Abstract

A new technique for measuring the refractive index profile of single-mode fibers based on the reflection method is described, and experimental results are demonstrated. When the core radius of a test fiber is only a few times larger than the laser beam spot size, the reflected power distribution does not indicate the refractive index correctly. However, the true index profile can be calculated from the beam spot size and the reflected power distribution with high accuracy: 0.3-μm spatial resolution and 5% relative refractive-index resolution are obtained for practical single-mode fibers.

© 1978 Optical Society of America

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References

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  1. W. E. Martine, Appl. Opt. 13, 9 (1974).
  2. D. Gloge, E. A. J. Marcatili, Bell Syst. Tech. J. 52, 9 (1973).
  3. T. Okoshi, K. Hotate, Appl. Opt. 15, 11 (1976).
  4. M. Ikeda, M. Tateda, H. Yoshikiyo, Appl. Opt. 14, 4 (1975).
    [CrossRef]
  5. Y. Suzaki, A. Tachibana, Appl. Opt. 14, 12 (1975).
    [CrossRef]

1976

T. Okoshi, K. Hotate, Appl. Opt. 15, 11 (1976).

1975

1974

W. E. Martine, Appl. Opt. 13, 9 (1974).

1973

D. Gloge, E. A. J. Marcatili, Bell Syst. Tech. J. 52, 9 (1973).

Gloge, D.

D. Gloge, E. A. J. Marcatili, Bell Syst. Tech. J. 52, 9 (1973).

Hotate, K.

T. Okoshi, K. Hotate, Appl. Opt. 15, 11 (1976).

Ikeda, M.

Marcatili, E. A. J.

D. Gloge, E. A. J. Marcatili, Bell Syst. Tech. J. 52, 9 (1973).

Martine, W. E.

W. E. Martine, Appl. Opt. 13, 9 (1974).

Okoshi, T.

T. Okoshi, K. Hotate, Appl. Opt. 15, 11 (1976).

Suzaki, Y.

Y. Suzaki, A. Tachibana, Appl. Opt. 14, 12 (1975).
[CrossRef]

Tachibana, A.

Y. Suzaki, A. Tachibana, Appl. Opt. 14, 12 (1975).
[CrossRef]

Tateda, M.

Yoshikiyo, H.

Appl. Opt.

W. E. Martine, Appl. Opt. 13, 9 (1974).

T. Okoshi, K. Hotate, Appl. Opt. 15, 11 (1976).

Y. Suzaki, A. Tachibana, Appl. Opt. 14, 12 (1975).
[CrossRef]

M. Ikeda, M. Tateda, H. Yoshikiyo, Appl. Opt. 14, 4 (1975).
[CrossRef]

Bell Syst. Tech. J.

D. Gloge, E. A. J. Marcatili, Bell Syst. Tech. J. 52, 9 (1973).

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Figures (7)

Fig. 1
Fig. 1

Step-index fiber reflected power distributions measured by Gaussian beam with spot size w.

Fig. 2
Fig. 2

Reflected power distributions and refractive-index porfiles for different gradient parameter α.

Fig. 3
Fig. 3

Coordinate for laser beam referred to fiber core.

Fig. 4
Fig. 4

Measured reflected power distribution (solid line) and calculated refractive-index profile (small circles) of a single-mode fiber.

Fig. 5
Fig. 5

Refractive-index profiles calculated from reflected power data involving 1% noise (computer simulation by step approximation).

Fig. 6
Fig. 6

Evaluation of calculation error. a and Δ are the true core radius and maximum relative index difference. is the distance from the index profile curve at the calculated point. δr and δf are deviations of r and f at a calculated point from the true index profile curve. = [(δf/Δ)2 + (δr/a)2]1/2

Fig. 7
Fig. 7

Refractive-index profiles calculated from reflected power data involving 1% noise [computer simulation by (α, Δ, α) approximation].

Equations (13)

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R = [ ( 1 n ) / ( 1 + n ) ] 2 .
f ( r ) = { Δ [ 1 ( r / a ) α ] ( r < a ) , 0 ( r a ) ,
f ̅ ( x , y ) = f ( r ) ,
r 2 = x 2 + y 2 .
p ( x , y ) = 1 π w 2 exp [ ( X x ) 2 + y 2 w 2 ] ,
F ̅ ( X ) = f ̅ ( x , y ) p ( x , y ) dxdy = 1 π w 2 f ̅ ( x , y ) exp [ ( X x ) 2 + y 2 w 2 ] dxdy = 1 π w 2 f ( r ) exp [ X 2 + r 2 w 2 + 2 r X w 2 cos θ ] rdrd θ = 2 w 2 exp ( X 2 w 2 ) 0 I 0 ( 2 X r w 2 ) exp ( r 2 w 2 ) f ( r ) rdr ,
f ( r ) = k = 1 g k ϕ k ( r ) ,
F ̅ ( X ) = k = 1 a * ( X , k ) g k ,
a * ( X , k ) = 2 w 2 exp ( X 2 w 2 ) 0 I 0 ( 2 X r w 2 ) exp ( r 2 w 2 ) ϕ ( r ) rdr .
F i = j = 1 M a i j g j ( i = 1 , 2 , . . . , N ) ,
a i j = a * ( X i , j ) ,
s = i = 1 N ( F i j = 1 M a i j g j ) 2 .
ϕ k ( r ) = { 1 [ ( k 1 ) / 10 r k / 10 ] 0 ( otherwise ) ,

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