Abstract

The effect of a modified cladding on the transmission of light through a step-index optical fiber is investigated using 3-D geometrical optics. Measurements of the light transmission of the optical fiber as a function of the modified cladding refractive index and length are presented for the case of focused illumination and compared with 3-D ray theory. The effect of defocus on the transmission of the modified fiber is also studied. Applications to intensity sensors are discussed.

© 1986 Optical Society of America

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References

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  1. A. M. Scheggi, M. Brenchy, G. Conforty, R. Falciai, “Optical Fiber Thermometer for Medical Use,” IEE Proc. 131, Part H, No. 4, 270 (1984).
  2. M. Gottlieb, G. Brandt, “Temperature Sensing in Optical Fibers Using Cladding and Jacket Loss Effect,” Appl. Opt. 20, 3867 (1981).
    [CrossRef] [PubMed]
  3. P. M. Kopera, V. J. Tekippe, “Transmission of Optical Fibers with a Short Section of Modified Cladding,” Opt. News 7, 44 (1981).
  4. P. M. Kopera, J. Melinger, V. J. Tekippe, “Modified Cladding Wavelength Dependent Fiber Optic Temperature Sensor,” Proc. Soc. Photo-Opt. Instrum. Eng. 412, 82 (1983).
  5. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).
  6. See, for example, M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1965) p. 40.
  7. Series A 1809× index matching liquid manufactured by R. P. Cargille Laboratories, Inc., 55 Commerce Rd., Cedar Grove, NJ 07009.
  8. See, for example, J. N. Fields, J. Cole, “Fiber Microbend Acoustic Fiber,” Appl. Opt. 19, 3265 (1980).
    [CrossRef]

1984 (1)

A. M. Scheggi, M. Brenchy, G. Conforty, R. Falciai, “Optical Fiber Thermometer for Medical Use,” IEE Proc. 131, Part H, No. 4, 270 (1984).

1983 (1)

P. M. Kopera, J. Melinger, V. J. Tekippe, “Modified Cladding Wavelength Dependent Fiber Optic Temperature Sensor,” Proc. Soc. Photo-Opt. Instrum. Eng. 412, 82 (1983).

1981 (2)

M. Gottlieb, G. Brandt, “Temperature Sensing in Optical Fibers Using Cladding and Jacket Loss Effect,” Appl. Opt. 20, 3867 (1981).
[CrossRef] [PubMed]

P. M. Kopera, V. J. Tekippe, “Transmission of Optical Fibers with a Short Section of Modified Cladding,” Opt. News 7, 44 (1981).

1980 (1)

Born, M.

See, for example, M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1965) p. 40.

Brandt, G.

Brenchy, M.

A. M. Scheggi, M. Brenchy, G. Conforty, R. Falciai, “Optical Fiber Thermometer for Medical Use,” IEE Proc. 131, Part H, No. 4, 270 (1984).

Cole, J.

Conforty, G.

A. M. Scheggi, M. Brenchy, G. Conforty, R. Falciai, “Optical Fiber Thermometer for Medical Use,” IEE Proc. 131, Part H, No. 4, 270 (1984).

Falciai, R.

A. M. Scheggi, M. Brenchy, G. Conforty, R. Falciai, “Optical Fiber Thermometer for Medical Use,” IEE Proc. 131, Part H, No. 4, 270 (1984).

Fields, J. N.

Gottlieb, M.

Kopera, P. M.

P. M. Kopera, J. Melinger, V. J. Tekippe, “Modified Cladding Wavelength Dependent Fiber Optic Temperature Sensor,” Proc. Soc. Photo-Opt. Instrum. Eng. 412, 82 (1983).

P. M. Kopera, V. J. Tekippe, “Transmission of Optical Fibers with a Short Section of Modified Cladding,” Opt. News 7, 44 (1981).

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

Melinger, J.

P. M. Kopera, J. Melinger, V. J. Tekippe, “Modified Cladding Wavelength Dependent Fiber Optic Temperature Sensor,” Proc. Soc. Photo-Opt. Instrum. Eng. 412, 82 (1983).

Scheggi, A. M.

A. M. Scheggi, M. Brenchy, G. Conforty, R. Falciai, “Optical Fiber Thermometer for Medical Use,” IEE Proc. 131, Part H, No. 4, 270 (1984).

Snyder, A. W.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

Tekippe, V. J.

P. M. Kopera, J. Melinger, V. J. Tekippe, “Modified Cladding Wavelength Dependent Fiber Optic Temperature Sensor,” Proc. Soc. Photo-Opt. Instrum. Eng. 412, 82 (1983).

P. M. Kopera, V. J. Tekippe, “Transmission of Optical Fibers with a Short Section of Modified Cladding,” Opt. News 7, 44 (1981).

Wolf, E.

See, for example, M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1965) p. 40.

Appl. Opt. (2)

IEE Proc. (1)

A. M. Scheggi, M. Brenchy, G. Conforty, R. Falciai, “Optical Fiber Thermometer for Medical Use,” IEE Proc. 131, Part H, No. 4, 270 (1984).

Opt. News (1)

P. M. Kopera, V. J. Tekippe, “Transmission of Optical Fibers with a Short Section of Modified Cladding,” Opt. News 7, 44 (1981).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

P. M. Kopera, J. Melinger, V. J. Tekippe, “Modified Cladding Wavelength Dependent Fiber Optic Temperature Sensor,” Proc. Soc. Photo-Opt. Instrum. Eng. 412, 82 (1983).

Other (3)

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

See, for example, M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1965) p. 40.

Series A 1809× index matching liquid manufactured by R. P. Cargille Laboratories, Inc., 55 Commerce Rd., Cedar Grove, NJ 07009.

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Figures (5)

Fig. 1
Fig. 1

Optical fiber with a modified cladding section.

Fig. 2
Fig. 2

Reflection and refraction of a source ray at Q at the fiber endface. Polar coordinates (r,ϕ) define the position of Q, and the projection of the ray path onto the endface makes an angle θϕ with the azimuthal direction at Q (adapted from Ref. 5).

Fig. 3
Fig. 3

Experimental setup.

Fig. 4
Fig. 4

Fiber transmission vs oil index of refraction and temperature: (a) L0 = 5 mm. Dotted curve—experimental results; solid curve—theoretical results based on Eq. (6); broken curves 1 and 2—theoretical calculations based on Eqs. (16a) and (16b), respectively. (b) Defocusing effects for N.A.eff = 0.15 and N.A.eff = 0.085.

Fig. 5
Fig. 5

Relative transmitted intensity vs the length of the modified cladding region. ncore = 1.46. (a) Curve 1—nmo.cl. = 1.452; curve 2—nmo.cl. = 1.468. The solid and broken curves are the appropriate theoretical calculations, and the squares and circles are the experimental results, (b) More general theoretical results: (1) nmo.cl. = 1.465; (2) nmo.cl. = 1.525; (3) nmo.cl. = 1.585; (4) nmo.cl. = 1.455; (5) nmo.cl. = 1-449; (6) nmo.cl. = 1.443.

Equations (19)

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P br ( 0 ) = 0 2 π d ϕ 0 ρ rdr 0 2 π d θ ϕ 0 θ max I ( r , θ 0 , ϕ , θ ϕ ) sin θ 0 d θ 0 .
θ c = sin 1 [ n mo . cl . / n co . ] .
R = { 1 ; θ z < θ c ( bound ray ) ( n core cos α n mo . cl . cos α t n core cos α + n mo . cl . cos α t ) 2 ; θ z > θ c ( refracting ray , Fresnel formula ) ,
z p = 2 ρ β g ( ρ ) n core 2 β 2 ,
β = n core cos θ z ;
l = r ρ n core sin θ z cos θ ϕ ;
g ( ρ ) = n core 2 β 2 l 2 .
R = { ( N [ N ] ) R [ N ] + 1 + [ 1 ( N [ N ] ) ] R [ N ] } .
z p = 2 ρ cot g ( θ z ) ,
R = ( n core sin θ n mo . cl . sin θ t n core sin θ + n mo . cl . sin θ t ) 2 ,
P br ( L 0 ) = 0 2 π d ϕ 0 ρ rdr 0 2 π d θ ϕ 0 θ max I ( r , θ 0 , ϕ , θ ϕ ) R sin θ 0 d θ 0 .
I = δ ( r ) f 2 P i 2 π r cos 3 θ 0 for 0 θ 0 < θ max , 0 for θ max θ 0 π 2 ,
P br ( L 0 ) P br ( 0 ) = 2 0 θ max R [ sin θ 0 / ( cos 3 θ 0 ) ] d θ 0 tan 2 ( θ max ) ,
N = L 0 2 ρ cot { sin 1 [ sin ( θ 0 ) / n core ] } .
N . A . eff = sin { arctan [ ρ / a ] } ,
P br ( L 0 ) P br ( 0 ) = 2 0 arctan [ ρ / a ] R [ sin θ 0 / ( cos 3 θ 0 ) ] d θ 0 tan 2 ( θ max ) .
n mo . cl . ( T ) = n mo . cl . ( 25 ° C ) + d n mo . cl . d T [ T 25 ° C ] = 1.468 0.00037 ° C 1 [ T 25 ° C ] ,
R = R L 0 / z p ,
R = exp [ ( 1 R ) L 0 / z p ] .

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