Abstract

A new method is presented to determine the refractive index and the diameter of unclad optical fibers. The technique is based on an analysis of the back-scattered light when a beam from a cw laser impinges upon the fiber. A geometrical-optics analysis shows that the position of a sharp cutoff in the radiation pattern determines the refractive index, whereas the distance between certain successive minima gives the diameter. The theory is compared to experimental observations, with excellent agreement.

© 1974 Optical Society of America

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References

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  1. D. Marcuse, Light Transmission Optics (Van Nostrand–Reinhold, New York, 1972).
  2. D. Marcuse, Bell Syst. Tech. J. 51, 229 (1972).
    [Crossref]
  3. D. Marcuse, Bell. Syst. Tech. J. 48, 3187 (1969).
    [Crossref]
  4. N. S. Kapany, Fiber Optics (Academic, New York, 1967).
  5. N. S. Kapany, J. Opt. Soc. Am. 47, 413 (1957).
    [Crossref]
  6. R. C. Faust, Proc. Phys. Soc. (London) B67, 138 (1954).
  7. R. P. Gagilano, R. M. Lumley, and G. S. Watkins, Proc. IEEE 57, 114 (1969).
    [Crossref]
  8. M. Koedam, Philips Tech. Rev. 27, 208 (1966).
  9. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

1972 (1)

D. Marcuse, Bell Syst. Tech. J. 51, 229 (1972).
[Crossref]

1969 (2)

D. Marcuse, Bell. Syst. Tech. J. 48, 3187 (1969).
[Crossref]

R. P. Gagilano, R. M. Lumley, and G. S. Watkins, Proc. IEEE 57, 114 (1969).
[Crossref]

1966 (1)

M. Koedam, Philips Tech. Rev. 27, 208 (1966).

1957 (1)

1954 (1)

R. C. Faust, Proc. Phys. Soc. (London) B67, 138 (1954).

Faust, R. C.

R. C. Faust, Proc. Phys. Soc. (London) B67, 138 (1954).

Gagilano, R. P.

R. P. Gagilano, R. M. Lumley, and G. S. Watkins, Proc. IEEE 57, 114 (1969).
[Crossref]

Kapany, N. S.

N. S. Kapany, J. Opt. Soc. Am. 47, 413 (1957).
[Crossref]

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

Kerker, M.

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

Koedam, M.

M. Koedam, Philips Tech. Rev. 27, 208 (1966).

Lumley, R. M.

R. P. Gagilano, R. M. Lumley, and G. S. Watkins, Proc. IEEE 57, 114 (1969).
[Crossref]

Marcuse, D.

D. Marcuse, Bell Syst. Tech. J. 51, 229 (1972).
[Crossref]

D. Marcuse, Bell. Syst. Tech. J. 48, 3187 (1969).
[Crossref]

D. Marcuse, Light Transmission Optics (Van Nostrand–Reinhold, New York, 1972).

Watkins, G. S.

R. P. Gagilano, R. M. Lumley, and G. S. Watkins, Proc. IEEE 57, 114 (1969).
[Crossref]

Bell Syst. Tech. J. (1)

D. Marcuse, Bell Syst. Tech. J. 51, 229 (1972).
[Crossref]

Bell. Syst. Tech. J. (1)

D. Marcuse, Bell. Syst. Tech. J. 48, 3187 (1969).
[Crossref]

J. Opt. Soc. Am. (1)

Philips Tech. Rev. (1)

M. Koedam, Philips Tech. Rev. 27, 208 (1966).

Proc. IEEE (1)

R. P. Gagilano, R. M. Lumley, and G. S. Watkins, Proc. IEEE 57, 114 (1969).
[Crossref]

Proc. Phys. Soc. (London) (1)

R. C. Faust, Proc. Phys. Soc. (London) B67, 138 (1954).

Other (3)

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

D. Marcuse, Light Transmission Optics (Van Nostrand–Reinhold, New York, 1972).

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

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Figures (8)

Fig. 1
Fig. 1

Setup to observe back-scattered light.

Fig. 2
Fig. 2

Incident, reflected, and refracted ray paths.

Fig. 3
Fig. 3

Rays incident upon fiber, traced for a single internal reflection.

Fig. 4
Fig. 4

Plot of θ and Φ vs l/a for a fiber of n = 1.50.

Fig. 5
Fig. 5

Plot of Lm/h vs δ for − 0.7, 0.01, 0.7.

Fig. 6
Fig. 6

Photographs of back-scattering patterns a: vitreous silica, n = 1.457, d = 280 μm; b: soda–lime silicate, n = 1.508, d = 424 μm; c: vitreous silica, n = 1.457, d = 176 μm.

Fig. 7
Fig. 7

Ray considerations to determine fiber diameter.

Fig. 8
Fig. 8

Plot of theoretical and experimental ΔL vs L.

Tables (2)

Tables Icon

Table I Results of refractive-index measurements.

Tables Icon

Table II Results of diameter measurements.

Equations (18)

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i 0 = i 1
n 0 sin i 0 = n sin r .
θ = π + 2 i - 4 r .
cos i m = ( n 2 - 1 3 ) 1 2 .
L m = h tan Φ m
Φ m = 4 sin - 1 [ 2 n 3 ( 1 - n 2 4 ) 1 2 ] - 2 sin - 1 [ 2 3 ( 1 - n 2 4 ) 1 2 ] .
Φ m = 22.84 - δ ( 1.58 ) + δ 2 ( 0.192 ) .
i = π θ 2 = 2 r - i ,
B C = a [ cos ( 2 r - i ) - cos i ]
C D = 2 n a cos r .
S = 4 n a cos r - 4 a sin r sin ( r - i ) .
S = 4 a [ ( 1 - sin 2 i n 2 ) 1 2 ( n + sin 2 i n ) - sin 2 i cos i n 2 ] .
S = 4 a [ n + Φ 2 16 ( 1 - n / 2 ) ] .
ϕ = 2 π S λ = 8 π a λ [ n + Φ 2 16 ( 1 - n / 2 ) ] .
ϕ 1 - ϕ 2 = 2 π = 8 π a λ [ Φ 1 2 - Φ 2 2 16 ( 1 - n / 2 ) ]
Φ 1 = [ Φ 2 2 + 4 λ a ( 1 - n / 2 ) ] 1 2 .
Δ L = L 1 - L 2 = 2 λ a h 2 L ( 1 - n / 2 )
a = 2 λ h 2 L ( Δ L ) ( 1 - n / 2 ) ,