Abstract

Intramodal dispersion in multimode graded-index power-law profiles has been investigated within the WKB approximation. It is found that the intramodal dispersion is mode dependent. The coupling between material and waveguide effects and the influence of waveguide parameters are particularly evidenced in the wavelength region around 1.3 μm where the material dispersion goes through zero.

© 1981 Optical Society of America

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References

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  1. W. A. Gamling, H. Matsumura, C. M. Ragdale, Microwaves Opt. Acoust. 3, 239 (1979).
    [CrossRef]
  2. D. Marcuse, Appl. Opt. 18, 2930 (1979).
    [CrossRef] [PubMed]
  3. A. W. Snyder, R. A. Sammut, Electron. Lett. 15, 269 (1979).
    [CrossRef]
  4. R. Olshansky, D. B. Keck, Appl. Opt. 15, 483 (1976).
    [CrossRef] [PubMed]
  5. E. A. J. Marcatili, Bell Syst. Tech. J. 56, 49 (1977).
  6. J. W. Fleming, Electron. Lett. 14, 326 (1978).
    [CrossRef]
  7. S. Kobayashi, S. Shibata, N. Shibata, T. Izawa in Technical Digest, First International Conference, IOOC (ECE, Tokyo, 1977), p. 309.
  8. C. C. Timmermann, Nachrichtentech. Z. 31, 822 (1978).

1979 (3)

W. A. Gamling, H. Matsumura, C. M. Ragdale, Microwaves Opt. Acoust. 3, 239 (1979).
[CrossRef]

A. W. Snyder, R. A. Sammut, Electron. Lett. 15, 269 (1979).
[CrossRef]

D. Marcuse, Appl. Opt. 18, 2930 (1979).
[CrossRef] [PubMed]

1978 (2)

J. W. Fleming, Electron. Lett. 14, 326 (1978).
[CrossRef]

C. C. Timmermann, Nachrichtentech. Z. 31, 822 (1978).

1977 (1)

E. A. J. Marcatili, Bell Syst. Tech. J. 56, 49 (1977).

1976 (1)

Fleming, J. W.

J. W. Fleming, Electron. Lett. 14, 326 (1978).
[CrossRef]

Gamling, W. A.

W. A. Gamling, H. Matsumura, C. M. Ragdale, Microwaves Opt. Acoust. 3, 239 (1979).
[CrossRef]

Izawa, T.

S. Kobayashi, S. Shibata, N. Shibata, T. Izawa in Technical Digest, First International Conference, IOOC (ECE, Tokyo, 1977), p. 309.

Keck, D. B.

Kobayashi, S.

S. Kobayashi, S. Shibata, N. Shibata, T. Izawa in Technical Digest, First International Conference, IOOC (ECE, Tokyo, 1977), p. 309.

Marcatili, E. A. J.

E. A. J. Marcatili, Bell Syst. Tech. J. 56, 49 (1977).

Marcuse, D.

Matsumura, H.

W. A. Gamling, H. Matsumura, C. M. Ragdale, Microwaves Opt. Acoust. 3, 239 (1979).
[CrossRef]

Olshansky, R.

Ragdale, C. M.

W. A. Gamling, H. Matsumura, C. M. Ragdale, Microwaves Opt. Acoust. 3, 239 (1979).
[CrossRef]

Sammut, R. A.

A. W. Snyder, R. A. Sammut, Electron. Lett. 15, 269 (1979).
[CrossRef]

Shibata, N.

S. Kobayashi, S. Shibata, N. Shibata, T. Izawa in Technical Digest, First International Conference, IOOC (ECE, Tokyo, 1977), p. 309.

Shibata, S.

S. Kobayashi, S. Shibata, N. Shibata, T. Izawa in Technical Digest, First International Conference, IOOC (ECE, Tokyo, 1977), p. 309.

Snyder, A. W.

A. W. Snyder, R. A. Sammut, Electron. Lett. 15, 269 (1979).
[CrossRef]

Timmermann, C. C.

C. C. Timmermann, Nachrichtentech. Z. 31, 822 (1978).

Appl. Opt. (2)

Bell Syst. Tech. J. (1)

E. A. J. Marcatili, Bell Syst. Tech. J. 56, 49 (1977).

Electron. Lett. (2)

J. W. Fleming, Electron. Lett. 14, 326 (1978).
[CrossRef]

A. W. Snyder, R. A. Sammut, Electron. Lett. 15, 269 (1979).
[CrossRef]

Microwaves Opt. Acoust. (1)

W. A. Gamling, H. Matsumura, C. M. Ragdale, Microwaves Opt. Acoust. 3, 239 (1979).
[CrossRef]

Nachrichtentech. Z. (1)

C. C. Timmermann, Nachrichtentech. Z. 31, 822 (1978).

Other (1)

S. Kobayashi, S. Shibata, N. Shibata, T. Izawa in Technical Digest, First International Conference, IOOC (ECE, Tokyo, 1977), p. 309.

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Figures (5)

Fig. 1
Fig. 1

First-order intramodal dispersion as a function of wavelength for some values of α. The designations L and H refer to lowest- and highest-order modes, respectively. N.A. = 0.15, R = 20.0 μm.

Fig. 2
Fig. 2

Same as Fig. 1 with expanded scale in the 1.3-μm region.

Fig. 3
Fig. 3

First-order spectral dispersion as a function of α for several modes in a fiber with N.A. = 0.15 and R = 20 μm.

Fig. 4
Fig. 4

Comparison of first-order intramodal and pure waveguide dispersion at λ = 1.3087 μm where Sm = 0.0. N.A. = 0.15, R = 20 μm.

Fig. 5
Fig. 5

Comparison of first-order intramodal dispersion of corresponding modes in different fiber structures. Each set of curves is labeled by N.A. and R. (μ,ν) denotes mode numbers [see Eq. (1)].

Tables (1)

Tables Icon

Table I Time Delay Within a Single Fiber Mode Due to Second-Order Spectral Dispersion as a Function of Fiber Length and Source Bandwidth

Equations (24)

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r 1 r 2 κ d r = r 1 r 2 k 0 [ n 2 ( r ) - ( β k 0 ) 2 - ν 2 r 2 k 0 2 ] 1 / 2 d r = ( μ + ½ ) π ,
v g = c N 1 β k 0 n 1 1 - B I ,
B = 1 - ( β k 0 n 1 ) 2 ,
I = r 2 r 2 ( 1 - p 2 ) F κ d r r 1 r 2 ( 1 + r 2 F F r ) F κ d r ,
F ( r , λ ) = 1 - n 2 ( r ) n 1 2 ,
N 1 = n 1 - λ n 1 λ ,
p = n 1 N 1 λ F F λ ,
Δ t s = L v g 2 { v g λ Δ λ + 1 2 [ 2 v g λ 2 - 2 v g ( v g λ ) 2 ] Δ λ 2 } ,
Δ t s = L S 1 Δ λ + L S 2 Δ λ 2 = Δ t s 1 + Δ t s 2 .
v g λ = c N 1 [ - λ ( n 1 N 1 ) n 1 N 1 β k 0 n 1 1 - B I - k 0 λ k 0 ( β k 0 ) ( 1 - B I ) + B k 0 I ( β k 0 ) + B k 0 ( I ) ( β k 0 ) n 1 ( 1 - B I ) 2 ] ,
λ ( n 1 N 1 ) = n 1 n 1 λ - λ ( n 1 λ ) 2 - λ n 1 2 n 1 λ 2 ,
k 0 ( β k 0 ) = n 1 N 1 ( 1 - B I ) - ( β k 0 ) 2 k 0 ( β k 0 ) ,
B k 0 = - 2 ( β k 0 ) n 1 2 k 0 ( β k 0 ) - 2 λ k 0 n 1 λ n 1 ( 1 - B ) .
β k 0 = β ω ω k 0 = c v g .
F = 2 Δ ( r a ) α .
I = I α = 2 - p α α + 2 ,
p α = n 1 N 1 λ Δ Δ λ .
k 0 ( I α ) = λ k 0 p α λ α + 2 .
v g λ = c λ N 1 2 2 n 1 λ 2 .
Δ t m = L λ c 2 n 1 λ 2 Δ λ = L S m Δ λ .
Δ t w = - L c α ( α + 2 ) 2 n 1 2 - ( β k 0 ) 2 ( β k 0 ) 3 [ α n 1 2 - 2 ( β k 0 ) 2 ] Δ λ λ 0 = L S w Δ λ ,
α = 2 ( β k 0 n 1 ) 2 .
S 2 = 1 2 S 1 λ 1 2 S m S m = 1 2 ( 1 c n 1 2 λ 2 + λ c · n 1 3 λ 3 ) .
S 2 - 0.04 psec / km · nm 2 .

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