Abstract

Changes in transverse refractive index induced by the photoelastic effect are calculated when an optical fiber is subjected to a uniformly applied diametral stress. For moderate values of the force per unit length applied to the fiber, we find that regions of comparable or higher refractive index than the core may be induced in the outer region of the fiber. Thus the stressed region is capable of acting as a mode converter that affects the transmission characteristics of the fiber and may enable coupling of energy in or out of the fiber.

© 1981 Optical Society of America

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References

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  1. J. F. Nye, Physical Properties of Crystals (Oxford U.P., London, 1957), p. 224.
  2. M. Frocht, Photoelasticity, Vol. 2 (Wiley, New York, 1948), pp. 125–129.
  3. Ref. 2, pp. 27–29.
  4. F. Kapron, N. Borrelli, D. Keck, IEEE J. Quantum Electron QE-8, 222 (1972).
    [CrossRef]
  5. M. Stein, S. Aisenberg, J. Stevens, in Physics of Fiber Optics, B. Bendow, S. S. Mitra, Eds (American Ceramic Society, Columbus, Ohio, 1980).
  6. R. Hiskes, in Digest of Topical Meeting on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1979), paper WF6.
  7. D. E. Gray, Ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1972), p. 3–104.
  8. D. A. Pinnow, “Electro-optic Materials,” in Laser Handbook, Vol. 1, F. Arecchi, E. Schulz-Dubois, Eds. (North-Holland, Amsterdam, 1972), p. 999.

1972 (1)

F. Kapron, N. Borrelli, D. Keck, IEEE J. Quantum Electron QE-8, 222 (1972).
[CrossRef]

Aisenberg, S.

M. Stein, S. Aisenberg, J. Stevens, in Physics of Fiber Optics, B. Bendow, S. S. Mitra, Eds (American Ceramic Society, Columbus, Ohio, 1980).

Borrelli, N.

F. Kapron, N. Borrelli, D. Keck, IEEE J. Quantum Electron QE-8, 222 (1972).
[CrossRef]

Frocht, M.

M. Frocht, Photoelasticity, Vol. 2 (Wiley, New York, 1948), pp. 125–129.

Hiskes, R.

R. Hiskes, in Digest of Topical Meeting on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1979), paper WF6.

Kapron, F.

F. Kapron, N. Borrelli, D. Keck, IEEE J. Quantum Electron QE-8, 222 (1972).
[CrossRef]

Keck, D.

F. Kapron, N. Borrelli, D. Keck, IEEE J. Quantum Electron QE-8, 222 (1972).
[CrossRef]

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Oxford U.P., London, 1957), p. 224.

Pinnow, D. A.

D. A. Pinnow, “Electro-optic Materials,” in Laser Handbook, Vol. 1, F. Arecchi, E. Schulz-Dubois, Eds. (North-Holland, Amsterdam, 1972), p. 999.

Stein, M.

M. Stein, S. Aisenberg, J. Stevens, in Physics of Fiber Optics, B. Bendow, S. S. Mitra, Eds (American Ceramic Society, Columbus, Ohio, 1980).

Stevens, J.

M. Stein, S. Aisenberg, J. Stevens, in Physics of Fiber Optics, B. Bendow, S. S. Mitra, Eds (American Ceramic Society, Columbus, Ohio, 1980).

IEEE J. Quantum Electron (1)

F. Kapron, N. Borrelli, D. Keck, IEEE J. Quantum Electron QE-8, 222 (1972).
[CrossRef]

Other (7)

M. Stein, S. Aisenberg, J. Stevens, in Physics of Fiber Optics, B. Bendow, S. S. Mitra, Eds (American Ceramic Society, Columbus, Ohio, 1980).

R. Hiskes, in Digest of Topical Meeting on Optical Fiber Communication (Optical Society of America, Washington, D.C., 1979), paper WF6.

D. E. Gray, Ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1972), p. 3–104.

D. A. Pinnow, “Electro-optic Materials,” in Laser Handbook, Vol. 1, F. Arecchi, E. Schulz-Dubois, Eds. (North-Holland, Amsterdam, 1972), p. 999.

J. F. Nye, Physical Properties of Crystals (Oxford U.P., London, 1957), p. 224.

M. Frocht, Photoelasticity, Vol. 2 (Wiley, New York, 1948), pp. 125–129.

Ref. 2, pp. 27–29.

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Figures (5)

Fig. 1
Fig. 1

Coordinate system for the fiber showing the applied external forces (F) and the resulting internal stresses (σ) at an arbitrary point.

Fig. 2
Fig. 2

Stresses in fiber. σ1, and σ2 vs distance along the horizontal x axis and vertical y axis measured from the fiber’s center.

Fig. 3
Fig. 3

Stress differences in fiber. (σ1σ2) vs distance along x and y axes. Solid curves pertain to application of forces via knife-edges, the dashed curve in (b) via flat plates.

Fig. 4
Fig. 4

Refractive-index change vs distance for flat plate case: (a) unstressed case; (b) stress alone; and (c) total effect.

Fig. 5
Fig. 5

Total refractive-index change vs force applied (F/L) at the fiber center (0,0) and at the point of maximum stress (0, ±yM).

Tables (1)

Tables Icon

Table I Refractive-lndex Change vs Force Applied

Equations (17)

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Δ ( 1 / n 2 ) k = - 2 n 0 3 Δ n k = q k j σ j             ( k , j = 1 , , 6 ) ,
( Δ n n ) S = ( Δ n x n ) S - ( Δ n y n ) S = - n 0 2 2 ( q 11 - q 12 ) ( σ 1 - σ 2 ) x , y
( σ 1 ) x , 0 = H ( D 2 - 4 x 2 D 2 + 4 x 2 ) 2 ,
( σ 2 ) x , 0 = - H [ 4 D 4 ( D 2 + 4 x 2 ) 2 - 1 ] ,
H = ( 2 π D ) F L .
( σ 1 ) 0 , y = H ,
( σ 2 ) 0 , y = - H D ( 2 D - 2 y + 2 D + 2 y - 1 D ) .
( Δ n n ) x , 0 S = n 0 2 2 ( q 12 - q 11 ) ( σ 1 - σ 2 ) x , 0 = n 0 2 2 ( q 12 - q 11 ) { 4 H D 2 ( D 2 - 4 x 2 ) / ( D 2 + 4 x 2 ) 2 } ,
( Δ n n ) 0 , y S = n 0 2 2 ( q 12 - q 11 ) ( σ 1 - σ 2 ) 0 , y = n 0 2 2 ( q 12 - q 11 ) × { 4 H D 2 / ( D 2 - 4 y 2 ) } .
( Δ n n ) 0 , 0 S = n 0 2 2 ( q 12 - q 11 ) ( σ 1 - σ 2 ) 0 , 0 = n 0 2 2 ( q 12 - q 11 ) { 4 H } = n 0 2 ( q 12 - q 11 ) { 4 π D · F L } .
( σ 1 - σ 2 ) 0 , y M 10 ( σ 1 - σ 2 ) 0 , 0 .
( Δ n n ) 0 , y M S 10 ( Δ n n ) 0 , 0 S .
( Δ n / n ) T = ( Δ n / n ) U + ( Δ n / n ) S .
s 11 = 0.95 s 12 = - 0.16 s 44 = 2.21 } × 10 - 7 in . 2 / lb ;             c 11 = 1.14 c 12 = 0.23 c 44 = 0.45 } × 10 7 lb / in . 2 ;             q 11 = 0.27 q 12 = 1.9 } × 10 - 8 in . 2 / lb .
i = s i j σ j             ( i , j = 1 , , 6 ) .
1 = s 11 σ 1 + s 12 σ 2             2 = s 12 σ 1 + s 11 σ 2 .
At x = y = 0 : 1 = 1.8 2 = - 3.8 } × 10 - 3 ; At x = 0 , y = ± y M : 1 = 9.2 2 = - 47 } × 10 - 3 ; At x = 0 , y = ± D / 2 : 1 = 2.7 2 = - 11 } × 10 - 3 ; At x = ± D / 2 , y = 0 : 1 = 2 = 0 because σ 1 = σ 2 = 0.

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