Abstract

A mathematical model is presented that predicts birefringence changes in an optical fiber as the cladding is removed. This model approximates a highly elliptical fiber core with a rectangular dielectric waveguide. The birefringence calculations obtained with the model compare well with experimental evidence obtained with real-time birefringence monitoring during cladding removal by chemical etching. The information is used to control the amount of cladding removed from a D fiber to within ~ 0.05 μm for use in the production of passive optical fiber components.

© 1992 Optical Society of America

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  1. R. H. Stolen, R. P. DePaula, “Single-mode fiber components,” Proc. IEEE 75, 1498–1511 (1987).
    [CrossRef]
  2. R. A. Bergh, G. Kotler, H. J. Shaw, “Single-mode fibre optic directional coupler,” Electron. Lett. 27, 260–261 (1980).
    [CrossRef]
  3. K. L. Belsley, J. B. Carroll, L. A. Hess, D. R. Huber, D. Schmadel, “Optically multiplexed interferometric fiber optic sensor system,” in Fiber Optic and Laser Sensors III, E. L. Moore, O. G. Ramer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.566, 257–264 (1985).
  4. A. Kumar, K. Thyagarajan, K. Ghatak, “Analysis of rectangular-core dielectric waveguides: an accurate perturbation approach,” Opt. Lett. 8, 63–65 (1983).
    [CrossRef] [PubMed]
  5. A. Kumar, V. Gupta, K. Thyagarajan, “Goemetrical birefringence of polished and D-shape fibers,” Opt. Commun. 61, 195–198 (1987).
    [CrossRef]
  6. A. Kumar, S. Pilevar, K. Thyagarajan, “Measurement on variation of birefringence with depth of polishing in elliptic core fibers,” Opt. Commun. 72, 187–189 (1989).
    [CrossRef]
  7. I. P. Kaminow, “Polarization in fibers,” Laser Focus 16(6), 80–84 (1980).
  8. C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, New York, 1989), p. 414.
  9. I. P. Kaminow, “Polarization in optical fibers,” IEEE J. Quantum Electron. QE-17, 15–22 (1981).
    [CrossRef]
  10. G. T. Pugmire, M. A. Jensen, R. H. Selfridge, “Controllable cladding removal for in-fiber integrated optics components,” in Optoelectronic Devices and Applications, S. Sriram, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1338, 2–10 (1990).
  11. J. D. Freeze, M. A. Jensen, R. H. Selfridge, “High-efficiency diffraction gratings in D-type fibers,” in Optical Fiber Communication Conference, Vol. 4 of OSA 1991 Technical Digest Series, (Optical Society of America, Washington, D.C., 1991), p. 46.

1989 (1)

A. Kumar, S. Pilevar, K. Thyagarajan, “Measurement on variation of birefringence with depth of polishing in elliptic core fibers,” Opt. Commun. 72, 187–189 (1989).
[CrossRef]

1987 (2)

A. Kumar, V. Gupta, K. Thyagarajan, “Goemetrical birefringence of polished and D-shape fibers,” Opt. Commun. 61, 195–198 (1987).
[CrossRef]

R. H. Stolen, R. P. DePaula, “Single-mode fiber components,” Proc. IEEE 75, 1498–1511 (1987).
[CrossRef]

1983 (1)

1981 (1)

I. P. Kaminow, “Polarization in optical fibers,” IEEE J. Quantum Electron. QE-17, 15–22 (1981).
[CrossRef]

1980 (2)

I. P. Kaminow, “Polarization in fibers,” Laser Focus 16(6), 80–84 (1980).

R. A. Bergh, G. Kotler, H. J. Shaw, “Single-mode fibre optic directional coupler,” Electron. Lett. 27, 260–261 (1980).
[CrossRef]

Balanis, C. A.

C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, New York, 1989), p. 414.

Belsley, K. L.

K. L. Belsley, J. B. Carroll, L. A. Hess, D. R. Huber, D. Schmadel, “Optically multiplexed interferometric fiber optic sensor system,” in Fiber Optic and Laser Sensors III, E. L. Moore, O. G. Ramer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.566, 257–264 (1985).

Bergh, R. A.

R. A. Bergh, G. Kotler, H. J. Shaw, “Single-mode fibre optic directional coupler,” Electron. Lett. 27, 260–261 (1980).
[CrossRef]

Carroll, J. B.

K. L. Belsley, J. B. Carroll, L. A. Hess, D. R. Huber, D. Schmadel, “Optically multiplexed interferometric fiber optic sensor system,” in Fiber Optic and Laser Sensors III, E. L. Moore, O. G. Ramer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.566, 257–264 (1985).

DePaula, R. P.

R. H. Stolen, R. P. DePaula, “Single-mode fiber components,” Proc. IEEE 75, 1498–1511 (1987).
[CrossRef]

Freeze, J. D.

J. D. Freeze, M. A. Jensen, R. H. Selfridge, “High-efficiency diffraction gratings in D-type fibers,” in Optical Fiber Communication Conference, Vol. 4 of OSA 1991 Technical Digest Series, (Optical Society of America, Washington, D.C., 1991), p. 46.

Ghatak, K.

Gupta, V.

A. Kumar, V. Gupta, K. Thyagarajan, “Goemetrical birefringence of polished and D-shape fibers,” Opt. Commun. 61, 195–198 (1987).
[CrossRef]

Hess, L. A.

K. L. Belsley, J. B. Carroll, L. A. Hess, D. R. Huber, D. Schmadel, “Optically multiplexed interferometric fiber optic sensor system,” in Fiber Optic and Laser Sensors III, E. L. Moore, O. G. Ramer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.566, 257–264 (1985).

Huber, D. R.

K. L. Belsley, J. B. Carroll, L. A. Hess, D. R. Huber, D. Schmadel, “Optically multiplexed interferometric fiber optic sensor system,” in Fiber Optic and Laser Sensors III, E. L. Moore, O. G. Ramer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.566, 257–264 (1985).

Jensen, M. A.

J. D. Freeze, M. A. Jensen, R. H. Selfridge, “High-efficiency diffraction gratings in D-type fibers,” in Optical Fiber Communication Conference, Vol. 4 of OSA 1991 Technical Digest Series, (Optical Society of America, Washington, D.C., 1991), p. 46.

G. T. Pugmire, M. A. Jensen, R. H. Selfridge, “Controllable cladding removal for in-fiber integrated optics components,” in Optoelectronic Devices and Applications, S. Sriram, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1338, 2–10 (1990).

Kaminow, I. P.

I. P. Kaminow, “Polarization in optical fibers,” IEEE J. Quantum Electron. QE-17, 15–22 (1981).
[CrossRef]

I. P. Kaminow, “Polarization in fibers,” Laser Focus 16(6), 80–84 (1980).

Kotler, G.

R. A. Bergh, G. Kotler, H. J. Shaw, “Single-mode fibre optic directional coupler,” Electron. Lett. 27, 260–261 (1980).
[CrossRef]

Kumar, A.

A. Kumar, S. Pilevar, K. Thyagarajan, “Measurement on variation of birefringence with depth of polishing in elliptic core fibers,” Opt. Commun. 72, 187–189 (1989).
[CrossRef]

A. Kumar, V. Gupta, K. Thyagarajan, “Goemetrical birefringence of polished and D-shape fibers,” Opt. Commun. 61, 195–198 (1987).
[CrossRef]

A. Kumar, K. Thyagarajan, K. Ghatak, “Analysis of rectangular-core dielectric waveguides: an accurate perturbation approach,” Opt. Lett. 8, 63–65 (1983).
[CrossRef] [PubMed]

Pilevar, S.

A. Kumar, S. Pilevar, K. Thyagarajan, “Measurement on variation of birefringence with depth of polishing in elliptic core fibers,” Opt. Commun. 72, 187–189 (1989).
[CrossRef]

Pugmire, G. T.

G. T. Pugmire, M. A. Jensen, R. H. Selfridge, “Controllable cladding removal for in-fiber integrated optics components,” in Optoelectronic Devices and Applications, S. Sriram, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1338, 2–10 (1990).

Schmadel, D.

K. L. Belsley, J. B. Carroll, L. A. Hess, D. R. Huber, D. Schmadel, “Optically multiplexed interferometric fiber optic sensor system,” in Fiber Optic and Laser Sensors III, E. L. Moore, O. G. Ramer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.566, 257–264 (1985).

Selfridge, R. H.

G. T. Pugmire, M. A. Jensen, R. H. Selfridge, “Controllable cladding removal for in-fiber integrated optics components,” in Optoelectronic Devices and Applications, S. Sriram, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1338, 2–10 (1990).

J. D. Freeze, M. A. Jensen, R. H. Selfridge, “High-efficiency diffraction gratings in D-type fibers,” in Optical Fiber Communication Conference, Vol. 4 of OSA 1991 Technical Digest Series, (Optical Society of America, Washington, D.C., 1991), p. 46.

Shaw, H. J.

R. A. Bergh, G. Kotler, H. J. Shaw, “Single-mode fibre optic directional coupler,” Electron. Lett. 27, 260–261 (1980).
[CrossRef]

Stolen, R. H.

R. H. Stolen, R. P. DePaula, “Single-mode fiber components,” Proc. IEEE 75, 1498–1511 (1987).
[CrossRef]

Thyagarajan, K.

A. Kumar, S. Pilevar, K. Thyagarajan, “Measurement on variation of birefringence with depth of polishing in elliptic core fibers,” Opt. Commun. 72, 187–189 (1989).
[CrossRef]

A. Kumar, V. Gupta, K. Thyagarajan, “Goemetrical birefringence of polished and D-shape fibers,” Opt. Commun. 61, 195–198 (1987).
[CrossRef]

A. Kumar, K. Thyagarajan, K. Ghatak, “Analysis of rectangular-core dielectric waveguides: an accurate perturbation approach,” Opt. Lett. 8, 63–65 (1983).
[CrossRef] [PubMed]

Electron. Lett. (1)

R. A. Bergh, G. Kotler, H. J. Shaw, “Single-mode fibre optic directional coupler,” Electron. Lett. 27, 260–261 (1980).
[CrossRef]

IEEE J. Quantum Electron. (1)

I. P. Kaminow, “Polarization in optical fibers,” IEEE J. Quantum Electron. QE-17, 15–22 (1981).
[CrossRef]

Laser Focus (1)

I. P. Kaminow, “Polarization in fibers,” Laser Focus 16(6), 80–84 (1980).

Opt. Commun. (2)

A. Kumar, V. Gupta, K. Thyagarajan, “Goemetrical birefringence of polished and D-shape fibers,” Opt. Commun. 61, 195–198 (1987).
[CrossRef]

A. Kumar, S. Pilevar, K. Thyagarajan, “Measurement on variation of birefringence with depth of polishing in elliptic core fibers,” Opt. Commun. 72, 187–189 (1989).
[CrossRef]

Opt. Lett. (1)

Proc. IEEE (1)

R. H. Stolen, R. P. DePaula, “Single-mode fiber components,” Proc. IEEE 75, 1498–1511 (1987).
[CrossRef]

Other (4)

K. L. Belsley, J. B. Carroll, L. A. Hess, D. R. Huber, D. Schmadel, “Optically multiplexed interferometric fiber optic sensor system,” in Fiber Optic and Laser Sensors III, E. L. Moore, O. G. Ramer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.566, 257–264 (1985).

C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, New York, 1989), p. 414.

G. T. Pugmire, M. A. Jensen, R. H. Selfridge, “Controllable cladding removal for in-fiber integrated optics components,” in Optoelectronic Devices and Applications, S. Sriram, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1338, 2–10 (1990).

J. D. Freeze, M. A. Jensen, R. H. Selfridge, “High-efficiency diffraction gratings in D-type fibers,” in Optical Fiber Communication Conference, Vol. 4 of OSA 1991 Technical Digest Series, (Optical Society of America, Washington, D.C., 1991), p. 46.

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Figures (9)

Fig. 1
Fig. 1

Geometry for approximating an elliptical core with a rectangular core.

Fig. 2
Fig. 2

Superposition of asymmetrical and symmetrical planar waveguides. The region of interest is the overlapping rectangle.

Fig. 3
Fig. 3

Asymmetrical planar wave guide used to obtain the y-direction phase constant.

Fig. 4
Fig. 4

Symmetrical infinite-slab waveguide for phase constants in the x direction.

Fig. 5
Fig. 5

Birefringence curve for a 633-nm fiber as a function of cladding thickness; the distance to the core is in micrometers.

Fig. 6
Fig. 6

Experimental arrangement used to monitor the effects of etching on fiber characteristics.

Fig. 7
Fig. 7

Output intensity of light for one polarization angle taken from the output of a 633-nm fiber as a function of cladding thickness; distance to core in micrometers.

Fig. 8
Fig. 8

Output from the experimental arrangement obtained for a 633-nm D fiber for a 2-cm etch length.

Fig. 9
Fig. 9

Predicted etch depth (μm) versus measured etch depths (μm, SEM) compared with the ideal curve.

Equations (19)

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k o 2 n 1 2 = h a i 2 = h a i 2 + β z a i 2 ;
k o 2 n 2 2 = q a i 2 = q a i 2 + β z a i 2 ;
k o 2 n 3 2 = - p a i 2 + β z a i 2 ,
Z y + ( y = b ) = Z 2 [ Z 3 + Z 2 tan h ( q a i d ) Z 2 + Z 3 tan h ( q a i d ) ] ,
Z y ( y = b ) = Z 1 [ Z 2 + j Z 1 tan ( 2 h a i b ) Z 1 + j Z 2 tan ( 2 h a i b ) ] ,
Z y + ( y = b ) = - Z y - ( y = b ) .
exp ( 2 q a i d ) ( Z 3 + Z 2 ) [ j ( Z 2 2 + Z 1 2 ) tan ( 2 h a i b ) + 2 Z 1 Z 2 ] = j ( Z 3 + Z 2 ) ( Z 1 2 - Z 2 2 ) tan ( 2 b h a i ) .
Z 1 = ω μ o h a x ,             Z 2 = ω μ o - j q a x ,             Z 3 = ω μ o - j p a x .
Z 1 = h a y ω 1 ,             Z 2 = - j q a y ω 2 ,             Z 3 = - j p a y ω 3 .
exp ( 2 q a i d ) 1 ( t i 2 q a i - s i 2 p a i ) exp ( 2 q a i d ) 1 ( t i 2 q a i - s i 2 p a i ) × [ ( r i 4 q a i 2 - s i 4 h a i 2 ) tan ( 2 h a i b ) + 2 r i 2 s i 2 h a i q a i ] = r i 4 q a i 2 + s i 4 h a i 2 t i 2 q a i + s i 2 p a i tan ( 2 h a i b ) ,
u i h s i tan ( h s i a ) = α s i ,
k o 2 n 1 2 = h s i 2 + β z s i 2 ;
k o 2 n 2 2 = α s i 2 + β z s i 2 ,
k o 2 n 1 2 = β z i 2 + h a i 2 + h s i 2 ,
( β z i ) 2 = β z s i 2 + β z a i 2 - k o 2 n 1 2 .
B = β z x - β z y k o .
n 1 = 1.4820 ,             n 2 = 1.4540 ,             n 3 = 1.33 , γ = 633 nm ,             2 a = 2.50 μ m ,             2 b = 1.25 μ m .
I ( 45 ° , 45 ° ) = 1 2 E o 2 cos 2 Φ 2 ,
Φ = ϕ x - ϕ y = ( β z x - β z y ) l + ( β z 0 x - β z 0 y ) ( L - l ) ,

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