Abstract

LP01–LP02 interference over an extended wavelength region is used to describe a new spectroscopic technique for determining the refractive-index profile of non-step-index optical fibers. The technique is illustrated with a fiber that shows an a-profile variation of the refractive index.

© 1996 Optical Society of America

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References

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  1. W. J. Bock, T. A. Eftimov, Proc. SPIE 2070, 65 (1993).
    [Crossref]
  2. M. Spajer, Opt. Lett. 13, 239 (1988).
    [Crossref] [PubMed]
  3. B. Y. Kim, J. N. Blake, S. Y. Huang, H. J. Shaw, Opt. Lett. 12, 729 (1987).
    [Crossref] [PubMed]
  4. A. Sharma, R. Posey, Opt. Commun. 124, 111 (1996).
    [Crossref]
  5. M. Spajer, B. Carquille, H. J. Mailotte, Opt. Commun. 60, 261 (1986).
    [Crossref]
  6. C. E. Covington, J. Blake, S. L. A. Carrara, Opt. Lett. 19, 676 (1994).
    [Crossref] [PubMed]
  7. K. Bohnert, G. C. deWit, J. Nehring, J. Lightwave Technol. 13, 94 (1995).
    [Crossref]
  8. A. M. Vengsarkar, W. C. Michie, L. Jankovic, B. Culshaw, R. O. Claus, J. Lightwave Technol. 12, 170 (1994).
    [Crossref]
  9. F. Brinkmeyer, S. Heckman, Opt. Lett. 9, 28 (1984).
    [Crossref] [PubMed]
  10. D. Uttam, Electron. Lett. 21, 1031 (1985).
    [Crossref]
  11. J. L. McMillan, Electron. Lett. 19, 240 (1983).
    [Crossref]
  12. A. Sharma, M. Dokhanian, Z. Wu, A. Williams, P. Venkateswarlu, Opt. Lett. 19, 1122 (1994).
    [PubMed]
  13. P. L. Baldeck, R. R. Alfano, J. Lightwave Technol. LT-5, 1712 (1987).
    [Crossref]
  14. L. G. Cohen, P. Kaiser, J. B. MacChesney, P. B. O'Conner, H. M. Presby, Appl. Phys. Lett. 28, 472 (1975).
    [Crossref]
  15. F. Gauthier, J. Auge, D. Gallon, M. Wehr, S. Blaison, IEEE J. Quantum Electron. QE-17, 885 (1981).
    [Crossref]
  16. T. Okoshi, Optical Fibers (Academic, New York, 1982).
  17. K. Oyamada, T. Okoshi, IEEE Trans. Microwave Theory Tech. MTT-28, 1113 (1980).
    [Crossref]
  18. R. H. West, J. Lightwave Technol. 62, 155 (1988).
    [Crossref]
  19. R. A. Greenwell, C. E. Barnes, G. W. Nelson, Proc. SPIE 867, 10 (1987).

1996 (1)

A. Sharma, R. Posey, Opt. Commun. 124, 111 (1996).
[Crossref]

1995 (1)

K. Bohnert, G. C. deWit, J. Nehring, J. Lightwave Technol. 13, 94 (1995).
[Crossref]

1994 (3)

1993 (1)

W. J. Bock, T. A. Eftimov, Proc. SPIE 2070, 65 (1993).
[Crossref]

1988 (2)

M. Spajer, Opt. Lett. 13, 239 (1988).
[Crossref] [PubMed]

R. H. West, J. Lightwave Technol. 62, 155 (1988).
[Crossref]

1987 (3)

R. A. Greenwell, C. E. Barnes, G. W. Nelson, Proc. SPIE 867, 10 (1987).

P. L. Baldeck, R. R. Alfano, J. Lightwave Technol. LT-5, 1712 (1987).
[Crossref]

B. Y. Kim, J. N. Blake, S. Y. Huang, H. J. Shaw, Opt. Lett. 12, 729 (1987).
[Crossref] [PubMed]

1986 (1)

M. Spajer, B. Carquille, H. J. Mailotte, Opt. Commun. 60, 261 (1986).
[Crossref]

1985 (1)

D. Uttam, Electron. Lett. 21, 1031 (1985).
[Crossref]

1984 (1)

1983 (1)

J. L. McMillan, Electron. Lett. 19, 240 (1983).
[Crossref]

1981 (1)

F. Gauthier, J. Auge, D. Gallon, M. Wehr, S. Blaison, IEEE J. Quantum Electron. QE-17, 885 (1981).
[Crossref]

1980 (1)

K. Oyamada, T. Okoshi, IEEE Trans. Microwave Theory Tech. MTT-28, 1113 (1980).
[Crossref]

1975 (1)

L. G. Cohen, P. Kaiser, J. B. MacChesney, P. B. O'Conner, H. M. Presby, Appl. Phys. Lett. 28, 472 (1975).
[Crossref]

Alfano, R. R.

P. L. Baldeck, R. R. Alfano, J. Lightwave Technol. LT-5, 1712 (1987).
[Crossref]

Auge, J.

F. Gauthier, J. Auge, D. Gallon, M. Wehr, S. Blaison, IEEE J. Quantum Electron. QE-17, 885 (1981).
[Crossref]

Baldeck, P. L.

P. L. Baldeck, R. R. Alfano, J. Lightwave Technol. LT-5, 1712 (1987).
[Crossref]

Barnes, C. E.

R. A. Greenwell, C. E. Barnes, G. W. Nelson, Proc. SPIE 867, 10 (1987).

Blaison, S.

F. Gauthier, J. Auge, D. Gallon, M. Wehr, S. Blaison, IEEE J. Quantum Electron. QE-17, 885 (1981).
[Crossref]

Blake, J.

Blake, J. N.

Bock, W. J.

W. J. Bock, T. A. Eftimov, Proc. SPIE 2070, 65 (1993).
[Crossref]

Bohnert, K.

K. Bohnert, G. C. deWit, J. Nehring, J. Lightwave Technol. 13, 94 (1995).
[Crossref]

Brinkmeyer, F.

Carquille, B.

M. Spajer, B. Carquille, H. J. Mailotte, Opt. Commun. 60, 261 (1986).
[Crossref]

Carrara, S. L. A.

Claus, R. O.

A. M. Vengsarkar, W. C. Michie, L. Jankovic, B. Culshaw, R. O. Claus, J. Lightwave Technol. 12, 170 (1994).
[Crossref]

Cohen, L. G.

L. G. Cohen, P. Kaiser, J. B. MacChesney, P. B. O'Conner, H. M. Presby, Appl. Phys. Lett. 28, 472 (1975).
[Crossref]

Covington, C. E.

Culshaw, B.

A. M. Vengsarkar, W. C. Michie, L. Jankovic, B. Culshaw, R. O. Claus, J. Lightwave Technol. 12, 170 (1994).
[Crossref]

deWit, G. C.

K. Bohnert, G. C. deWit, J. Nehring, J. Lightwave Technol. 13, 94 (1995).
[Crossref]

Dokhanian, M.

Eftimov, T. A.

W. J. Bock, T. A. Eftimov, Proc. SPIE 2070, 65 (1993).
[Crossref]

Gallon, D.

F. Gauthier, J. Auge, D. Gallon, M. Wehr, S. Blaison, IEEE J. Quantum Electron. QE-17, 885 (1981).
[Crossref]

Gauthier, F.

F. Gauthier, J. Auge, D. Gallon, M. Wehr, S. Blaison, IEEE J. Quantum Electron. QE-17, 885 (1981).
[Crossref]

Greenwell, R. A.

R. A. Greenwell, C. E. Barnes, G. W. Nelson, Proc. SPIE 867, 10 (1987).

Heckman, S.

Huang, S. Y.

Jankovic, L.

A. M. Vengsarkar, W. C. Michie, L. Jankovic, B. Culshaw, R. O. Claus, J. Lightwave Technol. 12, 170 (1994).
[Crossref]

Kaiser, P.

L. G. Cohen, P. Kaiser, J. B. MacChesney, P. B. O'Conner, H. M. Presby, Appl. Phys. Lett. 28, 472 (1975).
[Crossref]

Kim, B. Y.

MacChesney, J. B.

L. G. Cohen, P. Kaiser, J. B. MacChesney, P. B. O'Conner, H. M. Presby, Appl. Phys. Lett. 28, 472 (1975).
[Crossref]

Mailotte, H. J.

M. Spajer, B. Carquille, H. J. Mailotte, Opt. Commun. 60, 261 (1986).
[Crossref]

McMillan, J. L.

J. L. McMillan, Electron. Lett. 19, 240 (1983).
[Crossref]

Michie, W. C.

A. M. Vengsarkar, W. C. Michie, L. Jankovic, B. Culshaw, R. O. Claus, J. Lightwave Technol. 12, 170 (1994).
[Crossref]

Nehring, J.

K. Bohnert, G. C. deWit, J. Nehring, J. Lightwave Technol. 13, 94 (1995).
[Crossref]

Nelson, G. W.

R. A. Greenwell, C. E. Barnes, G. W. Nelson, Proc. SPIE 867, 10 (1987).

O'Conner, P. B.

L. G. Cohen, P. Kaiser, J. B. MacChesney, P. B. O'Conner, H. M. Presby, Appl. Phys. Lett. 28, 472 (1975).
[Crossref]

Okoshi, T.

K. Oyamada, T. Okoshi, IEEE Trans. Microwave Theory Tech. MTT-28, 1113 (1980).
[Crossref]

T. Okoshi, Optical Fibers (Academic, New York, 1982).

Oyamada, K.

K. Oyamada, T. Okoshi, IEEE Trans. Microwave Theory Tech. MTT-28, 1113 (1980).
[Crossref]

Posey, R.

A. Sharma, R. Posey, Opt. Commun. 124, 111 (1996).
[Crossref]

Presby, H. M.

L. G. Cohen, P. Kaiser, J. B. MacChesney, P. B. O'Conner, H. M. Presby, Appl. Phys. Lett. 28, 472 (1975).
[Crossref]

Sharma, A.

Shaw, H. J.

Spajer, M.

M. Spajer, Opt. Lett. 13, 239 (1988).
[Crossref] [PubMed]

M. Spajer, B. Carquille, H. J. Mailotte, Opt. Commun. 60, 261 (1986).
[Crossref]

Uttam, D.

D. Uttam, Electron. Lett. 21, 1031 (1985).
[Crossref]

Vengsarkar, A. M.

A. M. Vengsarkar, W. C. Michie, L. Jankovic, B. Culshaw, R. O. Claus, J. Lightwave Technol. 12, 170 (1994).
[Crossref]

Venkateswarlu, P.

Wehr, M.

F. Gauthier, J. Auge, D. Gallon, M. Wehr, S. Blaison, IEEE J. Quantum Electron. QE-17, 885 (1981).
[Crossref]

West, R. H.

R. H. West, J. Lightwave Technol. 62, 155 (1988).
[Crossref]

Williams, A.

Wu, Z.

Appl. Phys. Lett. (1)

L. G. Cohen, P. Kaiser, J. B. MacChesney, P. B. O'Conner, H. M. Presby, Appl. Phys. Lett. 28, 472 (1975).
[Crossref]

Electron. Lett. (2)

D. Uttam, Electron. Lett. 21, 1031 (1985).
[Crossref]

J. L. McMillan, Electron. Lett. 19, 240 (1983).
[Crossref]

IEEE J. Quantum Electron. (1)

F. Gauthier, J. Auge, D. Gallon, M. Wehr, S. Blaison, IEEE J. Quantum Electron. QE-17, 885 (1981).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

K. Oyamada, T. Okoshi, IEEE Trans. Microwave Theory Tech. MTT-28, 1113 (1980).
[Crossref]

J. Lightwave Technol. (4)

R. H. West, J. Lightwave Technol. 62, 155 (1988).
[Crossref]

P. L. Baldeck, R. R. Alfano, J. Lightwave Technol. LT-5, 1712 (1987).
[Crossref]

K. Bohnert, G. C. deWit, J. Nehring, J. Lightwave Technol. 13, 94 (1995).
[Crossref]

A. M. Vengsarkar, W. C. Michie, L. Jankovic, B. Culshaw, R. O. Claus, J. Lightwave Technol. 12, 170 (1994).
[Crossref]

Opt. Commun. (2)

A. Sharma, R. Posey, Opt. Commun. 124, 111 (1996).
[Crossref]

M. Spajer, B. Carquille, H. J. Mailotte, Opt. Commun. 60, 261 (1986).
[Crossref]

Opt. Lett. (5)

Proc. SPIE (2)

W. J. Bock, T. A. Eftimov, Proc. SPIE 2070, 65 (1993).
[Crossref]

R. A. Greenwell, C. E. Barnes, G. W. Nelson, Proc. SPIE 867, 10 (1987).

Other (1)

T. Okoshi, Optical Fibers (Academic, New York, 1982).

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Figures (4)

Fig. 1
Fig. 1

Schematic of the experimental setup. 1-mJ light pulses at 532 nm from a Nd:YAG laser produce 540–620-nm stimulated light emission from a 100-m-long fiber (S) by either SRS or supercontinuum generation. Lens X couples this light normally into the second test fiber, whose refractive-index profile is to be determined. To investigate LP01–LP02 modal interference in the test fiber, the output light is filtered with an aperture A and spectrally analyzed with a monochromator (M), using lens Y.

Fig. 2
Fig. 2

LP01–LP02 interference in the test fiber modulates the intensity of six broad SRS Stokes orders produced in the first fiber. The spacing δλ between consecutive interference fringes shows a maximum near 590 nm and is due to the fact that βλ dispersion curves for the two modes become parallel at this wavelength.

Fig. 3
Fig. 3

Numerically calculated variation of the intermodal phase |ϕ(λ)/2π| ≡ |(β01β02)L/2π| for length L = 52 cm of the test fiber. We arbitrarily assume that ϕ(λ) = 0 at 490 nm for step-index fiber and at 550 nm for α-profile fiber. The numerical aperture NA, core radius a, and non-step-index parameter α have the following values: Curve (A), NA = 0.114, a = 3.2 μm (as quoted by the manufacturer); curve (B), NA = 0.116, a = 3.2 μm; curve (C), NA = 0.114, a = 3.3 μm; curve (D), α = 30, NA = 0.13, a = 3.23 μm; curve (E), α = 30, NA = 0.134, a = 3.23 μm; curve (F), α = 32, NA = 0.134, a = 3.23 μm; curve (G), α = 30, NA = 0.134, a = 3.3 μm. The experimentally measured values (×) agree very closely with plot (E).

Fig. 4
Fig. 4

Variation of the phase difference |ϕ(λ)/2π|0 or the number of LP01–LP02 interference fringes between 550 nm and λ0 with the fiber parameter α. Point ● is for a step-index fiber.

Equations (3)

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ϕ ( λ ) = ( β 01 β 02 ) L ,
δ λ = 2 π / [ L ( Δ β ) / λ ) 2 π / ( ϕ / λ ) ,
ν ( 2 π / λ 0 ) a NA = 4.45 ,

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