Abstract

A recently developed, more accurate coupled-mode formulation for arbitrary parallel waveguides is applied to two single-mode weakly guiding coupled fibers. Propagation constants and coupling coefficients are calculated for both identical and dissimilar fiber pairs.

© 1986 Optical Society of America

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References

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  1. R. A. Bergh, H. C. Lefevre, H. J. Shaw, J. Lightwave Technol. LT-2, 91 (1984).
    [CrossRef]
  2. C. M. Davis, Opt. Eng. 24, 347 (1985).
  3. E. G. Rawson, M. D. Bailey, Electron. Lett. 15, 432 (1979).
    [CrossRef]
  4. C. C. Wang, W. K. Burns, C. A. Villaruel, Opt. Lett. 10, 49 (1985).
    [CrossRef] [PubMed]
  5. S. E. Miller, J. Lightwave Technol. LT-2, 488 (1984).
    [CrossRef]
  6. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983), pp. 570et seq.
  7. H. F. Taylor, A. Yariv, Proc. IEEE 62, 1044 (1974).
    [CrossRef]
  8. A. Hardy, W. Streifer, J. Lightwave Technol. LT-3, 1135 (1985).
    [CrossRef]
  9. I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products, 4th ed. (Academic, New York, 1980), p. 634, Eq. (5.54).
  10. M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (U.S. Government Printing Office, Washington, D.C., 1964), Chap. 9, Eqs. (9.1.5) and (9.6.6).

1985 (3)

C. M. Davis, Opt. Eng. 24, 347 (1985).

A. Hardy, W. Streifer, J. Lightwave Technol. LT-3, 1135 (1985).
[CrossRef]

C. C. Wang, W. K. Burns, C. A. Villaruel, Opt. Lett. 10, 49 (1985).
[CrossRef] [PubMed]

1984 (2)

R. A. Bergh, H. C. Lefevre, H. J. Shaw, J. Lightwave Technol. LT-2, 91 (1984).
[CrossRef]

S. E. Miller, J. Lightwave Technol. LT-2, 488 (1984).
[CrossRef]

1979 (1)

E. G. Rawson, M. D. Bailey, Electron. Lett. 15, 432 (1979).
[CrossRef]

1974 (1)

H. F. Taylor, A. Yariv, Proc. IEEE 62, 1044 (1974).
[CrossRef]

Abramowitz, M.

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (U.S. Government Printing Office, Washington, D.C., 1964), Chap. 9, Eqs. (9.1.5) and (9.6.6).

Bailey, M. D.

E. G. Rawson, M. D. Bailey, Electron. Lett. 15, 432 (1979).
[CrossRef]

Bergh, R. A.

R. A. Bergh, H. C. Lefevre, H. J. Shaw, J. Lightwave Technol. LT-2, 91 (1984).
[CrossRef]

Burns, W. K.

Davis, C. M.

C. M. Davis, Opt. Eng. 24, 347 (1985).

Gradshteyn, I. S.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products, 4th ed. (Academic, New York, 1980), p. 634, Eq. (5.54).

Hardy, A.

A. Hardy, W. Streifer, J. Lightwave Technol. LT-3, 1135 (1985).
[CrossRef]

Lefevre, H. C.

R. A. Bergh, H. C. Lefevre, H. J. Shaw, J. Lightwave Technol. LT-2, 91 (1984).
[CrossRef]

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983), pp. 570et seq.

Miller, S. E.

S. E. Miller, J. Lightwave Technol. LT-2, 488 (1984).
[CrossRef]

Rawson, E. G.

E. G. Rawson, M. D. Bailey, Electron. Lett. 15, 432 (1979).
[CrossRef]

Ryzhik, I. M.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products, 4th ed. (Academic, New York, 1980), p. 634, Eq. (5.54).

Shaw, H. J.

R. A. Bergh, H. C. Lefevre, H. J. Shaw, J. Lightwave Technol. LT-2, 91 (1984).
[CrossRef]

Snyder, A. W.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983), pp. 570et seq.

Stegun, I. A.

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (U.S. Government Printing Office, Washington, D.C., 1964), Chap. 9, Eqs. (9.1.5) and (9.6.6).

Streifer, W.

A. Hardy, W. Streifer, J. Lightwave Technol. LT-3, 1135 (1985).
[CrossRef]

Taylor, H. F.

H. F. Taylor, A. Yariv, Proc. IEEE 62, 1044 (1974).
[CrossRef]

Villaruel, C. A.

Wang, C. C.

Yariv, A.

H. F. Taylor, A. Yariv, Proc. IEEE 62, 1044 (1974).
[CrossRef]

Electron. Lett. (1)

E. G. Rawson, M. D. Bailey, Electron. Lett. 15, 432 (1979).
[CrossRef]

J. Lightwave Technol. (3)

S. E. Miller, J. Lightwave Technol. LT-2, 488 (1984).
[CrossRef]

R. A. Bergh, H. C. Lefevre, H. J. Shaw, J. Lightwave Technol. LT-2, 91 (1984).
[CrossRef]

A. Hardy, W. Streifer, J. Lightwave Technol. LT-3, 1135 (1985).
[CrossRef]

Opt. Eng. (1)

C. M. Davis, Opt. Eng. 24, 347 (1985).

Opt. Lett. (1)

Proc. IEEE (1)

H. F. Taylor, A. Yariv, Proc. IEEE 62, 1044 (1974).
[CrossRef]

Other (3)

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products, 4th ed. (Academic, New York, 1980), p. 634, Eq. (5.54).

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (U.S. Government Printing Office, Washington, D.C., 1964), Chap. 9, Eqs. (9.1.5) and (9.6.6).

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983), pp. 570et seq.

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Figures (3)

Fig. 1
Fig. 1

Illustrating the cross section of two coupled fibers.

Fig. 2
Fig. 2

(a) γaβa versus D and (b) κab versus D for two identical fibers.

Fig. 3
Fig. 3

(a) γβ versus D and (b) κab, κba versus D for two dissimilar coupled fibers, a and b. Here, a = 2.477 μm and b = 1.747 μm.

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

Ψ a ( x , y ) = { J 0 ( U a ρ a ) / J 0 ( U a ) 0 ρ a = r a / a 1 K 0 ( W a ρ a ) / K 0 ( W a ) 1 ρ a = r a / a <
U a a ( k 0 2 n 1 a 2 - β a 2 ) 1 / 2 ,
W a a ( β a 2 - k 0 2 n 2 2 ) 1 / 2 ,
E x ( x , y , z ) A ( z ) Ψ a ( x , y ) + B ( z ) Ψ b ( x , y ) ,
d A / d z = i γ a A + i κ a b B ,
d B / d z = i γ b B + i κ b a A .
γ p = β + ( κ ˜ p p - C κ ˜ q p ) / ( 1 - C 2 ) ,             p , q = a , b ,             p q ,
κ p q = [ κ ˜ p q + C ( β p - β q - κ ˜ q q ) ] / ( 1 - C 2 ) ,             p , q = a , b ,             p q ,
C = [ - Ψ a ( x , y ) Ψ b ( x , y ) d x d y ] / ( Φ a Φ b ) 1 / 2 ,
κ ˜ p q = ( k 0 / 2 n ) - Δ n p 2 Ψ p ( x , y ) Ψ q ( x , y ) × d x d y / ( Φ p Φ q ) 1 / 2 ,             p = a , b ,             q = a , b .
Φ p = - Ψ p 2 ( x , y ) d x d y ,             p = a , b ,
Δ n a 2 = { n 1 b 2 - n 2 2 2 n ( n 1 b - n 2 ) ( x , y ) waveguide b 0 otherwise ,
Δ n b 2 ¯ = { n 1 a 2 - n 2 2 2 n ( n 1 a - n 2 ) ( x , y ) waveguide a 0 otherwise .
Φ p = π p 2 [ K 1 ( W p ) V p K 0 ( W p ) U p ] 2 ,             p = a , b ,
V p 2 U p 2 + W p 2 ,             p = a , b .
C = [ U a U b K 0 ( W a ) K 0 ( W b ) π a b V a V b K 1 ( W a ) K 1 ( W b ) ] × - Ψ a ( x , y ) Ψ b ( x , y ) d x d y ,
κ ˜ a a = ( b / a ) 2 U a k 0 ( n 1 b - n 2 ) π V a 2 K 1 2 ( W a ) × 0 1 { 0 2 π [ K 0 ( W a ρ a ) ] 2 d θ b } ρ b d ρ b ,
κ ˜ a b = ( b / a ) U a U b K 0 ( W b ) k 0 ( n 1 b - n 2 ) π J 0 ( U b ) K 1 ( W a ) K 1 ( W b ) V a V b × 0 1 [ 0 2 π K 0 ( W a ρ a ) d θ b ] J 0 ( U b ρ b ) ρ b d ρ b .
ρ p r p / p = ( q / p ) [ ( D / q ) ] 2 + 2 ρ q ( D / q ) cos ( θ q ) + ρ q 2 ] 1 / 2 ,             p = a , b ,             q = a , b ,             p q ,

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