Abstract

When Gaussian pulses are transmitted through a monomode dielectric optical waveguide, the pulses are broadened. The total width of a received pulse consists of three components: The width of the emitted pulse and the broadening caused by dispersion in the waveguide together with both the bandwidth of the pulse and the linewidth of the source. The broadened pulses have an oscillating distortion function superimposed on them which deteriorates their resolution. The transmission capacity of an optical monomode transmission system can be calculated from the results of this paper by insertion of the appropriate parameters.

© 1978 Optical Society of America

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References

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  1. F. P. Kapron, D. B. Keck, Appl. Opt. 10, 1519 (1971).
    [CrossRef] [PubMed]
  2. K. Jürgensen, Appl. Opt. 16, 22 (1977).
    [CrossRef] [PubMed]
  3. K. Jürgensen, Appl. Opt. 14, 163 (1975).
    [PubMed]
  4. D. N. Payne, W. A. Gambling, Electron. Lett. 11, 176 (1975).
    [CrossRef]
  5. F. P. Kapron, Electron. Lett. 13, 96 (1977).
    [CrossRef]

1977 (2)

1975 (2)

D. N. Payne, W. A. Gambling, Electron. Lett. 11, 176 (1975).
[CrossRef]

K. Jürgensen, Appl. Opt. 14, 163 (1975).
[PubMed]

1971 (1)

Gambling, W. A.

D. N. Payne, W. A. Gambling, Electron. Lett. 11, 176 (1975).
[CrossRef]

Jürgensen, K.

Kapron, F. P.

Keck, D. B.

Payne, D. N.

D. N. Payne, W. A. Gambling, Electron. Lett. 11, 176 (1975).
[CrossRef]

Appl. Opt. (3)

Electron. Lett. (2)

D. N. Payne, W. A. Gambling, Electron. Lett. 11, 176 (1975).
[CrossRef]

F. P. Kapron, Electron. Lett. 13, 96 (1977).
[CrossRef]

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Equations (28)

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2 b = 2 a [ 1 + ( h 0 L / a 2 ) 2 ] 1 / 2 .
| r ( t * ) | 2 = ( b π ) 1 { exp [ ( t * + T / 2 ) 2 / b 2 ] + exp [ ( t * T / 2 ) 2 / b 2 ] + 2 exp [ T 2 / ( 2 b ) 2 ] · exp ( t * 2 / b 2 ) · cos [ T h 0 L t * / ( a b ) 2 ] } ,
I ( t , L = 0 ) = λ N 0 δ λ exp [ ( λ λ 0 ) 2 / ( Δ λ ) 2 ] · exp [ ( t / a ) 2 ] ,
I ( t , L ) = λ N 0 δ λ ( a / b λ 0 ) exp [ ( λ λ 0 ) 2 / ( Δ λ ) 2 ] · exp [ ( t L / υ λ ) 2 / b λ 0 2 ] .
1 / υ λ = d h / d ω = h = ( n λ · d n / d λ ) / c .
h 0 = ( d 2 h / d ω 2 ) λ 0 = λ 0 3 ( d 2 n / d λ 2 ) λ 0 / ( 2 π c 2 ) .
1 / υ λ = ( 1 / c ) [ n 0 λ 0 ( d n / d λ ) λ 0 ( λ λ 0 ) λ 0 ( d 2 n / d λ 2 ) λ 0 + ] .
I ( t * , L ) λ N 0 δ λ ( a / b λ 0 ) . exp [ ( λ λ 0 ) 2 ( b λ 0 2 + τ s 2 ) / ( Δ λ · b λ 0 ) 2 ( λ λ 0 ) · 2 t * τ s / ( Δ λ · b λ 0 2 ) ( t * / b λ 0 ) 2 ]
t * = t ( L / c ) [ n 0 λ 0 ( d n / d λ ) λ 0 ] ,
τ s = L λ 0 Δ λ ( d 2 n / d λ 2 ) λ 0 / c .
λ δ λ
d λ .
I ( t * , L ) N 0 π 1 / 2 Δ λ exp ( t * 2 / τ 2 ) · a / τ ,
τ = ( b λ 0 2 + τ s 2 ) 1 / 2 .
2 τ = 2 ( a 2 + τ p 2 + τ s 2 ) 1 / 2
a = half of the pulse width at the transmitter ,
τ p = L / ( 2 π a c 2 ) · λ 0 3 ( d 2 n / d λ 2 ) λ 0 ,
τ S = ( L / c ) λ 0 Δ λ ( d 2 n / d λ 2 ) λ 0 .
τ p = 2 π a · λ 0 3 L 2 2 c 2 ( d 2 n d λ 2 ) λ 0 ,
τ S = 2 2 c Δ λ λ 0 2 · λ 0 3 L 2 2 c 2 ( d 2 n d λ 2 ) λ 0 .
a = 1 nsec , λ 0 = 850 nm , c = 3 × 10 8 m · sec 1 , and L = 1 km .
[ d / ( d a ) ] ( a 2 + τ p 2 ) = 0
a optim = [ L λ 0 3 ( d 2 n / d λ 2 ) λ 0 / ( 2 π c 2 ) ] 1 / 2 .
I ( t * , L ) N 0 Δ λ π 1 / 2 a / ( b λ 0 2 + τ S 2 ) 1 / 2 { exp [ ( t * + T / 2 ) 2 / ( b λ 0 2 + τ S 2 ) ] + exp [ ( t * + T / 2 ) 2 / ( b λ 0 2 + τ S 2 ) ] + 2 exp { ( T / 2 b λ 0 ) 2 [ 1 + ( h 0 L τ S ) 2 a 4 ( b λ 0 2 + τ S 2 ) ] } · exp [ t * 2 / ( b λ 0 2 + τ S 2 ) ] · cos [ T h 0 L t * a 2 ( b λ 0 2 + τ S 2 ) ] } .
I ( t * , L ) N 0 Δ λ π 1 / 2 ( a / τ S ) { exp [ ( t * + T / 2 ) 2 / τ S 2 ] + exp [ ( t * T / 2 ) 2 / τ S 2 ] + 2 exp [ ( T / 2 a ) 2 ] · exp [ ( t * / τ S ) 2 ] · cos [ T h 0 L t * / ( a · τ S ) 2 ] } .
( 1 / 2 ) exp [ T / ( 2 τ S ) ] 2 R min .
N max = 1 / T min = [ 4 τ S 2 ln ( 2 R min ) ] 1 / 2
= c / { 2 L λ 0 Δ λ ( d 2 n / d λ 2 ) λ 0 [ ln ( 2 R min ) ] 1 / 2 } .

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