Abstract

I use the direct far-field method to measure the mode-field diameter of a single-mode fiber with an expanded uncertainty of 30 nm, with a coverage factor of 2. For a step-index fiber with a mode-field diameter of approximately 9 μm, the major sources of uncertainty are nonlinearity in the electronics, angular errors and scattered light in the apparatus, and the polarization and noncircularity of the mode of the fiber. The paper concludes by showing an inconsistency in the derivation of the far-field expression for mode-field diameter.

© 1998 Optical Society of America

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References

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  1. , “Measurement of mode field diameter of single-mode optical fiber,” Fiberoptic Test Procedure FOTP-191, Telecommunications Industry Association, 2500 Wilson Blvd., Suite 300, Arlington, Va. 22201-3834 (1998).
  2. K. Petermann, “Constraints for fundamental-mode spot size for broadband dispersion-compensated single-mode fibres,” Electron. Lett. 19, 712–714 (1983);C. Pask, “Physical interpretation of Petermann’s strange spot size for single-mode fibres,” Electron. Lett. 20, 144–145 (1984).
    [CrossRef]
  3. M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, A. Sharma, “Mode field diameter measurements in single-mode optical fibers,” J. Lightwave Technol. 7, 1139–1152 (1989).
    [CrossRef]
  4. D. L. Franzen, M. Young, A. H. Cherin, E. D. Head, M. J. Hackert, K. W. Raine, J. G. N. Baines, “Numerical aperture of multimode fibers by several methods: resolving differences,” J. Lightwave Technol.7, 896–900 (1989); E. M. Kim, D. L. Franzen, “Measurement of far-field radiation patterns from optical fibers,” in Optical Fiber Characterization, G. E. Chamberlain, G. W. Day, D. L. Franzen, E. M. Kim, M. Young, eds. Natl. Bur. Stand. (U.S.) Spec. Publ. 637 (U.S. GPO, Washington, D.C., 1983), Vol. 2, Chap. 4.
  5. M. Young, Optics and Lasers, including Fibers and Optical Waveguides, 4th ed. (Springer, New York, 1993), Sec. 5.5.4; see also M. Young, “The pinhole camera,” Phys. Teacher 27, 648–655 (1989); “Pinhole optics,” Appl. Opt. 10, 2763–2767 (1971).
  6. M. Young, Optics and Lasers, including Fibers and Optical Waveguides, 4th ed. (Springer, New York, 1993), Chap. 4, especially Eqs. (4.2), (4.3), and (4.22).
  7. M. Young, “Can you describe optical surface quality with one or two numbers?,” in Optical Specifications: Components and Systems, W. J. Smith, R. E. Fischer, eds., Proc. SPIE406, 12–22 (1983).
    [CrossRef]
  8. T. J. Drapela, D. L. Franzen, A. H. Cherin, R. J. Smith, “A comparison of far-field methods for determining mode field diameter of single-mode fibers using both Gaussian and Petermann definitions,” J. Lightwave Technol. 7, 1153–1157 (1989).
    [CrossRef]
  9. , Guide to the Expression of Uncertainty in Measurement (International Organization for Standardization, Case postale 56, CH-1211, Genève 20, Switzerland, 1993).
  10. J. W. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978), pp. 266–272.
  11. P. S. Lovely, C. S. Shaar, “Systematic errors in measurement of mode field diameter,” in Fiber Optic Networks & Coherent Technology in Fiber Optic Systems II, J. D. Chipman, H. R. D. Sunak, eds., Proc. SPIE841, 240–247 (1987).
    [CrossRef]
  12. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vettering, Numerical Recipes in C (Cambridge U. Press, New York, 1992), Chap. 4.
  13. Ref. 10, Chap. 3.
  14. W. T. Anderson, V. Shah, L. Curtis, A. J. Johnson, J. P. Kilmer, “Mode-field diameter measurements for single-mode fibers with non-Gaussian field profiles,” J. Lightwave Technol. LT-5, 211–217 (1987).
    [CrossRef]
  15. K. Enslein, A. Ralston, H. S. Wilf, Statistical Methods for Digital Computer (Wiley, New York, 1977).
  16. A. H. Cherin, An Introduction to Optical Fibers (McGraw-Hill, New York, 1983), Sect. 5-2.
  17. M. Young, “Optical fiber index profiles by the refracted-ray method,” Appl. Opt. 20, 3415–3422 (1981).
    [CrossRef] [PubMed]
  18. A. B. Sharma, S. J. Halme, M. M. Butusov, Optical Fiber Systems and Their Components (Springer, New York, 1981), Sec. 3.4.
  19. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968); M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).
  20. M. Young, R. C. Wittmann, “Vector theory of diffraction by a single-mode fiber: application to mode-field diameter measurements,” Opt. Lett. 18, 1715–1717 (1993).
    [CrossRef] [PubMed]
  21. A. Sommerfeld, Optics: Lectures on Theoretical Physics (Academic, New York, 1964), Vol. 4, Sec. 34.
  22. R. C. Wittmann, M. Young, “Are the formulas for mode-field diameter correct?,” submitted to the Symposium on Optical Fiber Measurements, Boulder, Colo., 15–17 September 1998.

1993 (1)

1989 (2)

M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, A. Sharma, “Mode field diameter measurements in single-mode optical fibers,” J. Lightwave Technol. 7, 1139–1152 (1989).
[CrossRef]

T. J. Drapela, D. L. Franzen, A. H. Cherin, R. J. Smith, “A comparison of far-field methods for determining mode field diameter of single-mode fibers using both Gaussian and Petermann definitions,” J. Lightwave Technol. 7, 1153–1157 (1989).
[CrossRef]

1987 (1)

W. T. Anderson, V. Shah, L. Curtis, A. J. Johnson, J. P. Kilmer, “Mode-field diameter measurements for single-mode fibers with non-Gaussian field profiles,” J. Lightwave Technol. LT-5, 211–217 (1987).
[CrossRef]

1983 (1)

K. Petermann, “Constraints for fundamental-mode spot size for broadband dispersion-compensated single-mode fibres,” Electron. Lett. 19, 712–714 (1983);C. Pask, “Physical interpretation of Petermann’s strange spot size for single-mode fibres,” Electron. Lett. 20, 144–145 (1984).
[CrossRef]

1981 (1)

Anderson, W. T.

W. T. Anderson, V. Shah, L. Curtis, A. J. Johnson, J. P. Kilmer, “Mode-field diameter measurements for single-mode fibers with non-Gaussian field profiles,” J. Lightwave Technol. LT-5, 211–217 (1987).
[CrossRef]

Artiglia, M.

M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, A. Sharma, “Mode field diameter measurements in single-mode optical fibers,” J. Lightwave Technol. 7, 1139–1152 (1989).
[CrossRef]

Baines, J. G. N.

D. L. Franzen, M. Young, A. H. Cherin, E. D. Head, M. J. Hackert, K. W. Raine, J. G. N. Baines, “Numerical aperture of multimode fibers by several methods: resolving differences,” J. Lightwave Technol.7, 896–900 (1989); E. M. Kim, D. L. Franzen, “Measurement of far-field radiation patterns from optical fibers,” in Optical Fiber Characterization, G. E. Chamberlain, G. W. Day, D. L. Franzen, E. M. Kim, M. Young, eds. Natl. Bur. Stand. (U.S.) Spec. Publ. 637 (U.S. GPO, Washington, D.C., 1983), Vol. 2, Chap. 4.

Butusov, M. M.

A. B. Sharma, S. J. Halme, M. M. Butusov, Optical Fiber Systems and Their Components (Springer, New York, 1981), Sec. 3.4.

Cherin, A. H.

T. J. Drapela, D. L. Franzen, A. H. Cherin, R. J. Smith, “A comparison of far-field methods for determining mode field diameter of single-mode fibers using both Gaussian and Petermann definitions,” J. Lightwave Technol. 7, 1153–1157 (1989).
[CrossRef]

D. L. Franzen, M. Young, A. H. Cherin, E. D. Head, M. J. Hackert, K. W. Raine, J. G. N. Baines, “Numerical aperture of multimode fibers by several methods: resolving differences,” J. Lightwave Technol.7, 896–900 (1989); E. M. Kim, D. L. Franzen, “Measurement of far-field radiation patterns from optical fibers,” in Optical Fiber Characterization, G. E. Chamberlain, G. W. Day, D. L. Franzen, E. M. Kim, M. Young, eds. Natl. Bur. Stand. (U.S.) Spec. Publ. 637 (U.S. GPO, Washington, D.C., 1983), Vol. 2, Chap. 4.

A. H. Cherin, An Introduction to Optical Fibers (McGraw-Hill, New York, 1983), Sect. 5-2.

Coppa, G.

M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, A. Sharma, “Mode field diameter measurements in single-mode optical fibers,” J. Lightwave Technol. 7, 1139–1152 (1989).
[CrossRef]

Curtis, L.

W. T. Anderson, V. Shah, L. Curtis, A. J. Johnson, J. P. Kilmer, “Mode-field diameter measurements for single-mode fibers with non-Gaussian field profiles,” J. Lightwave Technol. LT-5, 211–217 (1987).
[CrossRef]

Di Vita, P.

M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, A. Sharma, “Mode field diameter measurements in single-mode optical fibers,” J. Lightwave Technol. 7, 1139–1152 (1989).
[CrossRef]

Drapela, T. J.

T. J. Drapela, D. L. Franzen, A. H. Cherin, R. J. Smith, “A comparison of far-field methods for determining mode field diameter of single-mode fibers using both Gaussian and Petermann definitions,” J. Lightwave Technol. 7, 1153–1157 (1989).
[CrossRef]

Enslein, K.

K. Enslein, A. Ralston, H. S. Wilf, Statistical Methods for Digital Computer (Wiley, New York, 1977).

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vettering, Numerical Recipes in C (Cambridge U. Press, New York, 1992), Chap. 4.

Franzen, D. L.

T. J. Drapela, D. L. Franzen, A. H. Cherin, R. J. Smith, “A comparison of far-field methods for determining mode field diameter of single-mode fibers using both Gaussian and Petermann definitions,” J. Lightwave Technol. 7, 1153–1157 (1989).
[CrossRef]

D. L. Franzen, M. Young, A. H. Cherin, E. D. Head, M. J. Hackert, K. W. Raine, J. G. N. Baines, “Numerical aperture of multimode fibers by several methods: resolving differences,” J. Lightwave Technol.7, 896–900 (1989); E. M. Kim, D. L. Franzen, “Measurement of far-field radiation patterns from optical fibers,” in Optical Fiber Characterization, G. E. Chamberlain, G. W. Day, D. L. Franzen, E. M. Kim, M. Young, eds. Natl. Bur. Stand. (U.S.) Spec. Publ. 637 (U.S. GPO, Washington, D.C., 1983), Vol. 2, Chap. 4.

Gaskill, J. W.

J. W. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978), pp. 266–272.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968); M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

Hackert, M. J.

D. L. Franzen, M. Young, A. H. Cherin, E. D. Head, M. J. Hackert, K. W. Raine, J. G. N. Baines, “Numerical aperture of multimode fibers by several methods: resolving differences,” J. Lightwave Technol.7, 896–900 (1989); E. M. Kim, D. L. Franzen, “Measurement of far-field radiation patterns from optical fibers,” in Optical Fiber Characterization, G. E. Chamberlain, G. W. Day, D. L. Franzen, E. M. Kim, M. Young, eds. Natl. Bur. Stand. (U.S.) Spec. Publ. 637 (U.S. GPO, Washington, D.C., 1983), Vol. 2, Chap. 4.

Halme, S. J.

A. B. Sharma, S. J. Halme, M. M. Butusov, Optical Fiber Systems and Their Components (Springer, New York, 1981), Sec. 3.4.

Head, E. D.

D. L. Franzen, M. Young, A. H. Cherin, E. D. Head, M. J. Hackert, K. W. Raine, J. G. N. Baines, “Numerical aperture of multimode fibers by several methods: resolving differences,” J. Lightwave Technol.7, 896–900 (1989); E. M. Kim, D. L. Franzen, “Measurement of far-field radiation patterns from optical fibers,” in Optical Fiber Characterization, G. E. Chamberlain, G. W. Day, D. L. Franzen, E. M. Kim, M. Young, eds. Natl. Bur. Stand. (U.S.) Spec. Publ. 637 (U.S. GPO, Washington, D.C., 1983), Vol. 2, Chap. 4.

Johnson, A. J.

W. T. Anderson, V. Shah, L. Curtis, A. J. Johnson, J. P. Kilmer, “Mode-field diameter measurements for single-mode fibers with non-Gaussian field profiles,” J. Lightwave Technol. LT-5, 211–217 (1987).
[CrossRef]

Kilmer, J. P.

W. T. Anderson, V. Shah, L. Curtis, A. J. Johnson, J. P. Kilmer, “Mode-field diameter measurements for single-mode fibers with non-Gaussian field profiles,” J. Lightwave Technol. LT-5, 211–217 (1987).
[CrossRef]

Lovely, P. S.

P. S. Lovely, C. S. Shaar, “Systematic errors in measurement of mode field diameter,” in Fiber Optic Networks & Coherent Technology in Fiber Optic Systems II, J. D. Chipman, H. R. D. Sunak, eds., Proc. SPIE841, 240–247 (1987).
[CrossRef]

Petermann, K.

K. Petermann, “Constraints for fundamental-mode spot size for broadband dispersion-compensated single-mode fibres,” Electron. Lett. 19, 712–714 (1983);C. Pask, “Physical interpretation of Petermann’s strange spot size for single-mode fibres,” Electron. Lett. 20, 144–145 (1984).
[CrossRef]

Potenza, M.

M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, A. Sharma, “Mode field diameter measurements in single-mode optical fibers,” J. Lightwave Technol. 7, 1139–1152 (1989).
[CrossRef]

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vettering, Numerical Recipes in C (Cambridge U. Press, New York, 1992), Chap. 4.

Raine, K. W.

D. L. Franzen, M. Young, A. H. Cherin, E. D. Head, M. J. Hackert, K. W. Raine, J. G. N. Baines, “Numerical aperture of multimode fibers by several methods: resolving differences,” J. Lightwave Technol.7, 896–900 (1989); E. M. Kim, D. L. Franzen, “Measurement of far-field radiation patterns from optical fibers,” in Optical Fiber Characterization, G. E. Chamberlain, G. W. Day, D. L. Franzen, E. M. Kim, M. Young, eds. Natl. Bur. Stand. (U.S.) Spec. Publ. 637 (U.S. GPO, Washington, D.C., 1983), Vol. 2, Chap. 4.

Ralston, A.

K. Enslein, A. Ralston, H. S. Wilf, Statistical Methods for Digital Computer (Wiley, New York, 1977).

Shaar, C. S.

P. S. Lovely, C. S. Shaar, “Systematic errors in measurement of mode field diameter,” in Fiber Optic Networks & Coherent Technology in Fiber Optic Systems II, J. D. Chipman, H. R. D. Sunak, eds., Proc. SPIE841, 240–247 (1987).
[CrossRef]

Shah, V.

W. T. Anderson, V. Shah, L. Curtis, A. J. Johnson, J. P. Kilmer, “Mode-field diameter measurements for single-mode fibers with non-Gaussian field profiles,” J. Lightwave Technol. LT-5, 211–217 (1987).
[CrossRef]

Sharma, A.

M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, A. Sharma, “Mode field diameter measurements in single-mode optical fibers,” J. Lightwave Technol. 7, 1139–1152 (1989).
[CrossRef]

Sharma, A. B.

A. B. Sharma, S. J. Halme, M. M. Butusov, Optical Fiber Systems and Their Components (Springer, New York, 1981), Sec. 3.4.

Smith, R. J.

T. J. Drapela, D. L. Franzen, A. H. Cherin, R. J. Smith, “A comparison of far-field methods for determining mode field diameter of single-mode fibers using both Gaussian and Petermann definitions,” J. Lightwave Technol. 7, 1153–1157 (1989).
[CrossRef]

Sommerfeld, A.

A. Sommerfeld, Optics: Lectures on Theoretical Physics (Academic, New York, 1964), Vol. 4, Sec. 34.

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vettering, Numerical Recipes in C (Cambridge U. Press, New York, 1992), Chap. 4.

Vettering, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vettering, Numerical Recipes in C (Cambridge U. Press, New York, 1992), Chap. 4.

Wilf, H. S.

K. Enslein, A. Ralston, H. S. Wilf, Statistical Methods for Digital Computer (Wiley, New York, 1977).

Wittmann, R. C.

M. Young, R. C. Wittmann, “Vector theory of diffraction by a single-mode fiber: application to mode-field diameter measurements,” Opt. Lett. 18, 1715–1717 (1993).
[CrossRef] [PubMed]

R. C. Wittmann, M. Young, “Are the formulas for mode-field diameter correct?,” submitted to the Symposium on Optical Fiber Measurements, Boulder, Colo., 15–17 September 1998.

Young, M.

M. Young, R. C. Wittmann, “Vector theory of diffraction by a single-mode fiber: application to mode-field diameter measurements,” Opt. Lett. 18, 1715–1717 (1993).
[CrossRef] [PubMed]

M. Young, “Optical fiber index profiles by the refracted-ray method,” Appl. Opt. 20, 3415–3422 (1981).
[CrossRef] [PubMed]

M. Young, Optics and Lasers, including Fibers and Optical Waveguides, 4th ed. (Springer, New York, 1993), Chap. 4, especially Eqs. (4.2), (4.3), and (4.22).

M. Young, Optics and Lasers, including Fibers and Optical Waveguides, 4th ed. (Springer, New York, 1993), Sec. 5.5.4; see also M. Young, “The pinhole camera,” Phys. Teacher 27, 648–655 (1989); “Pinhole optics,” Appl. Opt. 10, 2763–2767 (1971).

M. Young, “Can you describe optical surface quality with one or two numbers?,” in Optical Specifications: Components and Systems, W. J. Smith, R. E. Fischer, eds., Proc. SPIE406, 12–22 (1983).
[CrossRef]

R. C. Wittmann, M. Young, “Are the formulas for mode-field diameter correct?,” submitted to the Symposium on Optical Fiber Measurements, Boulder, Colo., 15–17 September 1998.

D. L. Franzen, M. Young, A. H. Cherin, E. D. Head, M. J. Hackert, K. W. Raine, J. G. N. Baines, “Numerical aperture of multimode fibers by several methods: resolving differences,” J. Lightwave Technol.7, 896–900 (1989); E. M. Kim, D. L. Franzen, “Measurement of far-field radiation patterns from optical fibers,” in Optical Fiber Characterization, G. E. Chamberlain, G. W. Day, D. L. Franzen, E. M. Kim, M. Young, eds. Natl. Bur. Stand. (U.S.) Spec. Publ. 637 (U.S. GPO, Washington, D.C., 1983), Vol. 2, Chap. 4.

Appl. Opt. (1)

Electron. Lett. (1)

K. Petermann, “Constraints for fundamental-mode spot size for broadband dispersion-compensated single-mode fibres,” Electron. Lett. 19, 712–714 (1983);C. Pask, “Physical interpretation of Petermann’s strange spot size for single-mode fibres,” Electron. Lett. 20, 144–145 (1984).
[CrossRef]

J. Lightwave Technol. (3)

M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, A. Sharma, “Mode field diameter measurements in single-mode optical fibers,” J. Lightwave Technol. 7, 1139–1152 (1989).
[CrossRef]

T. J. Drapela, D. L. Franzen, A. H. Cherin, R. J. Smith, “A comparison of far-field methods for determining mode field diameter of single-mode fibers using both Gaussian and Petermann definitions,” J. Lightwave Technol. 7, 1153–1157 (1989).
[CrossRef]

W. T. Anderson, V. Shah, L. Curtis, A. J. Johnson, J. P. Kilmer, “Mode-field diameter measurements for single-mode fibers with non-Gaussian field profiles,” J. Lightwave Technol. LT-5, 211–217 (1987).
[CrossRef]

Opt. Lett. (1)

Other (16)

A. Sommerfeld, Optics: Lectures on Theoretical Physics (Academic, New York, 1964), Vol. 4, Sec. 34.

R. C. Wittmann, M. Young, “Are the formulas for mode-field diameter correct?,” submitted to the Symposium on Optical Fiber Measurements, Boulder, Colo., 15–17 September 1998.

, “Measurement of mode field diameter of single-mode optical fiber,” Fiberoptic Test Procedure FOTP-191, Telecommunications Industry Association, 2500 Wilson Blvd., Suite 300, Arlington, Va. 22201-3834 (1998).

K. Enslein, A. Ralston, H. S. Wilf, Statistical Methods for Digital Computer (Wiley, New York, 1977).

A. H. Cherin, An Introduction to Optical Fibers (McGraw-Hill, New York, 1983), Sect. 5-2.

A. B. Sharma, S. J. Halme, M. M. Butusov, Optical Fiber Systems and Their Components (Springer, New York, 1981), Sec. 3.4.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968); M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

, Guide to the Expression of Uncertainty in Measurement (International Organization for Standardization, Case postale 56, CH-1211, Genève 20, Switzerland, 1993).

J. W. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978), pp. 266–272.

P. S. Lovely, C. S. Shaar, “Systematic errors in measurement of mode field diameter,” in Fiber Optic Networks & Coherent Technology in Fiber Optic Systems II, J. D. Chipman, H. R. D. Sunak, eds., Proc. SPIE841, 240–247 (1987).
[CrossRef]

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vettering, Numerical Recipes in C (Cambridge U. Press, New York, 1992), Chap. 4.

Ref. 10, Chap. 3.

D. L. Franzen, M. Young, A. H. Cherin, E. D. Head, M. J. Hackert, K. W. Raine, J. G. N. Baines, “Numerical aperture of multimode fibers by several methods: resolving differences,” J. Lightwave Technol.7, 896–900 (1989); E. M. Kim, D. L. Franzen, “Measurement of far-field radiation patterns from optical fibers,” in Optical Fiber Characterization, G. E. Chamberlain, G. W. Day, D. L. Franzen, E. M. Kim, M. Young, eds. Natl. Bur. Stand. (U.S.) Spec. Publ. 637 (U.S. GPO, Washington, D.C., 1983), Vol. 2, Chap. 4.

M. Young, Optics and Lasers, including Fibers and Optical Waveguides, 4th ed. (Springer, New York, 1993), Sec. 5.5.4; see also M. Young, “The pinhole camera,” Phys. Teacher 27, 648–655 (1989); “Pinhole optics,” Appl. Opt. 10, 2763–2767 (1971).

M. Young, Optics and Lasers, including Fibers and Optical Waveguides, 4th ed. (Springer, New York, 1993), Chap. 4, especially Eqs. (4.2), (4.3), and (4.22).

M. Young, “Can you describe optical surface quality with one or two numbers?,” in Optical Specifications: Components and Systems, W. J. Smith, R. E. Fischer, eds., Proc. SPIE406, 12–22 (1983).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Schematic drawing of the far-field scanner showing the fiber, pinhole, and detector.

Fig. 2
Fig. 2

Far-field scan of a step-index fiber at 1310 nm. The logarithm of intensity is plotted as a function of angle.

Fig. 3
Fig. 3

Far-field scans of two step-index fibers and one dispersion-compensating fiber at 1310 nm.

Fig. 4
Fig. 4

Comparison of the results of this study (crosses) with an earlier interlaboratory comparison (open circles) of mode-field diameters of two step-index fibers and two dispersion-shifted fibers. Each circle represents the result of a different laboratory.

Fig. 5
Fig. 5

Change of measured mode-field diameter as a function of vertical positioning error. The solid curve is an estimate based on the sag formula.

Fig. 6
Fig. 6

Change of measured mode-field diameter as a function of lateral or horizontal positioning error. The open circles and squares are measured data. The dashed curve is a parabolic fit to the open-circle data. The solid curve is a theoretical curve that approximates the dashed curve. The crosses represent an attempt to correct for the offset mathematically.

Fig. 7
Fig. 7

Refractive-index profile of a step-index fiber. The left curve is the edge of the fiber and has a transition width of approximately 0.4 μm. The core displays a transition width of approximately 0.8 μm.

Fig. 8
Fig. 8

Superposition of eight scans of a dispersion-compensating fiber with four orientations 90° apart and two orthogonal, linear polarizations at each orientation.

Fig. 9
Fig. 9

Ratios of scans taken with orthogonal polarizations at each of the four orientations in Fig. 8.

Tables (5)

Tables Icon

Table 1 Mode-Field Diameter Calculated for Various Angular Increments, Simulated Data

Tables Icon

Table 2 Measured Mode-Field Diameter as a Function of Maximum Scanning Angle

Tables Icon

Table 3 Change of Mode-Field Diameter when a Constant Background is Added to Real Data

Tables Icon

Table 4 Change of Mode-Field Diameter when a Constant Background is Added to Simulated Dataa

Tables Icon

Table 5 Summary of Uncertainties

Equations (14)

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

2 w 0 = λ / π 2     I θ sin   θ   cos   θ   d   θ   I θ sin 3   θ   cos   θ   d   θ 1 / 2 ,
I θ = exp - 2   sin 2   θ /   sin 2   θ 0 ,
  f x d x = 3 / 8 f 1 + 7 / 16 f 2 + 23 / 24 f 3 + f 4 + f 5 + + f N - 4 + f N - 3 + 23 / 24 f N - 2 + 7 / 6 f N - 1 + 3 / 8 f N δ x ,
w 0 P = 2     | e r | 2 r   d r   | e r / r | 2 r   d r 1 / 2 ,
E θ = O θ HT e a r ,
E θ / O θ = HT e a r
e a r = HT - 1 E θ / O θ ,
2 w 0 P = λ / π 2     I θ tan   θ   d   θ   I θ sin 2   θ   tan   θ   d   θ 1 / 2 .
E θ = O θ HT e a r ,   z exp ik z z ,
e a r ,   z = HT - 1 E θ / O θ exp - ik z z .
w 0 a = 2     | e a r | 2   r d r   | e a r / r | 2 r d r 1 / 2 ,
e r = exp - r 2 / w 0 2 1 - r 1 - r 0 circ r / a ,
E sin   θ / O θ = exp - sin 2   θ / sin 2   θ 0 - r 1 - r 0 × exp - sin 2   θ / sin 2   θ 0 * somb a ξ ,
I θ / O 2 θ = exp - 2   sin 2   θ / sin 2   θ 0 - 2 r 1 - r 0 exp - sin 2   θ / sin 2   θ 0 exp - sin 2   θ / sin 2   θ 0 * somb a ξ ,

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