Abstract

Cross talk between neighboring optical fibers is shown to alter the absorption spectrum of the fibers. There is an enhancement of absorption at shorter wavelengths and a consequent shift of the absorption peak towards the short-wavelength end of the spectrum. Curves are presented to illustrate the effect. Results are given in a dimensionless form, applicable to fibers with arbitrary physical parameters.

© 1975 Optical Society of America

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References

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  1. N. S. Kapany, Fiber Optics (Academic, New York, 1967).
  2. W. H. Louisell, Coupled Mode and Parametric Electronics (Wiley, New York, 1960).
  3. A. W. Snyder, J. Opt. Soc. Am. 62, 1267 (1972).
    [Crossref]
  4. P. D. McIntyre and A. W. Snyder, J. Opt. Soc. Am. 63, 1518 (1973).
    [Crossref]
  5. D. Burkhardt, Symp. Soc. Exp. Biol. 16, 86 (1962).
  6. A. W. Snyder, IEEE Trans. MTT-17, 1130 (1969).
  7. A. W. Snyder, Proc. IEEE 60, 757 (1972).
    [Crossref]
  8. A. W. Snyder, IEEE Trans. MTT-17, 1138 (1969).
  9. P. D. McIntyre and A. W. Snyder, J. Opt. Soc. Am. 64, 285 (1974).
    [Crossref] [PubMed]
  10. A. W. Snyder and C. Pask, J. Opt. Soc. Am. 63, 761 (1973).
    [Crossref]
  11. A. W. Snyder and C. Pask, J. Comp. Physiol. 84, 59 (1973).
    [Crossref]
  12. R. Menzel, in The Compound Eye and Vision of Insects, edited by G. A. Horridge (Oxford U. P., Oxford, 1973).

1974 (1)

1973 (3)

1972 (2)

1969 (2)

A. W. Snyder, IEEE Trans. MTT-17, 1138 (1969).

A. W. Snyder, IEEE Trans. MTT-17, 1130 (1969).

1962 (1)

D. Burkhardt, Symp. Soc. Exp. Biol. 16, 86 (1962).

Burkhardt, D.

D. Burkhardt, Symp. Soc. Exp. Biol. 16, 86 (1962).

Kapany, N. S.

N. S. Kapany, Fiber Optics (Academic, New York, 1967).

Louisell, W. H.

W. H. Louisell, Coupled Mode and Parametric Electronics (Wiley, New York, 1960).

McIntyre, P. D.

Menzel, R.

R. Menzel, in The Compound Eye and Vision of Insects, edited by G. A. Horridge (Oxford U. P., Oxford, 1973).

Pask, C.

A. W. Snyder and C. Pask, J. Comp. Physiol. 84, 59 (1973).
[Crossref]

A. W. Snyder and C. Pask, J. Opt. Soc. Am. 63, 761 (1973).
[Crossref]

Snyder, A. W.

IEEE Trans. (2)

A. W. Snyder, IEEE Trans. MTT-17, 1130 (1969).

A. W. Snyder, IEEE Trans. MTT-17, 1138 (1969).

J. Comp. Physiol. (1)

A. W. Snyder and C. Pask, J. Comp. Physiol. 84, 59 (1973).
[Crossref]

J. Opt. Soc. Am. (4)

Proc. IEEE (1)

A. W. Snyder, Proc. IEEE 60, 757 (1972).
[Crossref]

Symp. Soc. Exp. Biol. (1)

D. Burkhardt, Symp. Soc. Exp. Biol. 16, 86 (1962).

Other (3)

N. S. Kapany, Fiber Optics (Academic, New York, 1967).

W. H. Louisell, Coupled Mode and Parametric Electronics (Wiley, New York, 1960).

R. Menzel, in The Compound Eye and Vision of Insects, edited by G. A. Horridge (Oxford U. P., Oxford, 1973).

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Figures (5)

FIG. 1
FIG. 1

Parameters for a two-fiber system. An HE11 mode is assumed excited with unit power in fiber 1.

FIG. 2
FIG. 2

Normalized absorption spectra of the illuminated fiber (fiber 1) in a two-fiber system (——), a fiber in isolation (— — —) and the bulk absorption α(λ) used in the calculations (-----), showing the enhancement of the ultraviolet peak due to coupling between two fibers. V (λ = 300 nm) = 4.0, δ = 0.03, αmaxl = 1.5, l/d = 100, and ds/d = 1.1.

FIG. 3
FIG. 3

Percentage of the incident power absorbed in the illuminated fiber (fiber 1) (——) and in the coupled fiber (fiber 2) (-·-·-), compared with a fiber in isolation (-----). Parameters are the same as in Fig. 2.

FIG. 4
FIG. 4

The enhancement of the uv peak due to cross talk, as a function of V (defined with λ = 300 nm). These values are taken from normalized absorption curves like Fig. 2, and represent the difference of percent power absorbed at the ultraviolet peak (λ = 340 nm), between the illuminated fiber in the two-fiber system and an identical fiber in isolation. δ = 0.03, αmaxl = 1.5, and l/d = 100.

FIG. 5
FIG. 5

Normalized absorption spectra of the illuminated fiber (——) in a two-fiber system and of an identical fiber in isolation (-----) for αmaxl = 1.5, 7.5, 75, ∞ (corresponding to l/d = 100, 500, 5000, ∞). V (λ = 300 nm) = 3.5, δ = 0.01, ds/d = 1.1.

Equations (16)

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P ( z ) = { cos 2 ( C 12 z ) e - γ z fiber 1 sin 2 ( C 12 z ) e - γ z fiber 2 ,
γ ( λ ) = α ( λ ) η ( λ ) .
γ ( λ ) = α ( λ ) η ( λ ) + α ( λ ) [ 1 - η ( λ ) ] .
P A ( λ ) = ω V f 1 ( λ ) E ( x , y , z ) 2 d V ,
E ( x , y , z ) 2 = P ( z ) e ( x , y ) 2 ,
α ( λ ) = ω ( μ / ) 1 / 2 1 ( λ ) ,
P A ( λ ) = α ( λ ) 0 l d z { cos 2 ( C 12 z ) sin 2 ( C 12 z ) } × e - γ z [ ( μ ) 1 / 2 A f e ( x , y ) 2 d A ]
P A ( λ ) = α ( λ ) η ( λ ) 0 l d z { cos 2 ( C 12 z ) sin 2 ( C 12 z ) } e - γ z .
0 z C 12 ( ξ ) d ξ = C 12 ¯ z ,
0 z η ( ξ ) d ξ ,
P A ( λ ) = ( α η 2 γ ) [ 1 - e - γ l ] ± X ( λ ) ,
X ( λ ) = ( α η 2 γ ) { 1 + e - γ l [ 2 C 12 / γ ) sin ( 2 C 12 l ) - cos ( 2 C 12 l ) ] 1 + ( 2 C 12 / γ ) 2 } ,
P T = ( α η γ ) [ 1 - e - γ l ] .
P A ( λ ) = 1 2 [ 1 - e - α η l ] ± X ( λ ) ,
X ( λ ) = 1 2 { 1 + e - α η l [ ( 2 C 12 / α η ) sin ( 2 C 12 l ) - cos ( 2 C 12 l ) ] 1 + ( 2 C 12 / α η ) 2 } ,
V = π d λ n 1 δ ,