Abstract

A theoretical analysis of the temperature sensitivity of a multimode biconical fiber coupler as well as that of a multimode uniform fiber coupler has been given. The results show that a biconical coupler has some advantages over an ordinary fiber coupler as a temperature sensor or as a temperature-independent coupler.

© 1986 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. N. Lagakos, J. A. Bucaro, J. Jarzynski, “Temperature-Induced Optical Phase Shifts in Fibers,” Appl. Opt. 20, 2305 (1981).
    [CrossRef] [PubMed]
  2. G. B. Hocker, “Fiber-Optic Sensing of Pressure and Temperature,” Appl. Opt. 18, 1445 (1979).
    [CrossRef] [PubMed]
  3. M. Gottlieb, G. B. Brandt, “Fiber-Optic Temperature Sensor Based on Internally Generated Thermal Radiation,” Appl. Opt. 20, 3408 (1981).
    [CrossRef] [PubMed]
  4. R. R. Dils, “High-Temperature Optical Fiber Thermometer,” J. Appl. Phys. 54, 1198 (1983).
    [CrossRef]
  5. G. K. Livingston, “Thermometry and Dosimetry of Heat with Specific Reference to the Liquid Crystal Optical Fiber Temperature Probe,” Radiat. Environ. Biophys. 17, 233 (1980).
    [CrossRef] [PubMed]
  6. K. Kyuma, S. Tai, T. Sawada, M. Nunoshita, “Fiber-Optic Instrument for Temperature Measurement,” IEEE J. Quantum Electron. QE-18, 676 (1982).
    [CrossRef]
  7. A. J. Rogers, “Polarization-Optical Time Domain Reflectometry: A Technique for the Measurement of Field Distributions,” Appl. Opt. 20, 1060 (1981).
    [CrossRef] [PubMed]
  8. J. H. Knox, P. M. Marshall, R. T. Murray, “Birefringent Filter Temperature Sensor,” paper presented at First International Conference on Optical Fiber Sensors, London, England (Apr. 1983)pp. 1–5.
  9. M. C. Farries, A. J. Rogers, “Temperature Dependence of the Kerr Effect in a Silica Optical Fiber,” Electron. Lett. 19, 890 (1983).
    [CrossRef]
  10. G. Meltz, J. R. Dunphy, W. W. Morey, E. Snitzer, “Cross-Talk Fiber-Optic Temperature Sensor,” Appl. Opt. 22, 464 (1983).
    [CrossRef] [PubMed]
  11. Y-F. Li, J. W. Y. Lit, “Coupling Efficiency of a Multimode Biconical Taper Coupler,” J. Opt. Soc. Am. A 2, 1301 (1985).
    [CrossRef]
  12. A. W. Snyder, P. D. McIntyre, “Crosstalk Between Light Pipes,” J. Opt. Soc. Am. 66, 877 (1976).
    [CrossRef]
  13. K. Ogawa, “Simplified Theory of the Multimode Fiber Coupler,” Bell Syst. Tech. J. 56, 729 (1977).

1985 (1)

1983 (3)

R. R. Dils, “High-Temperature Optical Fiber Thermometer,” J. Appl. Phys. 54, 1198 (1983).
[CrossRef]

M. C. Farries, A. J. Rogers, “Temperature Dependence of the Kerr Effect in a Silica Optical Fiber,” Electron. Lett. 19, 890 (1983).
[CrossRef]

G. Meltz, J. R. Dunphy, W. W. Morey, E. Snitzer, “Cross-Talk Fiber-Optic Temperature Sensor,” Appl. Opt. 22, 464 (1983).
[CrossRef] [PubMed]

1982 (1)

K. Kyuma, S. Tai, T. Sawada, M. Nunoshita, “Fiber-Optic Instrument for Temperature Measurement,” IEEE J. Quantum Electron. QE-18, 676 (1982).
[CrossRef]

1981 (3)

1980 (1)

G. K. Livingston, “Thermometry and Dosimetry of Heat with Specific Reference to the Liquid Crystal Optical Fiber Temperature Probe,” Radiat. Environ. Biophys. 17, 233 (1980).
[CrossRef] [PubMed]

1979 (1)

1977 (1)

K. Ogawa, “Simplified Theory of the Multimode Fiber Coupler,” Bell Syst. Tech. J. 56, 729 (1977).

1976 (1)

Brandt, G. B.

Bucaro, J. A.

Dils, R. R.

R. R. Dils, “High-Temperature Optical Fiber Thermometer,” J. Appl. Phys. 54, 1198 (1983).
[CrossRef]

Dunphy, J. R.

Farries, M. C.

M. C. Farries, A. J. Rogers, “Temperature Dependence of the Kerr Effect in a Silica Optical Fiber,” Electron. Lett. 19, 890 (1983).
[CrossRef]

Gottlieb, M.

Hocker, G. B.

Jarzynski, J.

Knox, J. H.

J. H. Knox, P. M. Marshall, R. T. Murray, “Birefringent Filter Temperature Sensor,” paper presented at First International Conference on Optical Fiber Sensors, London, England (Apr. 1983)pp. 1–5.

Kyuma, K.

K. Kyuma, S. Tai, T. Sawada, M. Nunoshita, “Fiber-Optic Instrument for Temperature Measurement,” IEEE J. Quantum Electron. QE-18, 676 (1982).
[CrossRef]

Lagakos, N.

Li, Y-F.

Lit, J. W. Y.

Livingston, G. K.

G. K. Livingston, “Thermometry and Dosimetry of Heat with Specific Reference to the Liquid Crystal Optical Fiber Temperature Probe,” Radiat. Environ. Biophys. 17, 233 (1980).
[CrossRef] [PubMed]

Marshall, P. M.

J. H. Knox, P. M. Marshall, R. T. Murray, “Birefringent Filter Temperature Sensor,” paper presented at First International Conference on Optical Fiber Sensors, London, England (Apr. 1983)pp. 1–5.

McIntyre, P. D.

Meltz, G.

Morey, W. W.

Murray, R. T.

J. H. Knox, P. M. Marshall, R. T. Murray, “Birefringent Filter Temperature Sensor,” paper presented at First International Conference on Optical Fiber Sensors, London, England (Apr. 1983)pp. 1–5.

Nunoshita, M.

K. Kyuma, S. Tai, T. Sawada, M. Nunoshita, “Fiber-Optic Instrument for Temperature Measurement,” IEEE J. Quantum Electron. QE-18, 676 (1982).
[CrossRef]

Ogawa, K.

K. Ogawa, “Simplified Theory of the Multimode Fiber Coupler,” Bell Syst. Tech. J. 56, 729 (1977).

Rogers, A. J.

M. C. Farries, A. J. Rogers, “Temperature Dependence of the Kerr Effect in a Silica Optical Fiber,” Electron. Lett. 19, 890 (1983).
[CrossRef]

A. J. Rogers, “Polarization-Optical Time Domain Reflectometry: A Technique for the Measurement of Field Distributions,” Appl. Opt. 20, 1060 (1981).
[CrossRef] [PubMed]

Sawada, T.

K. Kyuma, S. Tai, T. Sawada, M. Nunoshita, “Fiber-Optic Instrument for Temperature Measurement,” IEEE J. Quantum Electron. QE-18, 676 (1982).
[CrossRef]

Snitzer, E.

Snyder, A. W.

Tai, S.

K. Kyuma, S. Tai, T. Sawada, M. Nunoshita, “Fiber-Optic Instrument for Temperature Measurement,” IEEE J. Quantum Electron. QE-18, 676 (1982).
[CrossRef]

Appl. Opt. (5)

Bell Syst. Tech. J. (1)

K. Ogawa, “Simplified Theory of the Multimode Fiber Coupler,” Bell Syst. Tech. J. 56, 729 (1977).

Electron. Lett. (1)

M. C. Farries, A. J. Rogers, “Temperature Dependence of the Kerr Effect in a Silica Optical Fiber,” Electron. Lett. 19, 890 (1983).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. Kyuma, S. Tai, T. Sawada, M. Nunoshita, “Fiber-Optic Instrument for Temperature Measurement,” IEEE J. Quantum Electron. QE-18, 676 (1982).
[CrossRef]

J. Appl. Phys. (1)

R. R. Dils, “High-Temperature Optical Fiber Thermometer,” J. Appl. Phys. 54, 1198 (1983).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Radiat. Environ. Biophys. (1)

G. K. Livingston, “Thermometry and Dosimetry of Heat with Specific Reference to the Liquid Crystal Optical Fiber Temperature Probe,” Radiat. Environ. Biophys. 17, 233 (1980).
[CrossRef] [PubMed]

Other (1)

J. H. Knox, P. M. Marshall, R. T. Murray, “Birefringent Filter Temperature Sensor,” paper presented at First International Conference on Optical Fiber Sensors, London, England (Apr. 1983)pp. 1–5.

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 (7)

Fig. 1
Fig. 1

Schematic diagram of a biconical fiber coupler.

Fig. 2
Fig. 2

Path of a typical skew ray between reflections.

Fig. 3
Fig. 3

Ratio between powers of guiding modes and cladding modes, Pgu/Pcl, as functions of temperature.

Fig. 4
Fig. 4

Tc as a function of K: K = r2/r1 cosΩ.

Fig. 5
Fig. 5

Coupling efficiency of a multimode biconical fiber coupler as a function of temperature: r2 = 5 μm; z = 3500 μm; L = 5000 μm; t/r2 = 0.1; λ = 0.633 μm; n0 = 1.0; L is the taper length; t is the thickness of the fusion section between two cases; and z is the length of the fusion section; 1, r1 = 50 μm; 2, r1 = 100 μm; 3, r1 = 150 μm.

Fig. 6
Fig. 6

Coupling efficiency of an ordinary parallel multimode uniform fiber coupler: r = 50 μm; t/r = 0.005; 1, z = 3.5 mm; 2, z = 1000 mm.

Fig. 7
Fig. 7

Comparison of the variation of coupling efficiency vs temperature: curves 1–3, biconical coupler; the values of the parameters are the same as those in Fig. 5; curve 4, ordinary parallel multimode coupler with r = 50 /μm; z = 3500 μ; t/r = 0.005; λ = 0.633 μm; n0 = 1.0.

Tables (1)

Tables Icon

Table I Tcs is the Temperature at Which the Indices of Core and Cladding Cross Each Other; Tg is the Glass Transition Temperature

Equations (57)

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

C = P 3 / P 1 ,
R = P 3 P 2 + P 3 .
sin Θ M = ( n 1 2 n 2 2 ) 1 / 2 n 1
cos γ ̅ = sin Θ M sin Θ ,
sin Θ c = n 0 n 1 ,
F ( Θ M ) = 8 π r 2 Θ = 0 Θ M γ = 0 π / 2 I ( Θ ) t t α m ( Θ ) × exp ( β L ) cos 2 γ sin Θ d γ d Θ + 8 π r 2 Θ = Θ m Θ c γ = γ ̅ π / 2 I ( Θ ) t t α m ( Θ ) × exp ( β L ) cos 2 γ sin Θ d γ d Θ ,
I ( Θ ) = { 1 for Θ Θ c , 0 for Θ > Θ c ,
F ( Θ M ) = 2 π 2 r 2 l 0 ( 1 cos Θ M ) .
F ( Θ M ) = 1 cos Θ M .
sin Θ M = r 2 r 1 cos Ω ( n 1 2 n 2 2 ) 1 / 2 n 1 ,
sin Θ M = r 2 r 1 cos Ω ( n 1 2 n 0 2 ) 1 / 2 n 1 ,
cos γ ̅ ( Θ ) = sin Θ M / sin Θ ,
cos γ ̅ = sin Θ M / sin Θ .
P 1 = F ( Θ M ) .
P = F ( Θ M ) = 1 cos Θ M .
P = F ( Θ M ) = 1 cos Θ M .
η m = 1 2 [ 1 sin ( s z ) s z ] ,
s = 2 sin Θ M r exp ( υ t / r ) [ π υ ( 1 + t 2 r ) ] 1 / 2 ,
υ = k r ( n 1 2 n 2 2 ) 1 / 2 ;
η s = 0 1 sin 2 ( c z ) d x ,
C = 2 3 / 4 Δ 1 / 4 ( k π n 1 ) 1 / 2 r 3 / 2 ( 2 + t r ) x ( 1 x ) 1 / 4 exp [ t r ( 2 N ) 1 / 2 ( 1 x ) 1 / 2 ] ;
Δ = n 1 2 n 2 2 2 n 1 2 ;
N = υ 2 2 = r 2 k 2 n 1 2 Δ = 1 2 k 2 r 2 ( n 1 2 n 2 2 ) .
η s g = sin 2 ( ϕ ) ;
ϕ = π z / z b ,
n 1 2 n 2 2 n 1 2 n 0 2 K = r 2 r 1 cos Ω .
C a = R a = 1 2 ( 1 2 η ) P P 1 .
n 1 2 n 2 2 n 1 2 n 0 2 > K .
C b = 1 2 P P 1 ( 1 2 η ) P P 1 ,
R b = 1 2 ( 1 2 η ) P P .
d C a d T = d R a d T = P P 1 d η d T 1 P 1 2 ( 1 2 η ) ( P 1 d P d T P d P 1 d T ) .
d C b d T = d C a d T + 1 2 P 1 2 ( P 1 d P d T P d P 1 d T ) ,
d R b d T = P P d η d T 1 P 2 ( 1 2 η ) ( P d P d T P d P d T ) ,
d P 1 d T = n 2 n 1 ( ξ 1 ξ 2 ) ,
d P d T = K 2 cos Θ M n 2 2 n 1 2 ( ξ 1 ξ 2 ) ,
d P d T = K 2 cos Θ M n 0 2 n 1 2 ξ 1 .
ξ = 1 n d n d T .
d η m d T = 1 2 s z [ 1 + s z cos ( s z ) sin ( s z ) ] ( α + d s s d T ) ;
α = 1 z d z d T ,
d s s d T = 1 ( n 1 2 n 2 2 ) 1 / 2 { [ 1 2 ( n 1 2 n 2 2 ) 1 / 2 t k ] × ( n 1 2 ξ 1 n 2 2 ξ 2 ) ( n 1 2 n 2 2 ) 1 / 2 ξ 1 } .
d η s g d T = sin 2 ϕ d ϕ d T = sin 2 ϕ ( 1 z d z d T 1 z b d z b d T ) ϕ .
P P = 1 cos Θ M 1 cos Θ M = [ 1 ( 1 K 2 n 1 2 n 2 2 n 1 2 ) 1 / 2 ] / [ 1 ( 1 K 2 n 1 2 n 0 2 n 1 2 ) 1 / 2 ] ,
r 2 r 1 ,
K 1.
P P = n 1 2 n 2 2 n 1 2 n 0 2 ,
P P 1 < P P 1 .
C a = R a 0.5 ,
R b 0.5 ,
C b = 0.5 P P 1 = 0.5 K 2 n 1 2 n 0 2 n 1 2 n 2 2 .
d C a d T = d R a d T = d R b d T = 0 ,
d C b d T = K 2 ( n 1 2 n 2 2 ) 2 [ n 2 2 ( n 1 2 n 0 2 ) ξ 2 n 1 2 ( n 2 2 n 0 2 ) ξ 1 ] .
d C b d T = K 2 n 0 2 n 1 2 n 2 2 ξ .
T c = ( K 2 1 ) n 10 2 + n 20 2 K 2 n 0 2 [ ( 1 K 2 ) n 10 d n 1 d T n 20 d n 2 d T ] .
n 1 2 n 2 2 n 1 2 n 0 2 = K
n 1 2 n 2 2 n 1 2 n 0 2 > K or T < T c ,
n 1 2 n 2 2 n 1 2 n 0 2 < K or T > T c ,
d n d T ( 10 6 )

Metrics