Abstract

The power distribution as a function of propagation distance in a network of coupled optical waveguides is determined for several interesting cases. An electrically controllable coupler is proposed and analyzed in detail. High efficiency coupling and decoupling between two optical guides can be accomplished with the use of an electrooptically generated dynamic channel, of finite length, located in between the two guides.

© 1974 Optical Society of America

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References

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  1. A. Ihaya, H. Furuta, H. Noda, Proc. IEEE 60, 470 (1972).
    [CrossRef]
  2. S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, R. G. Hunsperger, Appl. Phys. Lett. 22, 46 (1973).
    [CrossRef]
  3. R. Bellman, Introduction to Matrix Algebra (McGraw-Hill, New York, 1970).
  4. E. Garmire, H. Stoll, A. Yariv, R. G. Hunsperger, Appl. Phys. Lett. 21, 87 (1972).
    [CrossRef]
  5. D. J. Channin, Appl. Phys. Lett. 19, 128 (1971).
    [CrossRef]
  6. E. A. J. Marcatilli, Bell Syst. Tech. J. 48, 2071 (1969).
  7. H. F. Taylor, J. Appl. Phys., 44, 3257 (1973).
    [CrossRef]

1973 (2)

S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, R. G. Hunsperger, Appl. Phys. Lett. 22, 46 (1973).
[CrossRef]

H. F. Taylor, J. Appl. Phys., 44, 3257 (1973).
[CrossRef]

1972 (2)

A. Ihaya, H. Furuta, H. Noda, Proc. IEEE 60, 470 (1972).
[CrossRef]

E. Garmire, H. Stoll, A. Yariv, R. G. Hunsperger, Appl. Phys. Lett. 21, 87 (1972).
[CrossRef]

1971 (1)

D. J. Channin, Appl. Phys. Lett. 19, 128 (1971).
[CrossRef]

1969 (1)

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

Bellman, R.

R. Bellman, Introduction to Matrix Algebra (McGraw-Hill, New York, 1970).

Channin, D. J.

D. J. Channin, Appl. Phys. Lett. 19, 128 (1971).
[CrossRef]

Furuta, H.

A. Ihaya, H. Furuta, H. Noda, Proc. IEEE 60, 470 (1972).
[CrossRef]

Garmire, E.

S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, R. G. Hunsperger, Appl. Phys. Lett. 22, 46 (1973).
[CrossRef]

E. Garmire, H. Stoll, A. Yariv, R. G. Hunsperger, Appl. Phys. Lett. 21, 87 (1972).
[CrossRef]

Garvin, H. L.

S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, R. G. Hunsperger, Appl. Phys. Lett. 22, 46 (1973).
[CrossRef]

Hunsperger, R. G.

S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, R. G. Hunsperger, Appl. Phys. Lett. 22, 46 (1973).
[CrossRef]

E. Garmire, H. Stoll, A. Yariv, R. G. Hunsperger, Appl. Phys. Lett. 21, 87 (1972).
[CrossRef]

Ihaya, A.

A. Ihaya, H. Furuta, H. Noda, Proc. IEEE 60, 470 (1972).
[CrossRef]

Marcatilli, E. A. J.

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

Noda, H.

A. Ihaya, H. Furuta, H. Noda, Proc. IEEE 60, 470 (1972).
[CrossRef]

Somekh, S.

S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, R. G. Hunsperger, Appl. Phys. Lett. 22, 46 (1973).
[CrossRef]

Stoll, H.

E. Garmire, H. Stoll, A. Yariv, R. G. Hunsperger, Appl. Phys. Lett. 21, 87 (1972).
[CrossRef]

Taylor, H. F.

H. F. Taylor, J. Appl. Phys., 44, 3257 (1973).
[CrossRef]

Yariv, A.

S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, R. G. Hunsperger, Appl. Phys. Lett. 22, 46 (1973).
[CrossRef]

E. Garmire, H. Stoll, A. Yariv, R. G. Hunsperger, Appl. Phys. Lett. 21, 87 (1972).
[CrossRef]

Appl. Phys. Lett. (3)

E. Garmire, H. Stoll, A. Yariv, R. G. Hunsperger, Appl. Phys. Lett. 21, 87 (1972).
[CrossRef]

D. J. Channin, Appl. Phys. Lett. 19, 128 (1971).
[CrossRef]

S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, R. G. Hunsperger, Appl. Phys. Lett. 22, 46 (1973).
[CrossRef]

Bell Syst. Tech. J. (1)

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

J. Appl. Phys. (1)

H. F. Taylor, J. Appl. Phys., 44, 3257 (1973).
[CrossRef]

Proc. IEEE (1)

A. Ihaya, H. Furuta, H. Noda, Proc. IEEE 60, 470 (1972).
[CrossRef]

Other (1)

R. Bellman, Introduction to Matrix Algebra (McGraw-Hill, New York, 1970).

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Figures (5)

Fig. 1
Fig. 1

Power distribution in coupled optical networks. Pn is the power in the nth guide as a function of the propagation distance z. K is the coupling constant between neighboring guides. Nonneighboring guides are assumed to be uncoupled. For the case where there is more than one input, these inputs are assumed to be in phase.

Fig. 2
Fig. 2

Different configurations of optical network that could be used in energy transfer, energy distribution, controlled switching (see text).

Fig. 3
Fig. 3

(a) Simplified (ECC) for thin film guides. γ is the percentage change of the index of refraction in the permanent guides. γ is also taken as the percentage change due to the electrooptic effect. (b) Another possible configuration for an ECC.

Fig. 4
Fig. 4

Dynamic efficiency and effective length of the ECC shown in Fig. 3(a), as a function of a/λ, for different values of n1 and γ. The value of D/a is taken equal to 1.5.

Fig. 5
Fig. 5

Possible configuration for a 4-channel optical demultiplexer. The dashed guides are electrically controllable.

Equations (13)

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( d E n ) / ( d z ) = - i K E n + 1 - i K E n - 1 for 2 n N - 1 , ( d E 1 ) / ( d z ) = - i K E 2 , ( d E N ) / ( d z ) = - i K E N - 1 ,
E n ( 0 ) = { 1 for n = m , 0 for n m .
( d / ( d ξ ) E = M · E E ( 0 ) = c ,
E n = ( - i ) n - m J n - m ( 2 ξ ) .
P 1 ( z ) = 1 4 [ cos ( K 2 z ) + 1 ] 2 , P 2 ( z ) = 1 2 [ sin ( K 2 z ) ] 2 , P 3 ( z ) = 1 4 [ cos ( K 2 z ) - 1 ] 2 ,
P 1 ( z ) = cos 2 ( K z ) , P 2 ( z ) = sin 2 ( K z ) ,
Δ P = sin 2 [ ( π / 2 ) ( K / K ) ] .
η = 1 - Δ P = cos 2 [ ( π / 2 ) ( K / K ) ] .
K = [ ( 2 s 2 δ ) / ( s 2 + δ 2 ) ] { exp [ - δ ( D - a ) ] } / ( κ a )
K = [ ( 2 s 2 δ ) / ( s 2 + δ 2 ) ] { exp [ - δ ( 2 D - a ) ] } / ( κ a ) ,
L = [ π / ( 2 2 ) ] [ ( s 2 + δ 2 ) / ( s 2 δ ) ] κ a exp [ δ ( D - a ) ] , η = cos 2 [ ( π / 2 ) exp ( - δ D ) ] .
a = 2.3 μ , D = 3.45 μ , and L = 304 μ .
a = 3.4 μ , D = 5.1 μ , and L = 920 μ .

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