Abstract

The temperature sensitivity of cross talk between closely spaced cores in a common cladding is calculated and compared with measurements. A periodic variation in core contrast is observed when one core is illuminated and the temperature is changed. The variation in light distribution, which is ascribable to a change in coupling between the cores, agrees with theoretical predictions. It is shown that cross talk can be made to be a sensitive, predictable function of temperature or by proper selection of materials, wavelength, and fiber geometry essentially temperature independent.

© 1983 Optical Society of America

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References

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  1. G. B. Hocker, Appl. Opt. 18, 1445 (1979).
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  4. L. Eyges, P. Wintersteiner, J. Opt. Soc. Am. 71, 1351 (1981).
  5. A. W. Snyder, J. Opt. Soc. Am. 62, 1267 (1972).
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  6. L. Prod’homme, Phys. Chem. Glasses 1, 119 (1960).
  7. G. Meltz, E. Snitzer, U.S. Patent4,295,738.
  8. J. F. Nye, Physical Properties of Crystals (Oxford, U.P., London, 1957), Chap. 13.
  9. S. P. Timoshenko, J. N. Goudier, Theory of Elasticity (McGraw-Hill, New York, 1970), Chap. 4.
  10. B. A. Boley, J. H. Weiner, Theory of Thermal Stresses (Wiley, New York, 1960), Chap. 9.
  11. D. Burgreen, Elements of Thermal Stress Analysis (C. P. Press, Jamaica, N.Y., 1971), Chaps. 3 and 4.
  12. R. Bellman, Introduction to Matrix Analysis (McGraw-Hill, New York, 1960), p. 215.
  13. J. R. Dunphy, G. Meltz, E. Snitzer, “Theoretical and Experimental Investigation and Development of a Fiber Optic Strain Sensor,” United Technologies Research Center, Report R81-925425-13, Final Technical Report Contract N00163-81-C-0069, Mar.1982.
  14. E. Snitzer, J. R. Dunphy, G. Meltz, “Fiber Optic Strain Sensors,” in Proceedings, International Conference on Fiber Optic Rotation Sensors and Related Technologies, (Springer, New York, 1982).
  15. W. A. Gambling et al., Microwaves Opt. Acoust. 1, 13 (1976).
    [CrossRef]
  16. N. S. Kapany, J Burke, Optical Waveguide (Academic, New York, 1972), p. 254.
  17. P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Chap. 7.
  18. J. P. DeLuca, C. G. Bergeron, J. Am. Ceram. Soc. 52, 629 (1969).
    [CrossRef]
  19. E. A. J. Marcatili, Bell Syst. Tech. 48, 2133 (1969).
  20. A. W. Snyder, Proc. IEEE 69, 6 (1981).
    [CrossRef]
  21. Y. L. Luke, Integrals of Bessel Functions (McGraw-Hill, New York, 1962), p. 278.

1981

1979

1976

W. A. Gambling et al., Microwaves Opt. Acoust. 1, 13 (1976).
[CrossRef]

1972

1969

J. P. DeLuca, C. G. Bergeron, J. Am. Ceram. Soc. 52, 629 (1969).
[CrossRef]

E. A. J. Marcatili, Bell Syst. Tech. 48, 2133 (1969).

1960

L. Prod’homme, Phys. Chem. Glasses 1, 119 (1960).

Bellman, R.

R. Bellman, Introduction to Matrix Analysis (McGraw-Hill, New York, 1960), p. 215.

Bergeron, C. G.

J. P. DeLuca, C. G. Bergeron, J. Am. Ceram. Soc. 52, 629 (1969).
[CrossRef]

Bergh, R. A.

Boley, B. A.

B. A. Boley, J. H. Weiner, Theory of Thermal Stresses (Wiley, New York, 1960), Chap. 9.

Bucaro, J. A.

Burgreen, D.

D. Burgreen, Elements of Thermal Stress Analysis (C. P. Press, Jamaica, N.Y., 1971), Chaps. 3 and 4.

Burke, J

N. S. Kapany, J Burke, Optical Waveguide (Academic, New York, 1972), p. 254.

DeLuca, J. P.

J. P. DeLuca, C. G. Bergeron, J. Am. Ceram. Soc. 52, 629 (1969).
[CrossRef]

Dunphy, J. R.

J. R. Dunphy, G. Meltz, E. Snitzer, “Theoretical and Experimental Investigation and Development of a Fiber Optic Strain Sensor,” United Technologies Research Center, Report R81-925425-13, Final Technical Report Contract N00163-81-C-0069, Mar.1982.

E. Snitzer, J. R. Dunphy, G. Meltz, “Fiber Optic Strain Sensors,” in Proceedings, International Conference on Fiber Optic Rotation Sensors and Related Technologies, (Springer, New York, 1982).

Eyges, L.

Feshbach, H.

P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Chap. 7.

Gambling, W. A.

W. A. Gambling et al., Microwaves Opt. Acoust. 1, 13 (1976).
[CrossRef]

Goudier, J. N.

S. P. Timoshenko, J. N. Goudier, Theory of Elasticity (McGraw-Hill, New York, 1970), Chap. 4.

Hocker, G. B.

Jarzynski, J.

Kapany, N. S.

N. S. Kapany, J Burke, Optical Waveguide (Academic, New York, 1972), p. 254.

Lagakos, N.

Lefevre, H. C.

Luke, Y. L.

Y. L. Luke, Integrals of Bessel Functions (McGraw-Hill, New York, 1962), p. 278.

Marcatili, E. A. J.

E. A. J. Marcatili, Bell Syst. Tech. 48, 2133 (1969).

Meltz, G.

E. Snitzer, J. R. Dunphy, G. Meltz, “Fiber Optic Strain Sensors,” in Proceedings, International Conference on Fiber Optic Rotation Sensors and Related Technologies, (Springer, New York, 1982).

J. R. Dunphy, G. Meltz, E. Snitzer, “Theoretical and Experimental Investigation and Development of a Fiber Optic Strain Sensor,” United Technologies Research Center, Report R81-925425-13, Final Technical Report Contract N00163-81-C-0069, Mar.1982.

G. Meltz, E. Snitzer, U.S. Patent4,295,738.

Morse, P. M.

P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Chap. 7.

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Oxford, U.P., London, 1957), Chap. 13.

Prod’homme, L.

L. Prod’homme, Phys. Chem. Glasses 1, 119 (1960).

Shaw, J. H.

Snitzer, E.

G. Meltz, E. Snitzer, U.S. Patent4,295,738.

J. R. Dunphy, G. Meltz, E. Snitzer, “Theoretical and Experimental Investigation and Development of a Fiber Optic Strain Sensor,” United Technologies Research Center, Report R81-925425-13, Final Technical Report Contract N00163-81-C-0069, Mar.1982.

E. Snitzer, J. R. Dunphy, G. Meltz, “Fiber Optic Strain Sensors,” in Proceedings, International Conference on Fiber Optic Rotation Sensors and Related Technologies, (Springer, New York, 1982).

Snyder, A. W.

Timoshenko, S. P.

S. P. Timoshenko, J. N. Goudier, Theory of Elasticity (McGraw-Hill, New York, 1970), Chap. 4.

Weiner, J. H.

B. A. Boley, J. H. Weiner, Theory of Thermal Stresses (Wiley, New York, 1960), Chap. 9.

Wintersteiner, P.

Appl. Opt.

Bell Syst. Tech.

E. A. J. Marcatili, Bell Syst. Tech. 48, 2133 (1969).

J. Am. Ceram. Soc.

J. P. DeLuca, C. G. Bergeron, J. Am. Ceram. Soc. 52, 629 (1969).
[CrossRef]

J. Opt. Soc. Am.

Microwaves Opt. Acoust.

W. A. Gambling et al., Microwaves Opt. Acoust. 1, 13 (1976).
[CrossRef]

Opt. Lett.

Phys. Chem. Glasses

L. Prod’homme, Phys. Chem. Glasses 1, 119 (1960).

Proc. IEEE

A. W. Snyder, Proc. IEEE 69, 6 (1981).
[CrossRef]

Other

Y. L. Luke, Integrals of Bessel Functions (McGraw-Hill, New York, 1962), p. 278.

N. S. Kapany, J Burke, Optical Waveguide (Academic, New York, 1972), p. 254.

P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Chap. 7.

G. Meltz, E. Snitzer, U.S. Patent4,295,738.

J. F. Nye, Physical Properties of Crystals (Oxford, U.P., London, 1957), Chap. 13.

S. P. Timoshenko, J. N. Goudier, Theory of Elasticity (McGraw-Hill, New York, 1970), Chap. 4.

B. A. Boley, J. H. Weiner, Theory of Thermal Stresses (Wiley, New York, 1960), Chap. 9.

D. Burgreen, Elements of Thermal Stress Analysis (C. P. Press, Jamaica, N.Y., 1971), Chaps. 3 and 4.

R. Bellman, Introduction to Matrix Analysis (McGraw-Hill, New York, 1960), p. 215.

J. R. Dunphy, G. Meltz, E. Snitzer, “Theoretical and Experimental Investigation and Development of a Fiber Optic Strain Sensor,” United Technologies Research Center, Report R81-925425-13, Final Technical Report Contract N00163-81-C-0069, Mar.1982.

E. Snitzer, J. R. Dunphy, G. Meltz, “Fiber Optic Strain Sensors,” in Proceedings, International Conference on Fiber Optic Rotation Sensors and Related Technologies, (Springer, New York, 1982).

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Figures (22)

Fig. 1
Fig. 1

Twin-core fiber geometry.

Fig. 2
Fig. 2

Phase refractive index vs V parameter.

Fig. 3
Fig. 3

Beat length vs V for various core separations.

Fig. 4
Fig. 4

Temperature sensitivity of step and gaussian profile circular twin-core fibers as a function of the V parameter.

Fig. 5
Fig. 5

Beat temperature Tb vs center-to-center core spacing for step and gaussian profile circular twin-core fibers.

Fig. 6
Fig. 6

Temperature independent V parameter vs core spacing.

Fig. 7
Fig. 7

Comparison of exact integral representation and approximate coupled-mode computations of the step-index two-core coupling factor.

Fig. 8
Fig. 8

Double-clad twin-core fiber.

Fig. 9
Fig. 9

Normal mode propagation constants of a multiple core array. β0 is the propagation constant of an isolated single core.

Fig. 10
Fig. 10

Cross talk in a three-core fiber.

Fig. 11
Fig. 11

Cross section of Type I twin-core fiber after second draw.

Fig. 12
Fig. 12

Electron microscope photograph of Type I twin-core fiber with end etched in hydrofluroic acid: magnification 7800×, angle of view 20°.

Fig. 13
Fig. 13

Type II twin-core preform cross section.

Fig. 14
Fig. 14

Measured change in cross talk with wavelength of type II fiber.

Fig. 15
Fig. 15

Predicted change in cross talk with wavelength of Type II fiber.

Fig. 16
Fig. 16

Experiment arrangement for measuring optical power transfer in twin-core fiber vs temperature.

Fig. 17
Fig. 17

Light signal from single core of type I twin-core fiber vs oven temperature.

Fig. 18
Fig. 18

Experimental arrangement for measuring the temperature sensitivity of type II fiber.

Fig. 19
Fig. 19

Temperature sensitivity of Type II fiber.

Fig. 20
Fig. 20

Diffusion profiles.

Fig. 21
Fig. 21

Diffusion profiles.

Fig. 22
Fig. 22

Effect of core–cladding interdiffusion.

Tables (4)

Tables Icon

Table I Coupling Factor

Tables Icon

Table II Twin-Core Fiber Characteristics

Tables Icon

Table III Predicted and Observed Effects of Core–Cladding Interdiffusion

Tables Icon

Table IV Thermal Characteristics

Equations (59)

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d ϕ d ξ = π L / λ b ( 1 L d L d ξ 1 / λ b d λ b d ξ ) .
π / λ b = ( N A 2 / λ n 1 ) ( 1 / a 2 ) A 2 s ( r 2 2 / a 2 ) ψ 1 ( r 1 ) ψ 2 ( r 2 ) r 2 d r 2 d θ ,
s ( r 2 2 / a 2 ) = [ n 2 ( r 2 2 / a 2 ) n 2 2 ] / N A 2 ,
F ( V ; d / a ) = V / 2 π A 2 s ψ 1 ψ 2 ( r 2 / a ) d ( r 2 / a ) d θ .
λ b / λ = 1 / 2 · n 1 / N A 2 · V / F .
Δ ϕ / ϕ = { n 2 2 n 1 2 n 2 2 ( ζ 1 ζ 2 ) + ( V / F ) d F / d V [ α + ζ 1 + n 2 2 n 1 2 n 2 2 ( ζ 1 ζ 2 ) ] } Δ T ,
d ϕ d T = ( 2 π L / λ ) ( N A 2 / n 1 ) ( α + ζ ) d F / d V .
Δ ϕ Δ T L = 2 π mrad / ° C cm .
Q = | I 1 I 2 I 1 + I 2 | = | cos 2 ϕ sin 2 ϕ | = | cos 2 ϕ | ,
Δ Q = | sin ( 2 Δ ϕ ) | = | sin ( 2 π Δ T / T b ) | .
Δ ϕ 0 Δ T L = 2 π n 1 λ ( α + ζ ) ,
2 Δ ϕ / Δ ϕ 0 = 2 ( N A / n 1 ) 2 d F / d V .
d F d V = 0.
Δ ϕ / Δ λ = ( π L / λ b 2 ) λ b / λ = ( 2 π L / λ 2 ) ( N A 2 / n 1 ) d F / d V .
Δ λ / λ 2 = n 1 2 L N A 2 d F / d V .
Δ ϕ = d ϕ / d λ · Δ λ + ( 1 / 2 ) d 2 ϕ / d λ 2 · ( Δ λ ) 2 + ,
d 2 ϕ d λ 2 = 2 π L N A 2 / n 1 [ ( 2 / λ 3 ) d F d V + ( V / λ 3 ) d 2 F d V 2 ] .
Δ λ / λ 2 = ± ( n 1 2 π L N A 3 a | F | ) 1 / 2 .
d 2 ϕ d T 2 = ( L / a ) ( N A / n 1 ) ( α + ζ ) 2 V ( F + V F ) ,
Δ ϕ / ϕ = z o r o + n 2 2 n 1 2 n 2 2 ( Δ n 1 n 1 Δ n 2 n 2 ) + V F d F d V [ r o + Δ n 1 n 1 + Δ n 2 2 n 1 2 n 2 2 ( Δ n 1 n 1 Δ n 2 n 2 ) ] ,
V F d F d V | 0 = z o r o + n 2 2 n 1 2 n 2 2 ( Δ n 1 n 1 Δ n 2 n 2 ) r o + Δ n 1 n 1 + n 2 2 n 1 2 n 2 2 ( Δ n 1 n 1 Δ n 2 n 2 ) ,
( V / F d F / d V ) | 0 = n 2 2 ( ζ 1 ζ 2 ) ( n 1 2 n 2 2 ) + n 1 2 ζ 1 n 2 2 ζ 2 ,
Δ n / n = [ ( 1 / n ) ( n / T ) υ = 0 α ( n 2 / 2 ) ( p 11 + 2 p 12 ) ] Δ T ( n 2 / 2 ) [ ( p 11 + p 12 ) ( r α Δ T ) + p 12 ( z α Δ T ) ] .
V F / F | 0 = z o r o ( r o α 1 Δ T ) + ( ζ 1 + α 1 ) Δ T n 1 2 / 2 [ ( p 11 + p 12 ) ( r o α 1 Δ T ) + p 12 ( z o α 1 Δ T ) ] ,
z o α 1 Δ T = ( 1 ν 1 ) σ r / E 1 ν 1 ( z o α 1 Δ T ) ,
z o α 1 Δ T = ( α 2 α 1 ) ( 1 g 2 / h 2 ) Δ T 1 + g 2 / h 2 ( E 1 / E 2 1 ) 2 ( ν 1 ν 2 ) 1 + E 2 / E 1 ( h 2 / g 2 1 ) σ r / E 1 ,
z o r o = ( 1 + ν 1 ) ( z α 1 Δ T ) ( 1 ν 1 ) σ r / E 1 ,
σ r = ( α 2 α 1 ) Δ T ( ν 2 ν 1 ) α ¯ Δ T 1 / E 2 ( h 2 + g 2 h 2 g 2 + ν 2 ) + 1 / E 1 ( 1 ν 1 ) + 2 ( ν 1 ν 2 ) 2 E 1 + E 2 ( h 2 / g 2 1 ) ,
α ¯ Δ T = α 1 Δ T + ( α 2 α 1 ) ( 1 g 2 / h 2 ) Δ T 1 + g 2 / h 2 ( E 1 / E 2 1 ) .
E i E i / ( 1 ν i 2 ) , ν i ν i / ( 1 ν i ) , α i ( 1 + ν i ) α i i = 1 , 2.
V F / F | 0 = ( 1 + ν ) × { ( 1 3 ν ) + 2 ( 1 ν ) ( ζ 1 + α 1 ) ( α 2 α 1 ) ( 1 g 2 / h 2 ) n 1 2 [ 1 2 ( p 11 + p 12 ) ( 1 3 ν ) + ( 1 ν ) p 12 ] } 1 .
E i ( ρ , z ) = j a i j e j ( ρ ) ,
A ( z ) = col [ a 1 ( z , , a N ( z ) ]
d A d z + i β 0 A = i Δ β B · A ,
B · Λ r = μ r · Λ r ,
β r = β 0 + μ r · Δ β .
A ( 0 ) [ a 1 ( 0 ) , , a k ( 0 ) , a N ( 0 ) ] [ 0 , , 1 , 0 ] , A ( z ) = exp ( i β 0 z ) r = 1 N λ k r Λ r exp ( i μ r π z / λ b ) ,
I k m ( z ) = r , q = 1 N λ k r λ m r λ k q λ m q exp [ i ( μ r μ q ) π z / λ b ] = r = 1 N ( λ k r λ m r ) 2 + 2 r < q λ k r λ m r λ k q λ m q × cos [ ( μ r μ q ) π z / λ b ] .
B = [ 0 1 · · · · 0 1 0 1 · 0 1 0 1 · · 1 0 1 0 1 0 ]
μ r = 2 cos [ r π / ( N + 1 ) ] r = 1 , 2 , , N ,
Λ r = ( 2 N + 1 ) 1 / 2 sin [ k r π / ( N + 1 ) ] k = 1 , 2 , , N ,
I k m = ( 2 N + 1 ) 2 r , q = 1 N sin [ π r k / ( N + 1 ) ] sin [ π r m / ( N + 1 ) ] sin [ π q k / ( N + 1 ) ] · sin [ π q m / ( N + 1 ) ] cos [ ( μ r μ q ) ϕ ] .
I ( L ) = ( cos 4 ( π L / 2 λ b ) 1 2 sin 2 ( π L 2 / λ b ) sin 4 ( π L / 2 λ b ) ) .
C ¯ C / C 0 = 1 4 π D t S exp ( r 2 / 4 D t ) d S ,
λ Δ ϕ / Δ λ ( α + ζ ) 1 d ϕ / d T .
E x = ψ ( r ) exp ( i β z ) ,
H y = ( / μ ) 1 / 2 E x ,
d a 1 d z + i β 0 a 1 = i Δ β a 2 ,
d a 2 d z + i β 0 a 2 = i Δ β a 1 ,
Δ β = ( N A 2 / λ n 1 ) 0 2 π 0 a s ( r 2 2 / a 2 ) ψ 1 ( r 1 ) ψ 2 ( r 2 ) ( r 2 / a ) · d ( r 2 / a ) d θ ,
A 1 , 2 1 μ ψ 1 , 2 2 r d r d θ = 1.
F ( V ; d / a ) = V / 2 π 0 2 π 0 a s ( r 2 2 / a 2 ) ψ 1 ( r 1 ) ψ 2 ( r 2 ) ( r 2 / a ) d ( r 2 / a ) d θ .
ψ ( r ) exp [ 1 2 ( r / r 0 ) 2 ] ,
s ( r 2 / ρ 2 ) = exp [ ( r / ρ ) 2 ] ,
r 0 2 = ρ 2 / ( V 1 ) ,
ψ ( r ) [ V 2 / ( V + 1 ] K 0 [ ( V 1 ) r / ρ ] exp [ 1 2 ( V 1 ) 2 / ( V + 1 ) ] .
Δ β = ( 2 π / λ ) ( N A 2 / n 1 ) ( V 1 ) ( V / V + 1 ) 2 exp [ 1 2 ( V 1 ) 2 / ( V + 1 ) ] K 0 [ ( V 1 ) d / ρ ] · 0 T exp ( t ) I 0 ( 2 y t ) d t ,
Δ β = π / λ b = ( 2 π / λ ) ( N A 2 / n 1 ) ( V 1 ) ( V / V + 1 ) 2 × exp [ ( V 1 ) 2 / ( V + 1 ) ] · K 0 [ ( V 1 ) d / ρ ] .
s ( r 2 / ρ 2 ) = 1 Γ ( m + 1 ) ( m + 1 ) r 2 / ρ 2 t m exp ( t ) d t m 0 .

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