Abstract

We have extended the Gloge-Marcatili analysis to include the effect of a refractive-index dip in a multimode fiber characterized a square-law profile. The analysis gives analytical expressions for the propagation characteristics and shows that the dip has a very significant effect on the impulse response.

© 1983 Optical Society of America

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References

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  1. W. A. Gambling, D. N. Payne, C. R. Hammond, S. R. Norman, Proc. IEEE 123, 570 (1976).
  2. E. Khular, A. Kumar, A. K. Ghatak, B. P. Pal, Opt. Commun. 23, 263 (1977).
    [CrossRef]
  3. D. Marcuse, H. M. Presby, Appl. Opt. 18, 3758 (1979).
    [PubMed]
  4. D. Gloge, E. A. J. Marcatili, Bell Syst. Tech. J. 52, 1563 (1973).

1979 (1)

1977 (1)

E. Khular, A. Kumar, A. K. Ghatak, B. P. Pal, Opt. Commun. 23, 263 (1977).
[CrossRef]

1976 (1)

W. A. Gambling, D. N. Payne, C. R. Hammond, S. R. Norman, Proc. IEEE 123, 570 (1976).

1973 (1)

D. Gloge, E. A. J. Marcatili, Bell Syst. Tech. J. 52, 1563 (1973).

Gambling, W. A.

W. A. Gambling, D. N. Payne, C. R. Hammond, S. R. Norman, Proc. IEEE 123, 570 (1976).

Ghatak, A. K.

E. Khular, A. Kumar, A. K. Ghatak, B. P. Pal, Opt. Commun. 23, 263 (1977).
[CrossRef]

Gloge, D.

D. Gloge, E. A. J. Marcatili, Bell Syst. Tech. J. 52, 1563 (1973).

Hammond, C. R.

W. A. Gambling, D. N. Payne, C. R. Hammond, S. R. Norman, Proc. IEEE 123, 570 (1976).

Khular, E.

E. Khular, A. Kumar, A. K. Ghatak, B. P. Pal, Opt. Commun. 23, 263 (1977).
[CrossRef]

Kumar, A.

E. Khular, A. Kumar, A. K. Ghatak, B. P. Pal, Opt. Commun. 23, 263 (1977).
[CrossRef]

Marcatili, E. A. J.

D. Gloge, E. A. J. Marcatili, Bell Syst. Tech. J. 52, 1563 (1973).

Marcuse, D.

Norman, S. R.

W. A. Gambling, D. N. Payne, C. R. Hammond, S. R. Norman, Proc. IEEE 123, 570 (1976).

Pal, B. P.

E. Khular, A. Kumar, A. K. Ghatak, B. P. Pal, Opt. Commun. 23, 263 (1977).
[CrossRef]

Payne, D. N.

W. A. Gambling, D. N. Payne, C. R. Hammond, S. R. Norman, Proc. IEEE 123, 570 (1976).

Presby, H. M.

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

D. Gloge, E. A. J. Marcatili, Bell Syst. Tech. J. 52, 1563 (1973).

Opt. Commun. (1)

E. Khular, A. Kumar, A. K. Ghatak, B. P. Pal, Opt. Commun. 23, 263 (1977).
[CrossRef]

Proc. IEEE (1)

W. A. Gambling, D. N. Payne, C. R. Hammond, S. R. Norman, Proc. IEEE 123, 570 (1976).

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Figures (2)

Fig. 1
Fig. 1

Square-law profile with a dip on the fiber axis.

Fig. 2
Fig. 2

Impulse response of a fiber with a square-law profile having a dip on the axis. The calculations assume equal excitation of modes and correspond to Δ = Δ′ = 0.01 = (b/a)2. The shaded area corresponds to a perfect square-law profile.

Equations (17)

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m ( β ) = 0 r 0 [ k 0 2 n 2 ( r ) - β 2 ] r d r ,
n 2 ( r ) = { n 3 2 [ 1 + ɛ ( r a ) ] 0 < r < b , n 1 2 [ 1 - 2 Δ ( r a ) 2 ] b < r < a , n 1 2 [ 1 - 2 Δ ] = n 2 2 r > a .
ɛ ( b a ) = 2 Δ 1 - 2 Δ [ 1 - Δ Δ ( b a ) 2 ] ,
2 Δ n 1 2 - n 3 2 n 1 2 .
m ( β ) = a 2 8 Δ k 1 2 ( k 1 2 - β 2 ) 2 - ϕ ,
k 1 = n 1 k 0 , ϕ = 1 6 V 1 2 [ 1 + 1 2 Δ Δ ( b a ) 2 ] , V 1 = k 0 b n 1 2 - n 3 2 . }
M = 1 4 V 2 - 1 6 V 1 2 [ 1 + 1 2 Δ Δ ( b a ) 2 ] ,
δ = 1 2 [ 1 - β 2 k 1 2 ] = 2 Δ a k 1 [ m ( β ) + ϕ ] 1 / 2 ,
m ( β ) + ϕ M + ϕ = ( δ Δ ) 2 .
Δ ( b a ) 2 < δ < Δ .
β 2 = k 1 2 - k 1 2 [ 8 Δ m a 2 k 1 2 + ψ ] 1 / 2 ,
ψ = 8 Δ a 2 k 1 2 ϕ = 8 3 Δ Δ ( b a ) 2 [ 1 + 1 2 Δ Δ ( b a ) 2 ] ,
τ = L n 1 c d β d k 1 = L n 1 c 1 ( 1 - 2 δ ) 1 / 2 [ 1 - δ - ψ 4 δ ] .
t τ c L n 1 - ( 1 - ψ 4 ) ( - ψ 4 δ + 1 2 δ 2 ) .
δ = Δ / 2 , ψ / 4 δ 4 Δ 2 / 3 ,
δ 2 / 2 = Δ 2 / 8.
1 M d m d t = ( 1 + ϕ m ) 2 δ Δ 2 · d δ d t = 2 Δ 2 [ ( 1 + ϕ M ) ( 1 + ϕ 4 δ 3 ) - 1 ] ,

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