Abstract

The theoretical characteristics of the scattered-light pattern from a clad glass fiber illuminated by a laser beam perpendicular to its axis agree closely with results of experimental measurements of the scattered light. A simplified geometric ray-tracing technique shows that for fibers with medium and small core sizes, specific angle ranges of the scattering pattern provide determinations of fiber diameter independent of core parameters. Measurements of the fringe modulation give relatively sensitive determinations of core diameter. Light scattering is a useful technique for determining the diameters of both clad and unclad fiber. Total-diameter determinations have accuracies of ±0.2 μm and core diameters, ±0.5 μm for 0.02 refractive-index difference between core and cladding.

© 1974 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Kerker and E. Matijević, J. Opt. Soc. Am. 51, 506 (1961).
    [CrossRef]
  2. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  3. J. L. Lundberg, J. Col. Int. Sci. 29, 565 (1969).
    [CrossRef]
  4. M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, New York, 1964).
  5. PIN 10 is a product of United Detector Technology Inc., Santa Monica, Calif.

1969 (1)

J. L. Lundberg, J. Col. Int. Sci. 29, 565 (1969).
[CrossRef]

1961 (1)

Born, M.

M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, New York, 1964).

Kerker, M.

Lundberg, J. L.

J. L. Lundberg, J. Col. Int. Sci. 29, 565 (1969).
[CrossRef]

Matijevic, E.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, New York, 1964).

J. Col. Int. Sci. (1)

J. L. Lundberg, J. Col. Int. Sci. 29, 565 (1969).
[CrossRef]

J. Opt. Soc. Am. (1)

Other (3)

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, New York, 1964).

PIN 10 is a product of United Detector Technology Inc., Santa Monica, Calif.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Schematic of fiber, showing coordinate axes.

Fig. 2
Fig. 2

Scattered light flux as a function of scattering angle θ calculated by use of the wave theory. Curve (a) was for an assumed fiber with a core diameter = 20 μm, core index = 1.557, a total diameter = 40.05 μm, and a cladding index = 1.457. Curve (b) was for a core index = 1.467 and curve (c) was for core index = 1.457, that is, an unclad fiber. Curves show increased modulation effects due to increased index difference between core and cladding.

Fig. 3
Fig. 3

Same results as in Fig. 2 for the scattering-angle range θ = 145–180°.

Fig. 4
Fig. 4

Cross section of fiber, showing paths of refracted and reflected rays that leave the fiber at same scattering angle θ.

Fig. 5
Fig. 5

Composite graphs of experimental and theoretical scattering patterns. (a) Compares wave theory to the experimentally measured patterns—heavy line shows experimental results; (b) is fringe position calculated from path difference between refracted and reflected rays using geometric ray tracing; (c) is fringe modulation found by geometrically calculating the interference between the refracted ray that traverses core and one that goes through only the cladding.

Fig. 6
Fig. 6

Same results as in Fig. 5, at scattering angles near θF, to show the cutoff of the interference fringes.

Fig. 7
Fig. 7

Cross section of fiber, which shows the refracted ray at the angle of incidence that just grazes the core. Bounds for the scattering angles θc and θu are indicated. Dashed ray is through cladding only and leaves at the same scattering angle as the ray through the core.

Fig. 8
Fig. 8

Graph showing fringe variation below θc, due to variations of core index, and lack of fringe variation above θc.

Fig. 9
Fig. 9

Schematic layout of motor-driven spectrometer table used to record fiber scattering patterns.

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

( r > b )             u = n = - F n { J n ( k r ) - b n H n ( k r ) } ,
( b > r > a )             u = n = - F n { B n 1 J n ( m 1 k r ) - b n 1 H n ( m 1 k r ) } ,
( r < a )             u = n = - F n { B n 2 J ( m 2 k r ) } ,
I p = | 2 π k r e ( i k r + i ω t - i 3 π 4 ) n = - b n e i n θ | 2 = λ π 2 r b 0 + 2 n = 1 b n cos ( n θ ) 2 ,
k = a m 2 sin δ = a m 1 sin γ = b m 1 sin β = b sin α ,
θ 2 = α - β + γ - δ .
P 2 = 2 m 2 a cos δ
P 1 = 2 m 1 ( b cos β - a cos γ ) .
P = P 2 + P 1 - λ 4 ,
U = 2 ( b cos α - b sin θ 2 ) + λ 2 ,
Δ = ( P - U ) ;
θ c = 2 [ sin - 1 ( a m 1 b ) - sin - 1 ( a b ) ]
θ u = 2 [ π 2 + sin - 1 [ a m 1 b ] - sin - 1 [ a b ] - sin - 1 [ m 1 m 2 ] ] .
Δ m = ( P 2 + P 1 ) - P c ,
Δ = 2 b [ sin θ 2 + ( m 1 2 + 1 - 2 m 1 cos θ 2 ) ] + λ 2 .
θ F = 2 [ π 2 - sin - 1 [ 1 m 1 ] + sin - 1 [ b a m 1 ] - sin - 1 [ b a m 2 ] . ]
θ F = 2 cos - 1 [ 1 m 1 ] .