Abstract

Information contained in the position of the peaks of backscattered light intensity from an unclad fiber, with laser light incident at right angles to the fiber axis, is utilized to determine the parameter b/λ (b = fiber radius, λ free space wavelength). For known laser wavelength the fiber diameter can thus be determined. The theory is based on an approximate ray analysis and is compared with the results of the exact wave theory. Good agreement is obtained. The accuracy of this procedure may vary between 1% and 10%.

© 1975 Optical Society of America

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References

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  1. H. M. Presby, J. Opt. Soc. Am. 64, 280 (1974).
    [CrossRef]
  2. H. M. Presby, D. Marcuse, Appl. Opt. 13, 2882 (1974).
    [CrossRef] [PubMed]
  3. H. M. Nussenzveig, J. Math. Phys. 10, 125 (1969).
    [CrossRef]
  4. D. Marcuse, H. M. Presby, J. Opt. Soc. Am. 65, 367 (1975).
    [CrossRef]
  5. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  6. L. S. Watkins, J. Opt. Soc. Am. 64, 767 (1974).
    [CrossRef]

1975

1974

1969

H. M. Nussenzveig, J. Math. Phys. 10, 125 (1969).
[CrossRef]

Appl. Opt.

J. Math. Phys.

H. M. Nussenzveig, J. Math. Phys. 10, 125 (1969).
[CrossRef]

J. Opt. Soc. Am.

Other

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

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Figures (5)

Fig. 1
Fig. 1

Schematic of the scattering geometry. The three scattered rays used in the approximate analysis are shown.

Fig. 2
Fig. 2

Definition of angles used in the ray analysis.

Fig. 3
Fig. 3

Backscattered light intensity in relative units for kb = 600 and n = 1.457. The lowest trace is obtained from the exact wave analysis, the center trace is the result of the approximate ray theory, the upper trace results by ignoring ray 1 (see Figs. 1 and 2).

Fig. 4
Fig. 4

This figure allows the determination of kb from the measured difference Δψ between the scattering peaks labeled 1 and 2 in Fig. 3. The parameter n is the refractive index of the fiber.

Fig. 5
Fig. 5

Same as Fig. 3 with kb = 100.

Equations (19)

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ψ = 4 arcsin x n 2 arcsin x ,
x = ( d i / b ) .
d ψ d x = 4 ( n 2 x 2 ) 1 / 2 2 ( 1 x 2 ) 1 / 2 .
x = ( 4 n 2 3 ) 1 / 2 ,
ψ max = 4 arcsin ( 4 n 2 3 n 2 ) 1 / 2 2 arcsin ( 4 n 2 3 ) 1 / 2 .
ψ max ψ ψ max .
Φ 2 , 3 = k b ( 4 n cos α + 1 + cos ψ 2 2 cos α i )
α i = arcsin x ,
α = arcsin x n ,
k = 2 π λ = free space propagation constant .
Φ r = π + k b ( 1 cos ψ 2 ) .
P ( ψ ) = | [ 4 ( n 2 x 2 2 ) 1 / 2 2 ( 1 x 2 2 ) 1 / 2 ] 1 / 2 exp ( i Φ 2 ) + [ 4 ( n 2 x 3 2 ) 1 / 2 2 ( 1 x 3 2 ) 1 / 2 ] 1 / 2 exp ( i Φ 3 ) ( cos ψ 2 2 ) 1 / 2 exp ( i Φ r ) | 2 .
x r = sin ψ 2 .
d ψ d x r = 2 cos ψ 2 .
k b = 4 ( 2 n ) π ψ m B 2 ψ m A 2 .
( Φ 2 Φ 3 ) 1 = 2 π
( Φ 2 Φ 3 ) 2 = 4 π .
Φ 2 Φ r = 2 n π n = integer
k b = 2 π Δ ψ ( x + sin ψ 2 ) ;

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