Abstract

An optical waveguide intersection on the same level, inducing no light leak, with higher refractive index in the intersecting point than in the guides, is proposed. This intersection is formed easily by the photopolymerization method, introducing double exposure at the intersecting point (typical guide width, ~0.1 mm; Δn 0.5% in the guide; and ~1% in the intersection). Very low losses were observed in the intersections, while large leak losses were observed in ordinary intersections, where the refractive index was equal to that of the guides. Observed losses were in good agreement with calculated ones.

© 1977 Optical Society of America

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References

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  1. H. W. Weber, R. Ulrich, E. A. Chandross, W. J. Tomlinson, Phys. Lett. 20, 143 (1972).
  2. E. A. Chandross, C. A. Pryde, W. J. Tomlinson, H. P. Weber, Appl. Phys. Lett. 24, 72 (1974).
    [CrossRef]
  3. P. K. Tien, Appl. Opt. 10, 2395 (1971).
    [CrossRef] [PubMed]
  4. M. Born, E. Wolf, Principles of Optics, (Pergamon, Oxford, 1970), pp. 36–47.
  5. T. Kurokawa, in The 21st Annual Meeting of the Japan Society of Applied Physics, Saitama (March1974).

1974 (1)

E. A. Chandross, C. A. Pryde, W. J. Tomlinson, H. P. Weber, Appl. Phys. Lett. 24, 72 (1974).
[CrossRef]

1972 (1)

H. W. Weber, R. Ulrich, E. A. Chandross, W. J. Tomlinson, Phys. Lett. 20, 143 (1972).

1971 (1)

Born, M.

M. Born, E. Wolf, Principles of Optics, (Pergamon, Oxford, 1970), pp. 36–47.

Chandross, E. A.

E. A. Chandross, C. A. Pryde, W. J. Tomlinson, H. P. Weber, Appl. Phys. Lett. 24, 72 (1974).
[CrossRef]

H. W. Weber, R. Ulrich, E. A. Chandross, W. J. Tomlinson, Phys. Lett. 20, 143 (1972).

Kurokawa, T.

T. Kurokawa, in The 21st Annual Meeting of the Japan Society of Applied Physics, Saitama (March1974).

Pryde, C. A.

E. A. Chandross, C. A. Pryde, W. J. Tomlinson, H. P. Weber, Appl. Phys. Lett. 24, 72 (1974).
[CrossRef]

Tien, P. K.

Tomlinson, W. J.

E. A. Chandross, C. A. Pryde, W. J. Tomlinson, H. P. Weber, Appl. Phys. Lett. 24, 72 (1974).
[CrossRef]

H. W. Weber, R. Ulrich, E. A. Chandross, W. J. Tomlinson, Phys. Lett. 20, 143 (1972).

Ulrich, R.

H. W. Weber, R. Ulrich, E. A. Chandross, W. J. Tomlinson, Phys. Lett. 20, 143 (1972).

Weber, H. P.

E. A. Chandross, C. A. Pryde, W. J. Tomlinson, H. P. Weber, Appl. Phys. Lett. 24, 72 (1974).
[CrossRef]

Weber, H. W.

H. W. Weber, R. Ulrich, E. A. Chandross, W. J. Tomlinson, Phys. Lett. 20, 143 (1972).

Wolf, E.

M. Born, E. Wolf, Principles of Optics, (Pergamon, Oxford, 1970), pp. 36–47.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

E. A. Chandross, C. A. Pryde, W. J. Tomlinson, H. P. Weber, Appl. Phys. Lett. 24, 72 (1974).
[CrossRef]

Phys. Lett. (1)

H. W. Weber, R. Ulrich, E. A. Chandross, W. J. Tomlinson, Phys. Lett. 20, 143 (1972).

Other (2)

M. Born, E. Wolf, Principles of Optics, (Pergamon, Oxford, 1970), pp. 36–47.

T. Kurokawa, in The 21st Annual Meeting of the Japan Society of Applied Physics, Saitama (March1974).

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Figures (8)

Fig. 1
Fig. 1

Two kinds of intersections: (a) ordinary intersection with equal refractive index; (b) proposed intersection with higher refractive index.

Fig. 2
Fig. 2

Coordinate system used to calculate the light leak in an intersection with equal refractive index.

Fig. 3
Fig. 3

Region that satisfies light leak conditions from the intersecting point.

Fig. 4
Fig. 4

Two calculated intersecting losses vs intersecting angle.

Fig. 5
Fig. 5

Two calculated intersecting losses vs refractive index difference.

Fig. 6
Fig. 6

Transmission interferogram of an intersection with higher refractive index, fabricated by the photopolymerization method in a 0.03-mm thick film. The interferogram was taken with λ = 546-nm light, using a silicon oil (n = 1.486) for the refractive index matching.

Fig. 7
Fig. 7

Light wave propagating in two kinds of intersecting guides. The 0.1-mm wide guide arrays with 5-l/mm density were formed so as to intersect mutually at right angles. The top photograph shows that intersecting loss was very large, due to light leak in intersections with equal refractive index. The bottom photograph shows that intersecting loss was negligibly small in intersections with higher refractive index.

Fig. 8
Fig. 8

Optical coding system for the coordinates detection.

Tables (1)

Tables Icon

Table I Composition of Casting Solution used in Intersecting Guides Formation

Equations (21)

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- d < x < d ,
- θ c < θ < θ c ,
cos θ c = n / ( n + Δ n ) .
d - x s + 1 < tan θ < d - x s
tan θ < - [ ( d + x ) / 1 ]
s = A B ¯ = 2 d · cot Ψ ,
1 = A B ¯ = 2 d / sin Ψ .
D = I I 0 = F ( x , θ ) d x d θ - d d - θ c θ c F ( x , θ ) d x d θ ,
D = - 1 sin Ψ · ln cos θ c θ c .
D = 1 sin Ψ · ( Δ n 2 n ) 1 / 2 ( Ψ > θ c ) .
R = R ( n 1 , n 2 , ϕ ) .
( π / 2 ) - Ψ - θ c < ϕ < ( π / 2 ) - Ψ + θ c ,
ϕ ( π / 2 ) - Ψ ,
R c = R ( n + Δ n , n + 2 Δ n , π / 2 - Ψ ) + R ( n + Δ n , n + 2 Δ n , π / 2 - Ψ ) · [ 1 - R ( n + Δ n , n + 2 Δ n , π / 2 - Ψ ) ] = 2 R ( n + Δ n , n + 2 Δ n , π / 2 - Ψ ) - R 2 ( n + Δ n , n + 2 Δ n , π / 2 - Ψ ) .
L D = - 10 · log ( 1 - D ) ,
L R = - 10 · log ( 1 - R c ) ,
C 2 = | 4 β 1 β 2 ( β 1 + β 2 ) 2 exp ( 2 i β 2 d ) + ( β 1 - β 2 ) 2 exp ( - 2 i β 2 d ) | 2 ,
β 1 ( n + Δ n / 2 ) k 0 ,
β 2 ( n + 3 Δ n / 2 ) k 0 ,
Δ P = 1 - C 2 ( Δ n / n ) 2 cos 2 ( 2 β 2 d ) .
R c = 1 2 · ( Δ n n ) 2

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