Abstract

This paper has two primary purposes. First, it provides an elementary description and tutorial overview of the refracted-ray method of measuring fiber index profiles. Second, it presents new results concerning the theoretical foundation, the linearity and precision, and other aspects of the method. In particular, we find that index differences may be measured to 5% or better and conclude by showing ~3% agreement with another laboratory and good agreement with numerical aperture measurements performed by participants in an interlaboratory comparison.

© 1981 Optical Society of America

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  1. W. J. Stewart, A New Technique for Measuring the Refractive Index Profiles of Graded Optical Fibers, in Technical Digest, IOOC (IECE, Tokyo, 1977), pp. 395–398.
  2. K. I. White, Practical Application of the Refracted Near-Field Technique for the Measurement of Optical Fiber Refractive Index Profiles, Opt. Quantum Electron. 11, 185 (1979).
    [CrossRef]
  3. M. Young, Calibration Technique for Refracted Near-Field Scanning of Optical Fibers, Appl. Opt. 19, 2479 (1980).
    [CrossRef] [PubMed]
  4. M. Young, Linearity and Resolution of Refracted Near-Field Scanning, in Technical Digest—Symposium on Optical Fiber Measurements, Natl. Bur. Stand. U.S. Spec. Publ. 597 (1980).
  5. M. Young, Refracted-Ray Scanning (Refracted Near-Field Scanning) for Measuring Index Profiles of Optical Fibers, Natl. Bur. Stand. U.S. Tech. Note 1038 (1981).
  6. M. J. Saunders, Optical Fiber Profiles Using the Refracted Near-Field Technique: a Comparison with Other Methods, Appl. Opt. 20, 1645 (1981); M. J. Saunders, Optical Fiber Profiles Using the Refracted Near-Field Technique: A Comparison with Interferometry, Technical Digest—Symposium on Optical Fiber Measurements, 1980, Digest supplement (Optical Electronic Metrology Group, U.S. National Bureau of Standards, Boulder, Colo. 80303, 1980); see also Ref. 4 for complete digest.
    [CrossRef] [PubMed]
  7. D. C. J. Reid, W. J. Stewart, Ultrahigh Resolution Refractive Near-Field Profiling, in Technical Digest, Third International Conference IOOC (Optical Society of America, Washington, D.C., 1981), paper TUG6.
  8. D. Marcuse, H. M. Presby, Index Profile Measurements of Fibers and Their Evaluation, Proc. IEEE 68, 666 (1980).
    [CrossRef]
  9. H. M. Presby, D. Marcuse, The Index-Profile Characterization of Fiber Preforms and Drawn Fibers, Proc. IEEE 68, 1198 (1980).
    [CrossRef]
  10. D. Gloge, E. A. J. Marcatili, Multimode Theory of Graded-Core Fibers, Bell Syst. Tech. J. 52, 1563 (1973).
  11. D. N. Payne, F. M. E. Sladen, M. J. Adams, Index Profile Determination in Graded Index Fibers, in Proceedings, First Conference on Optical Fibre Communication, IEE Conf. Publ.London132, 43 (1975).
  12. D. N. Payne, F. M. E. Sladen, M. J. Adams, Determination of Optical Fiber Refractive Index Profiles by a Near-Field Scanning Technique, Appl. Phys. Lett. 28, 255 (1976).
    [CrossRef]
  13. M. J. Adams, D. N. Payne, F. M. E. Sladen, Correction Factors for the Determination of Optical-Fibre Refractive-Index Profiles by the Near-Field Scan Technique, Electron. Lett. 12, 281 (1976).
    [CrossRef]
  14. M. J. Adams, D. N. Payne, F. M. E. Sladen, Length-Dependent Effects Due to Leaky Modes on Multimode Graded-Index Optical Fibers, Opt. Commun. 17, 204 (1976).
    [CrossRef]
  15. J. A. Arnaud, R. M. deRosier, Novel Technique for Measuring the Index Profile of Optical Fibers, Bell Syst. Tech. J. 55, 1489 (1976).
  16. G. T. Sumner, A New Technique for Refractive Index Profile Measurement in Multimode Optical Fibres, Opt. Quantum Electron. 9, 79 (1977).
    [CrossRef]
  17. For simplicity of nomenclature and for avoiding confusion, I shall refer to both these methods as near-field scanning. When it is necessary to distinguish between them, I shall use the terms entrance-face scanning and exit-face scanning. Likewise, I will not use the somewhat cumbersome term refracted near-field scanning but rather will refer to the refracted-ray method.
  18. K. Petermann, Uncertainties of the Leaky Mode Correction for Near-Square-Law Optical Fibers, Electron. Lett. 13, 513 (1977).
    [CrossRef]
  19. M. Young, Optics and Lasers, An Engineering Physics Approach (Springer, New York, 1977), Chap. 3.
  20. A. W. Snyder, Leaky-Ray Theory of Optical Waveguides of Circular Cross Section, Appl. Phys. 4, 273 (1974).
    [CrossRef]
  21. A. W. Snyder, D. J. Mitchell, C. Pask, Failure of Geometric Optics for Analysis of Circular Fibers, J. Opt. Soc. Am. 64, 608 (1974).
    [CrossRef]
  22. A. W. Snyder, D. J. Mitchell, Leaky Rays on Circular Optical Fibers, J. Opt. Soc. Am. 64, 615 (1974).
    [CrossRef]
  23. W. J. Stewart, Detail Resolution in Optical Fibre Index Profiling Methods, AGARD Conf. Proc.219, 28-1 (1977). This work is also expanded in an unpublished paper.
  24. W. J. Stewart, Resolution of Near-Field Optical Fiber Refractive Index Profiling Methods, in Proceedings, International Meeting on Scanned Image Microscopy, London 1980 (Academic, New York, 1981), pp. 233–239.
  25. L. C. Martin, Technical Optics, Vol. 2 (Pitman and Sons, London, 1960), Chap. 3.
  26. I. H. Malitson, Interspecimen Comparison of the Refractive Index of Fused Silica, J. Opt. Soc. Am. 55, 1205 (1965).
    [CrossRef]
  27. J. W. Fleming, Material Dispersion of Lightguide Glasses, Electron. Lett. 14, 326 (1978).
    [CrossRef]
  28. J. W. Fleming, Dispersion in Step-Index Silicone-Clad Fibers, Appl. Opt. 18, 4000 (1979).
    [CrossRef] [PubMed]
  29. I am indebted to Michael Liva and William Sacher of Cargille Laboratories for providing the liquids along with their indices, their Sellmeier coefficients, and a statement of accuracy.
  30. M. G. Natrella, Experimental Statistics, Natl. Bur. Stand. U.S. Handb.91, 5-22, 5-23, 5-27 (1963).
  31. D. L. Franzen, E. M. Kim, Interlaboratory Measurement Comparison to Determine the Radiation Angle (N.A.) of Graded-Index Optical Fibers, Appl. Opt. 20, 1218 (1981).
    [CrossRef] [PubMed]

1981 (3)

1980 (4)

M. Young, Calibration Technique for Refracted Near-Field Scanning of Optical Fibers, Appl. Opt. 19, 2479 (1980).
[CrossRef] [PubMed]

M. Young, Linearity and Resolution of Refracted Near-Field Scanning, in Technical Digest—Symposium on Optical Fiber Measurements, Natl. Bur. Stand. U.S. Spec. Publ. 597 (1980).

D. Marcuse, H. M. Presby, Index Profile Measurements of Fibers and Their Evaluation, Proc. IEEE 68, 666 (1980).
[CrossRef]

H. M. Presby, D. Marcuse, The Index-Profile Characterization of Fiber Preforms and Drawn Fibers, Proc. IEEE 68, 1198 (1980).
[CrossRef]

1979 (2)

K. I. White, Practical Application of the Refracted Near-Field Technique for the Measurement of Optical Fiber Refractive Index Profiles, Opt. Quantum Electron. 11, 185 (1979).
[CrossRef]

J. W. Fleming, Dispersion in Step-Index Silicone-Clad Fibers, Appl. Opt. 18, 4000 (1979).
[CrossRef] [PubMed]

1978 (1)

J. W. Fleming, Material Dispersion of Lightguide Glasses, Electron. Lett. 14, 326 (1978).
[CrossRef]

1977 (2)

G. T. Sumner, A New Technique for Refractive Index Profile Measurement in Multimode Optical Fibres, Opt. Quantum Electron. 9, 79 (1977).
[CrossRef]

K. Petermann, Uncertainties of the Leaky Mode Correction for Near-Square-Law Optical Fibers, Electron. Lett. 13, 513 (1977).
[CrossRef]

1976 (4)

D. N. Payne, F. M. E. Sladen, M. J. Adams, Determination of Optical Fiber Refractive Index Profiles by a Near-Field Scanning Technique, Appl. Phys. Lett. 28, 255 (1976).
[CrossRef]

M. J. Adams, D. N. Payne, F. M. E. Sladen, Correction Factors for the Determination of Optical-Fibre Refractive-Index Profiles by the Near-Field Scan Technique, Electron. Lett. 12, 281 (1976).
[CrossRef]

M. J. Adams, D. N. Payne, F. M. E. Sladen, Length-Dependent Effects Due to Leaky Modes on Multimode Graded-Index Optical Fibers, Opt. Commun. 17, 204 (1976).
[CrossRef]

J. A. Arnaud, R. M. deRosier, Novel Technique for Measuring the Index Profile of Optical Fibers, Bell Syst. Tech. J. 55, 1489 (1976).

1974 (3)

1973 (1)

D. Gloge, E. A. J. Marcatili, Multimode Theory of Graded-Core Fibers, Bell Syst. Tech. J. 52, 1563 (1973).

1965 (1)

1963 (1)

M. G. Natrella, Experimental Statistics, Natl. Bur. Stand. U.S. Handb.91, 5-22, 5-23, 5-27 (1963).

Adams, M. J.

D. N. Payne, F. M. E. Sladen, M. J. Adams, Determination of Optical Fiber Refractive Index Profiles by a Near-Field Scanning Technique, Appl. Phys. Lett. 28, 255 (1976).
[CrossRef]

M. J. Adams, D. N. Payne, F. M. E. Sladen, Correction Factors for the Determination of Optical-Fibre Refractive-Index Profiles by the Near-Field Scan Technique, Electron. Lett. 12, 281 (1976).
[CrossRef]

M. J. Adams, D. N. Payne, F. M. E. Sladen, Length-Dependent Effects Due to Leaky Modes on Multimode Graded-Index Optical Fibers, Opt. Commun. 17, 204 (1976).
[CrossRef]

D. N. Payne, F. M. E. Sladen, M. J. Adams, Index Profile Determination in Graded Index Fibers, in Proceedings, First Conference on Optical Fibre Communication, IEE Conf. Publ.London132, 43 (1975).

Arnaud, J. A.

J. A. Arnaud, R. M. deRosier, Novel Technique for Measuring the Index Profile of Optical Fibers, Bell Syst. Tech. J. 55, 1489 (1976).

deRosier, R. M.

J. A. Arnaud, R. M. deRosier, Novel Technique for Measuring the Index Profile of Optical Fibers, Bell Syst. Tech. J. 55, 1489 (1976).

Fleming, J. W.

J. W. Fleming, Dispersion in Step-Index Silicone-Clad Fibers, Appl. Opt. 18, 4000 (1979).
[CrossRef] [PubMed]

J. W. Fleming, Material Dispersion of Lightguide Glasses, Electron. Lett. 14, 326 (1978).
[CrossRef]

Franzen, D. L.

Gloge, D.

D. Gloge, E. A. J. Marcatili, Multimode Theory of Graded-Core Fibers, Bell Syst. Tech. J. 52, 1563 (1973).

Kim, E. M.

Malitson, I. H.

Marcatili, E. A. J.

D. Gloge, E. A. J. Marcatili, Multimode Theory of Graded-Core Fibers, Bell Syst. Tech. J. 52, 1563 (1973).

Marcuse, D.

D. Marcuse, H. M. Presby, Index Profile Measurements of Fibers and Their Evaluation, Proc. IEEE 68, 666 (1980).
[CrossRef]

H. M. Presby, D. Marcuse, The Index-Profile Characterization of Fiber Preforms and Drawn Fibers, Proc. IEEE 68, 1198 (1980).
[CrossRef]

Martin, L. C.

L. C. Martin, Technical Optics, Vol. 2 (Pitman and Sons, London, 1960), Chap. 3.

Mitchell, D. J.

Natrella, M. G.

M. G. Natrella, Experimental Statistics, Natl. Bur. Stand. U.S. Handb.91, 5-22, 5-23, 5-27 (1963).

Pask, C.

Payne, D. N.

D. N. Payne, F. M. E. Sladen, M. J. Adams, Determination of Optical Fiber Refractive Index Profiles by a Near-Field Scanning Technique, Appl. Phys. Lett. 28, 255 (1976).
[CrossRef]

M. J. Adams, D. N. Payne, F. M. E. Sladen, Length-Dependent Effects Due to Leaky Modes on Multimode Graded-Index Optical Fibers, Opt. Commun. 17, 204 (1976).
[CrossRef]

M. J. Adams, D. N. Payne, F. M. E. Sladen, Correction Factors for the Determination of Optical-Fibre Refractive-Index Profiles by the Near-Field Scan Technique, Electron. Lett. 12, 281 (1976).
[CrossRef]

D. N. Payne, F. M. E. Sladen, M. J. Adams, Index Profile Determination in Graded Index Fibers, in Proceedings, First Conference on Optical Fibre Communication, IEE Conf. Publ.London132, 43 (1975).

Petermann, K.

K. Petermann, Uncertainties of the Leaky Mode Correction for Near-Square-Law Optical Fibers, Electron. Lett. 13, 513 (1977).
[CrossRef]

Presby, H. M.

D. Marcuse, H. M. Presby, Index Profile Measurements of Fibers and Their Evaluation, Proc. IEEE 68, 666 (1980).
[CrossRef]

H. M. Presby, D. Marcuse, The Index-Profile Characterization of Fiber Preforms and Drawn Fibers, Proc. IEEE 68, 1198 (1980).
[CrossRef]

Reid, D. C. J.

D. C. J. Reid, W. J. Stewart, Ultrahigh Resolution Refractive Near-Field Profiling, in Technical Digest, Third International Conference IOOC (Optical Society of America, Washington, D.C., 1981), paper TUG6.

Saunders, M. J.

Sladen, F. M. E.

M. J. Adams, D. N. Payne, F. M. E. Sladen, Correction Factors for the Determination of Optical-Fibre Refractive-Index Profiles by the Near-Field Scan Technique, Electron. Lett. 12, 281 (1976).
[CrossRef]

M. J. Adams, D. N. Payne, F. M. E. Sladen, Length-Dependent Effects Due to Leaky Modes on Multimode Graded-Index Optical Fibers, Opt. Commun. 17, 204 (1976).
[CrossRef]

D. N. Payne, F. M. E. Sladen, M. J. Adams, Determination of Optical Fiber Refractive Index Profiles by a Near-Field Scanning Technique, Appl. Phys. Lett. 28, 255 (1976).
[CrossRef]

D. N. Payne, F. M. E. Sladen, M. J. Adams, Index Profile Determination in Graded Index Fibers, in Proceedings, First Conference on Optical Fibre Communication, IEE Conf. Publ.London132, 43 (1975).

Snyder, A. W.

Stewart, W. J.

W. J. Stewart, A New Technique for Measuring the Refractive Index Profiles of Graded Optical Fibers, in Technical Digest, IOOC (IECE, Tokyo, 1977), pp. 395–398.

W. J. Stewart, Detail Resolution in Optical Fibre Index Profiling Methods, AGARD Conf. Proc.219, 28-1 (1977). This work is also expanded in an unpublished paper.

W. J. Stewart, Resolution of Near-Field Optical Fiber Refractive Index Profiling Methods, in Proceedings, International Meeting on Scanned Image Microscopy, London 1980 (Academic, New York, 1981), pp. 233–239.

D. C. J. Reid, W. J. Stewart, Ultrahigh Resolution Refractive Near-Field Profiling, in Technical Digest, Third International Conference IOOC (Optical Society of America, Washington, D.C., 1981), paper TUG6.

Sumner, G. T.

G. T. Sumner, A New Technique for Refractive Index Profile Measurement in Multimode Optical Fibres, Opt. Quantum Electron. 9, 79 (1977).
[CrossRef]

White, K. I.

K. I. White, Practical Application of the Refracted Near-Field Technique for the Measurement of Optical Fiber Refractive Index Profiles, Opt. Quantum Electron. 11, 185 (1979).
[CrossRef]

Young, M.

M. Young, Refracted-Ray Scanning (Refracted Near-Field Scanning) for Measuring Index Profiles of Optical Fibers, Natl. Bur. Stand. U.S. Tech. Note 1038 (1981).

M. Young, Calibration Technique for Refracted Near-Field Scanning of Optical Fibers, Appl. Opt. 19, 2479 (1980).
[CrossRef] [PubMed]

M. Young, Linearity and Resolution of Refracted Near-Field Scanning, in Technical Digest—Symposium on Optical Fiber Measurements, Natl. Bur. Stand. U.S. Spec. Publ. 597 (1980).

M. Young, Optics and Lasers, An Engineering Physics Approach (Springer, New York, 1977), Chap. 3.

Appl. Opt. (4)

Appl. Phys. (1)

A. W. Snyder, Leaky-Ray Theory of Optical Waveguides of Circular Cross Section, Appl. Phys. 4, 273 (1974).
[CrossRef]

Appl. Phys. Lett. (1)

D. N. Payne, F. M. E. Sladen, M. J. Adams, Determination of Optical Fiber Refractive Index Profiles by a Near-Field Scanning Technique, Appl. Phys. Lett. 28, 255 (1976).
[CrossRef]

Bell Syst. Tech. J. (2)

D. Gloge, E. A. J. Marcatili, Multimode Theory of Graded-Core Fibers, Bell Syst. Tech. J. 52, 1563 (1973).

J. A. Arnaud, R. M. deRosier, Novel Technique for Measuring the Index Profile of Optical Fibers, Bell Syst. Tech. J. 55, 1489 (1976).

Electron. Lett. (3)

K. Petermann, Uncertainties of the Leaky Mode Correction for Near-Square-Law Optical Fibers, Electron. Lett. 13, 513 (1977).
[CrossRef]

M. J. Adams, D. N. Payne, F. M. E. Sladen, Correction Factors for the Determination of Optical-Fibre Refractive-Index Profiles by the Near-Field Scan Technique, Electron. Lett. 12, 281 (1976).
[CrossRef]

J. W. Fleming, Material Dispersion of Lightguide Glasses, Electron. Lett. 14, 326 (1978).
[CrossRef]

Experimental Statistics (1)

M. G. Natrella, Experimental Statistics, Natl. Bur. Stand. U.S. Handb.91, 5-22, 5-23, 5-27 (1963).

J. Opt. Soc. Am. (3)

Natl. Bur. Stand. U.S. Tech. Note 1038 (1)

M. Young, Refracted-Ray Scanning (Refracted Near-Field Scanning) for Measuring Index Profiles of Optical Fibers, Natl. Bur. Stand. U.S. Tech. Note 1038 (1981).

Opt. Commun. (1)

M. J. Adams, D. N. Payne, F. M. E. Sladen, Length-Dependent Effects Due to Leaky Modes on Multimode Graded-Index Optical Fibers, Opt. Commun. 17, 204 (1976).
[CrossRef]

Opt. Quantum Electron. (2)

G. T. Sumner, A New Technique for Refractive Index Profile Measurement in Multimode Optical Fibres, Opt. Quantum Electron. 9, 79 (1977).
[CrossRef]

K. I. White, Practical Application of the Refracted Near-Field Technique for the Measurement of Optical Fiber Refractive Index Profiles, Opt. Quantum Electron. 11, 185 (1979).
[CrossRef]

Proc. IEEE (2)

D. Marcuse, H. M. Presby, Index Profile Measurements of Fibers and Their Evaluation, Proc. IEEE 68, 666 (1980).
[CrossRef]

H. M. Presby, D. Marcuse, The Index-Profile Characterization of Fiber Preforms and Drawn Fibers, Proc. IEEE 68, 1198 (1980).
[CrossRef]

Technical Digest—Symposium on Optical Fiber Measurements (1)

M. Young, Linearity and Resolution of Refracted Near-Field Scanning, in Technical Digest—Symposium on Optical Fiber Measurements, Natl. Bur. Stand. U.S. Spec. Publ. 597 (1980).

Other (9)

W. J. Stewart, A New Technique for Measuring the Refractive Index Profiles of Graded Optical Fibers, in Technical Digest, IOOC (IECE, Tokyo, 1977), pp. 395–398.

D. C. J. Reid, W. J. Stewart, Ultrahigh Resolution Refractive Near-Field Profiling, in Technical Digest, Third International Conference IOOC (Optical Society of America, Washington, D.C., 1981), paper TUG6.

For simplicity of nomenclature and for avoiding confusion, I shall refer to both these methods as near-field scanning. When it is necessary to distinguish between them, I shall use the terms entrance-face scanning and exit-face scanning. Likewise, I will not use the somewhat cumbersome term refracted near-field scanning but rather will refer to the refracted-ray method.

M. Young, Optics and Lasers, An Engineering Physics Approach (Springer, New York, 1977), Chap. 3.

D. N. Payne, F. M. E. Sladen, M. J. Adams, Index Profile Determination in Graded Index Fibers, in Proceedings, First Conference on Optical Fibre Communication, IEE Conf. Publ.London132, 43 (1975).

I am indebted to Michael Liva and William Sacher of Cargille Laboratories for providing the liquids along with their indices, their Sellmeier coefficients, and a statement of accuracy.

W. J. Stewart, Detail Resolution in Optical Fibre Index Profiling Methods, AGARD Conf. Proc.219, 28-1 (1977). This work is also expanded in an unpublished paper.

W. J. Stewart, Resolution of Near-Field Optical Fiber Refractive Index Profiling Methods, in Proceedings, International Meeting on Scanned Image Microscopy, London 1980 (Academic, New York, 1981), pp. 233–239.

L. C. Martin, Technical Optics, Vol. 2 (Pitman and Sons, London, 1960), Chap. 3.

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Figures (7)

Fig. 1
Fig. 1

The lower the index of the fiber, the greater the vertex angle of the emergent cone.

Fig. 2
Fig. 2

A function useful for describing the power transmitted by a non-Lambertian source.

Fig. 3
Fig. 3

Experimental setup: Q, quarterwave plate; MO, microscope objective; BS, beam splitter; A, aperture stop; OS, opaque stop; F, fiber; WL, white light source; CL, condensing lens; D, detector; EP, eyepiece; GF, green filter; MY, experimenter. Fiber extends through cell to image plane of MO; see Fig. 4 for detail of cell.

Fig. 4
Fig. 4

Detail of cell assembly and focusing optics. Outside the capillary the fiber is confined to the plane perpendicular to the direction of scan.

Fig. 5
Fig. 5

Normalized voltage as a function of index difference between vitreous silica and oil for a particular stop position. Estimates of random and systematic error are indicated.

Fig. 6
Fig. 6

Refracted-ray scan of fiber DF-E. Glitch to left of center is likely due to contamination by dirt or a shard of glass.

Fig. 7
Fig. 7

Refracted-ray scan of step fiber. Arrowheads show region calculated to be free of leaky rays. Artifacts can be diminished by translating stop axially but at the expense of destroying calibration and possibly affecting resolution.

Tables (3)

Tables Icon

Table II Interlaboratory Comparison of Numerical Apertures

Tables Icon

Table III Interlaboratory Comparison of Index Difference Δn

Equations (10)

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

n 2 ( r ) = n L 2 + sin 2 θ - sin 2 θ ,
P ( θ ) = A ( sin 2 θ - sin 2 θ s ) ,
2 n L Δ n ( r ) = ( sin 2 θ - sin 2 θ s ) [ P ( θ ) - P 0 ] / P 0 ,
L ( θ ) = L 0 cos m θ ,
1 - cos m + 2 θ .
P ( θ ) = A ( cos m + 2 θ s - cos m + 2 θ )
α < 2 [ ( N 2 / N F 2 ) - 1 ] ,
r / a < ( 1 - N F 2 / N 2 ) 1 / 2 ,
D F = n λ / 2 ( N . A . ) 2 .
sin 2 U = n 2 ( 0 ) - n c 2 ,

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