the deflection observation. Coupled wave was propagated in the ti-diffused LiNbO3 waveguide and deflected by the grating in the As-Se-S-Ge overlayer. Dotted line indicates the fractional part of the guided wave passed through the grating without deflection.

Fig. 11
Fig. 11

Light deflection for the TE0 mode in a Ti-diffused LiNbO3 waveguide with a 4100-A loaded film. The light streak corresponds to the schematic expression in Fig. 10.

Equations (42)

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n ( x ) = n a 0 > x = n f 0 x t = n s + Δ n s exp ( - x / d ) x > t } ,
J ν - 1 [ g ( 0 ) ] - J ν + 1 [ g ( 0 ) ] J ν [ g ( 0 ) ] = α · 2 ( n f 2 - n eff 2 ) 1 / 2 ( 2 n s Δ n s ) 1 / 2 ξ S - tan b t 1 + ξ S tan b t ,
g ( x ) = 2 d k ( 2 n s Δ n s ) 1 / 2 · exp ( - x / 2 d ) ,
ν = 2 d k ( n eff 2 - n s 2 ) 1 , 2 ,
b = k ( n f 2 - n eff 2 ) 1 / 2 ,
S = [ ( n eff 2 - n a 2 ) / ( n f 2 - n eff 2 ) ] 1 / 2 ,
α = 1 ξ = 1 } for TE modes ,
α = [ ( n s + Δ n s ) / n f ] 2 ξ = ( n f / n a ) 2 } for TM modes .
E ( x ) = c α exp ( γ x ) = c α [ cos b x + ξ ( γ / b ) sin b x ] = c α [ cos b t + ξ ( γ / b ) sin b t ] · J ν [ g ( x ) ] J ν [ g ( 0 ) ] x < 0 0 x t x > t } ,
γ = k ( n eff 2 - n a 2 ) 1 / 2 ,
α = { 1 for TE mode [ n ( x ) ] - 2 for TM mode .
2 E - ( · E ) + β 2 E = 0 ,
β = ω 2 μ ,
β 2 = β 0 2 + ω 2 μ Δ n 2 ( x ) · 0 [ exp ( i K y ) + exp ( - i K y ) ] ,
K = 2 π / Λ .
cos θ B · d A i ( z ) d z = - i κ cos 2 θ B · A d ( z ) ,
cos θ B · d A d ( z ) d z + i ϑ A d ( z ) = - i κ cos 2 θ B · A i ( z ) ,
A i ( 0 ) = 1 A d ( 0 ) = 0 } .
A d ( L ) = - i · exp ( - i ζ ) · sin ( ϕ 2 + ζ 2 ) 1 / 2 [ 1 + ( ζ 2 / ϕ 2 ) ] 1 / 2 ,
ζ = ( L / 2 ) ( ϑ / cos θ B ) ,
ϕ = κ cos 2 θ B · L / cos θ B .
A d ( L ) = - i · sin ϕ = - i · sin ( κ cos 2 θ B L / cos θ B ) .
L 0 = ( π cos θ B / 2 cos 2 θ B ) × { ( ω 0 / 4 ) 0 t Δ n 2 ( x ) [ E y ( m ) ( x ) ] 2 d x } - 1 .
η = A d ( L ) · A d * ( L ) = sin 2 ( ϕ 2 + ζ 2 ) 1 / 2 1 + ( ζ 2 / ϕ 2 ) .
ϑ = ( β 0 2 - β d 2 ) / 2 β 0 = K · sin θ B - K 2 · λ / 4 π n eff .
ϑ = Δ θ · K · cos θ B - Δ λ · K 2 / 4 π n eff .
ζ = Δ θ · L · K / 2.
ζ = - Δ λ · K 2 · L / 8 π n eff cos θ B .
E = 1 [ A 1 ( z ) / 2 ] · E y ( 1 ) ( x ) · exp ( - i β 1 r ) + c . c . ,
A 1 ( z ) = ( 0 A 1 y A 1 z ) ,
β 1 = ( 0 β 1 y β 1 z ) ,
r = ( x y z ) .
1 ( - i β 1 z ) · Δ A 1 ( z ) z · E y ( 1 ) ( x ) · exp ( - r β 1 r ) + 1 ( β 0 2 - β 1 2 ) A 1 ( z ) 2 · E y ( 1 ) ( x ) · exp ( - i β 1 r ) + 1 ( β 0 2 - β 1 2 ) A 1 ( z ) 2 · E y ( 1 ) ( x ) · exp ( - i β 1 r ) + Σ ω 2 μ Δ n 2 ( x ) · 0 [ exp ( - i K y ) + exp ( - i K y ) ] A 1 ( z ) 2 × E y ( 1 ) ( x ) · exp ( - i β 1 · r ) = 0
- E y ( 1 ) ( x ) · E y ( m ) ( x ) d x = 2 ω μ β m · δ 1 , m ,
( - i β i z ) A i ( z ) z · exp ( - i β i r ) + ( - β d z ) A d ( z ) z · exp ( - i β d r ) + ( i β 1 ) ( 1 / 2 ) A i z ( z ) z · exp ( - i β i r ) + ( i β d ) ( 1 / 2 ) A d z ( z ) z · exp ( - i β d r ) + ( β 0 2 - β i 2 ) A i ( z ) 2 · exp ( - i β i r ) + ( β 0 2 - β d 2 ) A d ( z ) 2 · exp ( - i β d r ) = - β 0 ω 0 2 · [ exp ( i K y ) + exp ( - i K y ) ] [ A i ( z ) 2 · exp ( - i β i r ) + A d ( z ) 2 · exp ( - i β d r ) ] · I ,
I = - Δ n 2 ( x ) [ E y ( m ) ( x ) ] 2 d x .
β i = β d - K ,
κ = ω 0 4 0 t Δ n 2 ( x ) [ E y ( m ) ( x ) ] 2 d x .
ϑ = ( β 0 2 - β d 2 ) / 2 β 0 .
cos θ B = β i z / β 0 = β d z / β 0 .
E x = 1 ω 1 β 1 z B 1 ( z ) 2 · H y ( 1 ) ( x ) · exp ( - β 1 r ) + c . c . ,
κ = μ 0 ω 4 · 0 t Δ n 2 ( x ) [ H y ( m ) ( x ) ] 2 d x .

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