Abstract

Design analysis has been performed on a passive planar multibranch waveguide optical power divider in a z-cut LiNbO3 substrate. Specifically, 5- and 3-branch waveguide structures were investigated with the effective index and field matching methods, taking into account the phase changes in the branches at the branching interface. Conditions for equal power division were examined regarding the appropriate branching angle and the relative index distribution in the branches. Illustrative numerical examples are presented and discussed.

© 1983 Optical Society of America

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References

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  1. H. Sasaki, R. M. De La Rue, Electron. Lett. 12, 459 (1976).
    [CrossRef]
  2. W. K. Burns, A. B. Lee, A. F. Milton, Appl. Phys. Lett. 29, 790 (1976).
    [CrossRef]
  3. M. Masuda, G. L. Yip, Proc. Soc. Photo-Opt. Instrum. Eng. 239, 152 (1980).
  4. M. Masuda, G. L. Yip, Appl. Phys. Lett. 37, 20 (1980).
    [CrossRef]
  5. T. Tamir, Integrated Optics (Springer, New York, 1975).
  6. H. F. Taylor, Appl. Opt. 13, 642 (1974).
    [CrossRef] [PubMed]
  7. H. F. Taylor, Appl. Opt. 16, 711 (1977).
    [CrossRef] [PubMed]
  8. I. Anderson, Proc. IEE (London) 2, 7 (1978).
  9. H. Yajima, in Proceedings, Symposium on Optical and Acoustical Micro-Electronics, J. Fox, Ed. (Polytechnic Press, Brooklyn, 1974), p. 339.
  10. W. K. Burns, A. F. Milton, IEEE J. Quantum Electron. QE-11, 32 (1975).
    [CrossRef]
  11. M. Belanger, G. L. Yip, J. Opt. Soc. Am. 72, 1822 (1982).
  12. D. Marcuse, Bell Syst. Tech. J. 49, 273 (1970).
  13. E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2071 (1969).
  14. J. E. Goell, Bell Syst. Tech. J. 48, 2133 (1969).
  15. H. Sasaki, I. Anderson, IEEE J. Quantum Electron. QE-10, 883 (1978).
    [CrossRef]
  16. A. Yariv, Introduction to Optical Electronics (Holt, Rinehart Winston, New York, 1976), Chap. 13.

1982 (1)

M. Belanger, G. L. Yip, J. Opt. Soc. Am. 72, 1822 (1982).

1980 (2)

M. Masuda, G. L. Yip, Proc. Soc. Photo-Opt. Instrum. Eng. 239, 152 (1980).

M. Masuda, G. L. Yip, Appl. Phys. Lett. 37, 20 (1980).
[CrossRef]

1978 (2)

I. Anderson, Proc. IEE (London) 2, 7 (1978).

H. Sasaki, I. Anderson, IEEE J. Quantum Electron. QE-10, 883 (1978).
[CrossRef]

1977 (1)

1976 (2)

H. Sasaki, R. M. De La Rue, Electron. Lett. 12, 459 (1976).
[CrossRef]

W. K. Burns, A. B. Lee, A. F. Milton, Appl. Phys. Lett. 29, 790 (1976).
[CrossRef]

1975 (1)

W. K. Burns, A. F. Milton, IEEE J. Quantum Electron. QE-11, 32 (1975).
[CrossRef]

1974 (1)

1970 (1)

D. Marcuse, Bell Syst. Tech. J. 49, 273 (1970).

1969 (2)

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

J. E. Goell, Bell Syst. Tech. J. 48, 2133 (1969).

Anderson, I.

I. Anderson, Proc. IEE (London) 2, 7 (1978).

H. Sasaki, I. Anderson, IEEE J. Quantum Electron. QE-10, 883 (1978).
[CrossRef]

Belanger, M.

M. Belanger, G. L. Yip, J. Opt. Soc. Am. 72, 1822 (1982).

Burns, W. K.

W. K. Burns, A. B. Lee, A. F. Milton, Appl. Phys. Lett. 29, 790 (1976).
[CrossRef]

W. K. Burns, A. F. Milton, IEEE J. Quantum Electron. QE-11, 32 (1975).
[CrossRef]

De La Rue, R. M.

H. Sasaki, R. M. De La Rue, Electron. Lett. 12, 459 (1976).
[CrossRef]

Goell, J. E.

J. E. Goell, Bell Syst. Tech. J. 48, 2133 (1969).

Lee, A. B.

W. K. Burns, A. B. Lee, A. F. Milton, Appl. Phys. Lett. 29, 790 (1976).
[CrossRef]

Marcatili, E. A. J.

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

Marcuse, D.

D. Marcuse, Bell Syst. Tech. J. 49, 273 (1970).

Masuda, M.

M. Masuda, G. L. Yip, Proc. Soc. Photo-Opt. Instrum. Eng. 239, 152 (1980).

M. Masuda, G. L. Yip, Appl. Phys. Lett. 37, 20 (1980).
[CrossRef]

Milton, A. F.

W. K. Burns, A. B. Lee, A. F. Milton, Appl. Phys. Lett. 29, 790 (1976).
[CrossRef]

W. K. Burns, A. F. Milton, IEEE J. Quantum Electron. QE-11, 32 (1975).
[CrossRef]

Sasaki, H.

H. Sasaki, I. Anderson, IEEE J. Quantum Electron. QE-10, 883 (1978).
[CrossRef]

H. Sasaki, R. M. De La Rue, Electron. Lett. 12, 459 (1976).
[CrossRef]

Tamir, T.

T. Tamir, Integrated Optics (Springer, New York, 1975).

Taylor, H. F.

Yajima, H.

H. Yajima, in Proceedings, Symposium on Optical and Acoustical Micro-Electronics, J. Fox, Ed. (Polytechnic Press, Brooklyn, 1974), p. 339.

Yariv, A.

A. Yariv, Introduction to Optical Electronics (Holt, Rinehart Winston, New York, 1976), Chap. 13.

Yip, G. L.

M. Belanger, G. L. Yip, J. Opt. Soc. Am. 72, 1822 (1982).

M. Masuda, G. L. Yip, Appl. Phys. Lett. 37, 20 (1980).
[CrossRef]

M. Masuda, G. L. Yip, Proc. Soc. Photo-Opt. Instrum. Eng. 239, 152 (1980).

Appl. Opt. (2)

Appl. Phys. Lett. (2)

W. K. Burns, A. B. Lee, A. F. Milton, Appl. Phys. Lett. 29, 790 (1976).
[CrossRef]

M. Masuda, G. L. Yip, Appl. Phys. Lett. 37, 20 (1980).
[CrossRef]

Bell Syst. Tech. J. (3)

D. Marcuse, Bell Syst. Tech. J. 49, 273 (1970).

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

J. E. Goell, Bell Syst. Tech. J. 48, 2133 (1969).

Electron. Lett. (1)

H. Sasaki, R. M. De La Rue, Electron. Lett. 12, 459 (1976).
[CrossRef]

IEEE J. Quantum Electron. (2)

W. K. Burns, A. F. Milton, IEEE J. Quantum Electron. QE-11, 32 (1975).
[CrossRef]

H. Sasaki, I. Anderson, IEEE J. Quantum Electron. QE-10, 883 (1978).
[CrossRef]

J. Opt. Soc. Am. (1)

M. Belanger, G. L. Yip, J. Opt. Soc. Am. 72, 1822 (1982).

Proc. IEE (London) (1)

I. Anderson, Proc. IEE (London) 2, 7 (1978).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

M. Masuda, G. L. Yip, Proc. Soc. Photo-Opt. Instrum. Eng. 239, 152 (1980).

Other (3)

T. Tamir, Integrated Optics (Springer, New York, 1975).

H. Yajima, in Proceedings, Symposium on Optical and Acoustical Micro-Electronics, J. Fox, Ed. (Polytechnic Press, Brooklyn, 1974), p. 339.

A. Yariv, Introduction to Optical Electronics (Holt, Rinehart Winston, New York, 1976), Chap. 13.

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Figures (6)

Fig. 1
Fig. 1

Geometry of the problem: (A) branch interface of a general 5-branch waveguide; (B) symmetric 5-branch waveguide; (C) symmetric 3-branch waveguide.

Fig. 2
Fig. 2

Power distribution in a 5-branch waveguide as a function of the branching angle.

Fig. 3
Fig. 3

Power distribution in a 5-branch waveguide as a function of ΔN1,5: (A) θ = 1°; (B) θ = 2°.

Fig. 4
Fig. 4

Power distribution in a 5-branch waveguide as a function of ΔN1,2,4,5.

Fig. 5
Fig. 5

Power distribution in a 5-branch waveguide as a function of N1,5: (A) θ = 1°; ΔN2,4 = 0.25% Δns(0.01); (B) θ = 1°; ΔN2,4 = 3% Δns(0.01).

Fig. 6
Fig. 6

Power distribution in a 3-branch waveguide. (A) as a function of the branching angle; (B) as a function of ΔN1,3 for θ = 1°.

Tables (3)

Tables Icon

Table I Coupling Coefficients Between the Bent Branches and the Central One

Tables Icon

Table II Transmission Coefficients Between the Main Guide and the Branches

Tables Icon

Table III Transmission Coefficients Between the Main Guide and the Branches

Equations (41)

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E yo = E o ξ o ( x o ) exp ( j β o z o ) .
E yi = E i ξ i ( x i ) exp ( j β i z i ) ; i = 1 , 2 , , 5 .
x i = μ i [ x + pD i + q ( D i 1 D i ) / 2 ] ,
x i = μ i [ x + pD i 1 + q ( D i D i 1 ) / 2 ] ,
z i = α i [ x + pD i + q ( D i 1 D i ) / 2 ] = δ i x i ,
z i = α i [ x + pD i 1 + q ( D i D i 1 ) / 2 ] = δ i x i ,
μ 1 = cos ( θ 1 + θ 2 ) , α 1 = sin ( θ 1 + θ 2 ) , δ 1 = tan ( θ 1 + θ 2 ) , μ 2 = cos θ 2 , α 2 = sin θ 2 , δ 2 = tan θ 2 , μ 4 = cos θ 4 , α 4 = sin θ 4 , δ 4 = tan θ 4 , μ 5 = cos ( θ 4 + θ 5 ) , α 5 = sin ( θ 4 + θ 5 ) , δ 5 = tan ( θ 4 + θ 5 ) ,
E 0 ξ 0 ( x 0 ) = E 1 ξ 1 ( x 1 ) exp ( j β 1 δ 1 x 1 ) + E 2 ξ 2 ( x 2 ) exp ( j β 2 δ 2 x 2 ) + E 3 ξ 3 ( x 3 ) + E 4 ξ 4 ( x 4 ) exp ( j β 4 δ 4 x 4 ) + E 5 ξ 5 ( x 5 ) exp ( j β 5 δ 5 x 5 ) + E rad ,
ϕ i = p β i δ i x i ; i = 1 , 2 , , 5 ,
E 5 I 55 = E o I 50 E 1 I 51 E 2 I 52 E 3 I 53 E 4 I 54 ,
I ij = ξ i ( x i ) ξ j ( x i ) exp j ( ϕ i + ϕ j ) dx j .
E o I io = j = 1 j E j I ij ; i = 1 , 2 , 3 , 4 , 5
P i = E is 2 2 ω μ ξ yi 2 ( x i ) dx i = 1 .
E is = 2 ω μ β i I ii , i = 0 , 1 , , 5 ,
[ K ij ] [ A i / A o ] = [ K io ] ,
K ij = β i β j I ij I ii I jj ,
A i = E i E is .
P tot = i = 1 5 | A i / A o | 2 .
P s = 1 P tot .
E y = A cos ( k 3 x ) ;
k 3 2 = k 0 2 N 3 2 β 0 2 , E y = A cosh ( k 3 x ) ;
k 3 2 = β 0 2 k 0 2 N 3 2 .
E y = B cos k 4 ( x d 2 ) ± C sin k 4 ( x d 2 )
k 4 2 = k 2 2 = k 0 2 N 4 2 β 0 2 ,
E y = B cosh k 4 ( x d 2 ) ± C sinh k 4 ( x d 2 )
k 4 2 = k 2 2 = β 0 2 k 0 2 N 4 2 ,
E y = D cosh k 5 ( x 3 d 2 ) ± F sinh k 4 ( x 3 d 2 )
k 5 2 = k 1 2 = k 0 2 N 5 2 β 0 2 ,
E y = G exp [ γ s ( x 5 d 2 ) ]
γ s 2 = β 0 2 k 0 2 n ext 2 ,
H z = 1 j ω μ 0 E y x .
E yi = A i cos k i x i ,
k i 2 = k o 2 N i 2 β i 2 .
E yi = C i exp [ γ i ( x i d i 2 ) ] ,
γ i 2 = β i 2 k o 2 n ext 2 ,
H z = 1 j ω μ 0 E yi x i .
[ 1 ( K 34 + K 32 ) ( K 35 + K 31 ) K 43 ( 1 + K 42 ) ( K 45 + K 41 ) K 53 ( K 52 + K 54 ) ( 1 + K 51 ) ] [ A 3 / A 0 A 4 / A 0 A 5 / A 0 ] = [ K 30 K 40 K 50 ] ,
[ 1 K 32 ( K 23 + K 31 ) ( 1 + K 31 ) ] [ A 2 / A 0 A 3 / A 0 ] = [ K 20 K 30 ] .
P i = 1 ( K 0 θ c γ 0 ) = 0.9 ,
γ 0 = k 0 ( β ̅ 2 n 1 2 ) 1 / 2
K 0 = 2 ( n 2 2 β ̅ 2 ) ( β ̅ 2 n 1 2 ) 1 / 2 β ̅ d ( n 2 2 n 1 2 ) ,

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