Abstract

We present a method for determining the refractive-index profile of polymer optical fiber preforms through a direct-deflection measurement. The method is simple to use, compact, and has good resolution. The profile is obtained from the deflection data by numerically integrating the differential-ray equation for a radial refractive-index gradient. Corrections for topographical deviations are also discussed. Results for both graded-index and step-index fibers are presented.

© 2002 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
  3. M. G. Kuzyk, U. C. Paek, C. W. Dirk, “Guest-host polymer fibers for nonlinear optics,” Appl. Phys. Lett. 59, 902–904 (1991).
    [CrossRef]
  4. D. W. Garvey, K. Zimmerman, P. Young, J. Tostenrude, J. S. Townsend, Z. Zhou, M. Lobel, M. Dayton, R. Wittorf, M. G. Kuzyk, “Single-mode nonlinear-optical polymer fibers,” J. Opt. Soc. Am. B 13, 2017–2023 (1996).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  7. D. J. Welker, M. G. Kuzyk, “All-optical switching in a dye-doped polymer fiber Fabry–Perot waveguide,” Appl. Phys. Lett. 69, 1835–1836 (1996).
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  8. D. J. Welker, M. G. Kuzyk, “Photomechanical stabilization in a polymer fiber-based all-optical circuit,” Appl. Phys. Lett. 64, 809–811 (1994).
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  9. D. J. Welker, M. G. Kuzyk, “Optical and mechanical multistability in a dye-doped polymer fiber Fabry–Perot waveguide,” Appl. Phys. Lett. 66, 2792–2794 (1995).
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  10. S. R. Vigil, Z. Zhou, B. K. Canfield, J. Tostenrude, M. G. Kuzyk, “Dual-core single-mode polymer fiber coupler,” J. Opt. Soc. Am. B 15, 895–900 (1998).
    [CrossRef]
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    [CrossRef]
  23. A. A. Hamza, A. M. Nasr, “Interferometric studies on multi-mode step-index optical fibres,” Pure Appl. Opt. 7, 449–456 (1998).
    [CrossRef]
  24. A. A. Hamza, T. Z. N. Sokkar, M. A. Mabrouk, M. A. El-Morsy, “Refractive index profile of polyethylene fiber using interactive multiple-beam Fizeau fringe analysis,” J. Appl. Polym. Sci. 77, 3090–3106 (2000).
    [CrossRef]
  25. B. X. Chen, H. Hamanaka, K. Iwamura, “Recovery of refractive-index profiles of planar graded-index waveguides from measured mode indices: an iteration method,” J. Opt. Soc. Am. A 9, 1301–1305 (1992).
    [CrossRef]
  26. R. Oven, S. Batchelor, D. G. Ashworth, D. Gelder, J. M. Bradshaw, “Iterative refinement technique for reconstructing refractive index profiles from mode indices,” Electron. Lett. 31, 229–231 (1995).
    [CrossRef]
  27. F. Gonella, A. Quaranta, A. Sambo, F. Caccavale, I. Mansour, “Construction of glass waveguide refractive index profiles by the effective-index finite-difference method,” Opt. Mat. 5, 321–326 (1996).
    [CrossRef]
  28. S. Batchelor, R. Oven, D. G. Ashworth, “Reconstruction of refractive index profiles from multiple wavelength mode indices,” Opt. Commun. 131, 31–36 (1996).
    [CrossRef]
  29. K. I. White, “Practical application of the refracted near-field technique for the measurement of optical fibre refractive index profiles,” Opt. Quant. Electron. 11, 185–196 (1978).
    [CrossRef]
  30. M. Young, “Calibration technique for refracted near-field scanning of optical fibers,” Appl. Opt. 19, 2479–2480 (1980).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  32. T. Müller, “Resolution improvement in refracted near-field index measurement by a lens-shaped liquid cell,” Electron. Lett. 19, 580–582 (1983).
    [CrossRef]
  33. N. Gisin, “Correcting refracted near field refractive index profile measurements for Gaussian intensity distributions,” Opt. Commun. 83, 295–299 (1991).
    [CrossRef]
  34. I. Mansour, F. Caccavale, “An improved procedure to calculate the refractive index profile from the measured near-field intensity,” J. Lightwave Technol. 14, 423–428 (1996).
    [CrossRef]
  35. N. Gisin, R. Passy, P. Stamp, N. Hori, S. Nagano, “New optical configuration for nondestructive measurements of refractive-index profiles of LiNbO3 waveguides,” Appl. Opt. 33, 1726–1731 (1994).
    [CrossRef] [PubMed]
  36. B. Groebil, B. Gisin, N. Gisin, H. Zbinden, “Measuring refractive index profiles of integrated LiNbO3 waveguides,” Opt. Eng. 34, 2309–3214 (1995).
    [CrossRef]
  37. T. Yabu, S. Sawa, M. Geshiro, “Measurement of refractive index distribution of optical waveguides by the propagation mode near-field method employing an improved inverse analysis,” Electron. Commun. Jpn. 79, 21–29 (1996).
  38. P. Oberson, B. Gisin, B. Huttner, N. Gisin, “Refracted near-field measurements of refractive index and geometry of silica-on-silicon integrated optical waveguides,” Appl. Opt. 37, 7268–7272 (1998).
    [CrossRef]
  39. M. J. Saunders, “Optical fiber profiles using the refracted near-field technique: A comparison with other methods,” Appl. Opt. 20, 1645–1651 (1981).
    [CrossRef] [PubMed]
  40. W. J. Stewart, “Optical fiber and preform profiling technology,” IEEE J. Quantum Electron. 18, 1451–1465 (1982).
    [CrossRef]
  41. A. A. Hamza, T. Z. N. Sokkar, K. A. El-Farahaty, H. M. El-Dessouky, “Comparative study on interferometric techniques for measurement of the optical properties of a fiber,” J. Opt. 1, 41–50 (1999).
  42. S. T. Huntington, P. Mulvaney, A. Roberts, K. A. Nugent, M. Bazylenko, “Atomic force microscopy for the determination of refractive index profiles of optical fibers and waveguides: a quantitative study,” J. Appl. Phys. 820, 2730–2734 (1997).
    [CrossRef]
  43. S. T. Huntington, A. Roberts, K. A. Nugent, P. Mulvaney, M. Bazylenko, “Fibre and waveguide refractive index measurements with AFM resolution,” Jpn. J. Appl. Phys. 37, 62–64 (1998).
  44. P. L. Chu, “Nondestructive measurement of index profile of an optical-fibre preform,” Electron. Lett. 13, 736–738 (1977).
    [CrossRef]
  45. D. Peri, P. L. Chu, “Measurement of refractive-index profile of optical-fibre preform by means of spatial filtering,” Electron. Lett. 17, 371–372 (1981).
    [CrossRef]
  46. J. Sochacki, M. Sochaka, C. Gomez-Reino, “Reconstruction of axially nonsymmetric refractive index profiles from ray deflection by means of the Abel integral transform,” Opt. Commun. 71, 20–22 (1989).
    [CrossRef]
  47. P. Skok, M. Miller, “Spatial filtering method of oblique slit for measurement of refractive-index profile of optical-fibre preforms,” Electron. Lett. 23, 859–860 (1987).
    [CrossRef]
  48. W. Urbanczyk, K. Pietraszkiewicz, W. A. Wozniak, “Novel bifunctional systems for measuring the refractive index profile and residual stress birefringence in optical fibers and preforms,” Opt. Eng. 31, 491–499 (1992).
    [CrossRef]
  49. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon Press, Oxford, UK1980).

2000 (2)

Z. Xiong, G. D. Peng, P. L. Chu, “Nonlinear coupling and optical switching in a β-carotene-doped twin-core polymer optical fiber,” Opt. Eng. 39, 624–627 (2000).
[CrossRef]

A. A. Hamza, T. Z. N. Sokkar, M. A. Mabrouk, M. A. El-Morsy, “Refractive index profile of polyethylene fiber using interactive multiple-beam Fizeau fringe analysis,” J. Appl. Polym. Sci. 77, 3090–3106 (2000).
[CrossRef]

1999 (3)

T. Z. N. Sokkar, M. A. Mabrouk, H. F. El-Bawab, “Refractive-index profile of GRIN optical fiber considering the area under the interference fringe shift: II. The mismatching case,” J. Opt. A 1, 64–72 (1999).
[CrossRef]

H. El-Ghandoor, E. A. El-Ghafar, R. Hassan, “Refractive index profiling of a GRIN optical fiber using a modulated speckled sheet of light,” Opt. Laser Technol. 31, 481–488 (1999).
[CrossRef]

A. A. Hamza, T. Z. N. Sokkar, K. A. El-Farahaty, H. M. El-Dessouky, “Comparative study on interferometric techniques for measurement of the optical properties of a fiber,” J. Opt. 1, 41–50 (1999).

1998 (4)

S. T. Huntington, A. Roberts, K. A. Nugent, P. Mulvaney, M. Bazylenko, “Fibre and waveguide refractive index measurements with AFM resolution,” Jpn. J. Appl. Phys. 37, 62–64 (1998).

P. Oberson, B. Gisin, B. Huttner, N. Gisin, “Refracted near-field measurements of refractive index and geometry of silica-on-silicon integrated optical waveguides,” Appl. Opt. 37, 7268–7272 (1998).
[CrossRef]

S. R. Vigil, Z. Zhou, B. K. Canfield, J. Tostenrude, M. G. Kuzyk, “Dual-core single-mode polymer fiber coupler,” J. Opt. Soc. Am. B 15, 895–900 (1998).
[CrossRef]

A. A. Hamza, A. M. Nasr, “Interferometric studies on multi-mode step-index optical fibres,” Pure Appl. Opt. 7, 449–456 (1998).
[CrossRef]

1997 (2)

M. A. Mabrouk, H. F. El-Bawab, “Refractive index profile of GRIN optical fibre considering the area under the interference fringe shift. I. The matching case,” Pure Appl. Opt. 6, 247–256 (1997).
[CrossRef]

S. T. Huntington, P. Mulvaney, A. Roberts, K. A. Nugent, M. Bazylenko, “Atomic force microscopy for the determination of refractive index profiles of optical fibers and waveguides: a quantitative study,” J. Appl. Phys. 820, 2730–2734 (1997).
[CrossRef]

1996 (10)

T. Yabu, S. Sawa, M. Geshiro, “Measurement of refractive index distribution of optical waveguides by the propagation mode near-field method employing an improved inverse analysis,” Electron. Commun. Jpn. 79, 21–29 (1996).

R. Posey, L. Philips, D. Diggs, A. Sharma, “LP01-LP02 interference using a spectrally extended light source: measurement of the non-step-refractive-index profile of optical fibers,” Opt. Lett. 21, 1357–1359 (1996).
[CrossRef] [PubMed]

F. Gonella, A. Quaranta, A. Sambo, F. Caccavale, I. Mansour, “Construction of glass waveguide refractive index profiles by the effective-index finite-difference method,” Opt. Mat. 5, 321–326 (1996).
[CrossRef]

S. Batchelor, R. Oven, D. G. Ashworth, “Reconstruction of refractive index profiles from multiple wavelength mode indices,” Opt. Commun. 131, 31–36 (1996).
[CrossRef]

I. Mansour, F. Caccavale, “An improved procedure to calculate the refractive index profile from the measured near-field intensity,” J. Lightwave Technol. 14, 423–428 (1996).
[CrossRef]

V. N. Van, A. Brunet-Bruneau, S. Fisson, J. M. Frigerio, G. Vuye, Y. Wang, F. Abelès, J. Rivory, M. Berger, P. Chaton, “Determination of refractive-index profiles by a combination of visible and infrared ellipsometry measurements,” Appl. Opt. 35, 5540–5544 (1996).
[CrossRef]

E. Nihei, T. Ishigure, Y. Koike, “High-bandwidth, graded-index polymer optical fiber for near-infrared use,” Appl. Opt. 35, 7085–7090 (1996).
[CrossRef] [PubMed]

D. W. Garvey, K. Zimmerman, P. Young, J. Tostenrude, J. S. Townsend, Z. Zhou, M. Lobel, M. Dayton, R. Wittorf, M. G. Kuzyk, “Single-mode nonlinear-optical polymer fibers,” J. Opt. Soc. Am. B 13, 2017–2023 (1996).
[CrossRef]

D. W. Garvey, Q. Li, M. G. Kuzyk, C. W. Dirk, S. Martinez, “Sagnac interferometric intensity-dependent refractive-index measurements of polymer optical fiber,” Opt. Lett. 21, 104–106 (1996).
[CrossRef] [PubMed]

D. J. Welker, M. G. Kuzyk, “All-optical switching in a dye-doped polymer fiber Fabry–Perot waveguide,” Appl. Phys. Lett. 69, 1835–1836 (1996).
[CrossRef]

1995 (5)

D. J. Welker, M. G. Kuzyk, “Optical and mechanical multistability in a dye-doped polymer fiber Fabry–Perot waveguide,” Appl. Phys. Lett. 66, 2792–2794 (1995).
[CrossRef]

J. A. Ferrari, E. Frins, A. Rondoni, G. Montaldo, “Retrieval algorithm for refractive-index profile of fibers from transverse interferograms,” Opt. Commun. 117, 25–30 (1995).
[CrossRef]

Z. Z. Wu, H. Davis, S. K. Batra, “Correct ray-tracing analysis for interference microscopy of fibers,” Proc. R. Soc. London Ser. A 450, 23–36 (1995).
[CrossRef]

R. Oven, S. Batchelor, D. G. Ashworth, D. Gelder, J. M. Bradshaw, “Iterative refinement technique for reconstructing refractive index profiles from mode indices,” Electron. Lett. 31, 229–231 (1995).
[CrossRef]

B. Groebil, B. Gisin, N. Gisin, H. Zbinden, “Measuring refractive index profiles of integrated LiNbO3 waveguides,” Opt. Eng. 34, 2309–3214 (1995).
[CrossRef]

1994 (2)

1993 (1)

A. Tagaya, Y. Koike, T. Kinoshita, E. Nihei, T. Yamamoto, K. Sasaki, “Polymer optical fiber amplifier,” Appl. Phys. Lett. 63, 883–884 (1993).
[CrossRef]

1992 (3)

M. Hai, X. Jianping, Z. Hui, S. Yuensheng, C. Nong, “Measuring abberations of a gradient-index rod lens with holographic shearing interferometry,” Int. J. Optoelectron. 7, 53–56 (1992).

B. X. Chen, H. Hamanaka, K. Iwamura, “Recovery of refractive-index profiles of planar graded-index waveguides from measured mode indices: an iteration method,” J. Opt. Soc. Am. A 9, 1301–1305 (1992).
[CrossRef]

W. Urbanczyk, K. Pietraszkiewicz, W. A. Wozniak, “Novel bifunctional systems for measuring the refractive index profile and residual stress birefringence in optical fibers and preforms,” Opt. Eng. 31, 491–499 (1992).
[CrossRef]

1991 (2)

N. Gisin, “Correcting refracted near field refractive index profile measurements for Gaussian intensity distributions,” Opt. Commun. 83, 295–299 (1991).
[CrossRef]

M. G. Kuzyk, U. C. Paek, C. W. Dirk, “Guest-host polymer fibers for nonlinear optics,” Appl. Phys. Lett. 59, 902–904 (1991).
[CrossRef]

1990 (1)

Y. Ohtsuka, E. Nihei, Y. Koike, “Graded-index optical fibers of methyl methacrylate—vinyl benzoate copolymer with low loss and high bandwidth,” Appl. Phys. Lett. 57, 120–122 (1990).
[CrossRef]

1989 (1)

J. Sochacki, M. Sochaka, C. Gomez-Reino, “Reconstruction of axially nonsymmetric refractive index profiles from ray deflection by means of the Abel integral transform,” Opt. Commun. 71, 20–22 (1989).
[CrossRef]

1987 (1)

P. Skok, M. Miller, “Spatial filtering method of oblique slit for measurement of refractive-index profile of optical-fibre preforms,” Electron. Lett. 23, 859–860 (1987).
[CrossRef]

1986 (1)

1983 (1)

T. Müller, “Resolution improvement in refracted near-field index measurement by a lens-shaped liquid cell,” Electron. Lett. 19, 580–582 (1983).
[CrossRef]

1982 (1)

W. J. Stewart, “Optical fiber and preform profiling technology,” IEEE J. Quantum Electron. 18, 1451–1465 (1982).
[CrossRef]

1981 (3)

1980 (1)

1979 (1)

1978 (2)

C. Saekeang, P. L. Chu, “Backscattering of light from optical fibers with arbitrary refractive-index distributions: uniform approximation approach,” J. Opt. Soc. Am. 68, 1298–1305 (1978).
[CrossRef]

K. I. White, “Practical application of the refracted near-field technique for the measurement of optical fibre refractive index profiles,” Opt. Quant. Electron. 11, 185–196 (1978).
[CrossRef]

1977 (1)

P. L. Chu, “Nondestructive measurement of index profile of an optical-fibre preform,” Electron. Lett. 13, 736–738 (1977).
[CrossRef]

Abelès, F.

Ashworth, D. G.

S. Batchelor, R. Oven, D. G. Ashworth, “Reconstruction of refractive index profiles from multiple wavelength mode indices,” Opt. Commun. 131, 31–36 (1996).
[CrossRef]

R. Oven, S. Batchelor, D. G. Ashworth, D. Gelder, J. M. Bradshaw, “Iterative refinement technique for reconstructing refractive index profiles from mode indices,” Electron. Lett. 31, 229–231 (1995).
[CrossRef]

Batchelor, S.

S. Batchelor, R. Oven, D. G. Ashworth, “Reconstruction of refractive index profiles from multiple wavelength mode indices,” Opt. Commun. 131, 31–36 (1996).
[CrossRef]

R. Oven, S. Batchelor, D. G. Ashworth, D. Gelder, J. M. Bradshaw, “Iterative refinement technique for reconstructing refractive index profiles from mode indices,” Electron. Lett. 31, 229–231 (1995).
[CrossRef]

Batra, S. K.

Z. Z. Wu, H. Davis, S. K. Batra, “Correct ray-tracing analysis for interference microscopy of fibers,” Proc. R. Soc. London Ser. A 450, 23–36 (1995).
[CrossRef]

Bazylenko, M.

S. T. Huntington, A. Roberts, K. A. Nugent, P. Mulvaney, M. Bazylenko, “Fibre and waveguide refractive index measurements with AFM resolution,” Jpn. J. Appl. Phys. 37, 62–64 (1998).

S. T. Huntington, P. Mulvaney, A. Roberts, K. A. Nugent, M. Bazylenko, “Atomic force microscopy for the determination of refractive index profiles of optical fibers and waveguides: a quantitative study,” J. Appl. Phys. 820, 2730–2734 (1997).
[CrossRef]

Berger, M.

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon Press, Oxford, UK1980).

Bradshaw, J. M.

R. Oven, S. Batchelor, D. G. Ashworth, D. Gelder, J. M. Bradshaw, “Iterative refinement technique for reconstructing refractive index profiles from mode indices,” Electron. Lett. 31, 229–231 (1995).
[CrossRef]

Brunet-Bruneau, A.

Caccavale, F.

F. Gonella, A. Quaranta, A. Sambo, F. Caccavale, I. Mansour, “Construction of glass waveguide refractive index profiles by the effective-index finite-difference method,” Opt. Mat. 5, 321–326 (1996).
[CrossRef]

I. Mansour, F. Caccavale, “An improved procedure to calculate the refractive index profile from the measured near-field intensity,” J. Lightwave Technol. 14, 423–428 (1996).
[CrossRef]

Canfield, B. K.

Chaton, P.

Chen, B. X.

Chu, P. L.

Z. Xiong, G. D. Peng, P. L. Chu, “Nonlinear coupling and optical switching in a β-carotene-doped twin-core polymer optical fiber,” Opt. Eng. 39, 624–627 (2000).
[CrossRef]

D. Peri, P. L. Chu, “Measurement of refractive-index profile of optical-fibre preform by means of spatial filtering,” Electron. Lett. 17, 371–372 (1981).
[CrossRef]

C. Saekeang, P. L. Chu, “Backscattering of light from optical fibers with arbitrary refractive-index distributions: uniform approximation approach,” J. Opt. Soc. Am. 68, 1298–1305 (1978).
[CrossRef]

P. L. Chu, “Nondestructive measurement of index profile of an optical-fibre preform,” Electron. Lett. 13, 736–738 (1977).
[CrossRef]

Davis, H.

Z. Z. Wu, H. Davis, S. K. Batra, “Correct ray-tracing analysis for interference microscopy of fibers,” Proc. R. Soc. London Ser. A 450, 23–36 (1995).
[CrossRef]

Dayton, M.

Diggs, D.

Dirk, C. W.

El-Bawab, H. F.

T. Z. N. Sokkar, M. A. Mabrouk, H. F. El-Bawab, “Refractive-index profile of GRIN optical fiber considering the area under the interference fringe shift: II. The mismatching case,” J. Opt. A 1, 64–72 (1999).
[CrossRef]

M. A. Mabrouk, H. F. El-Bawab, “Refractive index profile of GRIN optical fibre considering the area under the interference fringe shift. I. The matching case,” Pure Appl. Opt. 6, 247–256 (1997).
[CrossRef]

El-Dessouky, H. M.

A. A. Hamza, T. Z. N. Sokkar, K. A. El-Farahaty, H. M. El-Dessouky, “Comparative study on interferometric techniques for measurement of the optical properties of a fiber,” J. Opt. 1, 41–50 (1999).

El-Farahaty, K. A.

A. A. Hamza, T. Z. N. Sokkar, K. A. El-Farahaty, H. M. El-Dessouky, “Comparative study on interferometric techniques for measurement of the optical properties of a fiber,” J. Opt. 1, 41–50 (1999).

El-Ghafar, E. A.

H. El-Ghandoor, E. A. El-Ghafar, R. Hassan, “Refractive index profiling of a GRIN optical fiber using a modulated speckled sheet of light,” Opt. Laser Technol. 31, 481–488 (1999).
[CrossRef]

El-Ghandoor, H.

H. El-Ghandoor, E. A. El-Ghafar, R. Hassan, “Refractive index profiling of a GRIN optical fiber using a modulated speckled sheet of light,” Opt. Laser Technol. 31, 481–488 (1999).
[CrossRef]

El-Morsy, M. A.

A. A. Hamza, T. Z. N. Sokkar, M. A. Mabrouk, M. A. El-Morsy, “Refractive index profile of polyethylene fiber using interactive multiple-beam Fizeau fringe analysis,” J. Appl. Polym. Sci. 77, 3090–3106 (2000).
[CrossRef]

Ferrari, J. A.

J. A. Ferrari, E. Frins, A. Rondoni, G. Montaldo, “Retrieval algorithm for refractive-index profile of fibers from transverse interferograms,” Opt. Commun. 117, 25–30 (1995).
[CrossRef]

Fisson, S.

Frigerio, J. M.

Frins, E.

J. A. Ferrari, E. Frins, A. Rondoni, G. Montaldo, “Retrieval algorithm for refractive-index profile of fibers from transverse interferograms,” Opt. Commun. 117, 25–30 (1995).
[CrossRef]

Garvey, D. W.

Gelder, D.

R. Oven, S. Batchelor, D. G. Ashworth, D. Gelder, J. M. Bradshaw, “Iterative refinement technique for reconstructing refractive index profiles from mode indices,” Electron. Lett. 31, 229–231 (1995).
[CrossRef]

Geshiro, M.

T. Yabu, S. Sawa, M. Geshiro, “Measurement of refractive index distribution of optical waveguides by the propagation mode near-field method employing an improved inverse analysis,” Electron. Commun. Jpn. 79, 21–29 (1996).

Gisin, B.

P. Oberson, B. Gisin, B. Huttner, N. Gisin, “Refracted near-field measurements of refractive index and geometry of silica-on-silicon integrated optical waveguides,” Appl. Opt. 37, 7268–7272 (1998).
[CrossRef]

B. Groebil, B. Gisin, N. Gisin, H. Zbinden, “Measuring refractive index profiles of integrated LiNbO3 waveguides,” Opt. Eng. 34, 2309–3214 (1995).
[CrossRef]

Gisin, N.

P. Oberson, B. Gisin, B. Huttner, N. Gisin, “Refracted near-field measurements of refractive index and geometry of silica-on-silicon integrated optical waveguides,” Appl. Opt. 37, 7268–7272 (1998).
[CrossRef]

B. Groebil, B. Gisin, N. Gisin, H. Zbinden, “Measuring refractive index profiles of integrated LiNbO3 waveguides,” Opt. Eng. 34, 2309–3214 (1995).
[CrossRef]

N. Gisin, R. Passy, P. Stamp, N. Hori, S. Nagano, “New optical configuration for nondestructive measurements of refractive-index profiles of LiNbO3 waveguides,” Appl. Opt. 33, 1726–1731 (1994).
[CrossRef] [PubMed]

N. Gisin, “Correcting refracted near field refractive index profile measurements for Gaussian intensity distributions,” Opt. Commun. 83, 295–299 (1991).
[CrossRef]

Gomez-Reino, C.

J. Sochacki, M. Sochaka, C. Gomez-Reino, “Reconstruction of axially nonsymmetric refractive index profiles from ray deflection by means of the Abel integral transform,” Opt. Commun. 71, 20–22 (1989).
[CrossRef]

Gonella, F.

F. Gonella, A. Quaranta, A. Sambo, F. Caccavale, I. Mansour, “Construction of glass waveguide refractive index profiles by the effective-index finite-difference method,” Opt. Mat. 5, 321–326 (1996).
[CrossRef]

Groebil, B.

B. Groebil, B. Gisin, N. Gisin, H. Zbinden, “Measuring refractive index profiles of integrated LiNbO3 waveguides,” Opt. Eng. 34, 2309–3214 (1995).
[CrossRef]

Hai, M.

M. Hai, X. Jianping, Z. Hui, S. Yuensheng, C. Nong, “Measuring abberations of a gradient-index rod lens with holographic shearing interferometry,” Int. J. Optoelectron. 7, 53–56 (1992).

Hamanaka, H.

Hamza, A. A.

A. A. Hamza, T. Z. N. Sokkar, M. A. Mabrouk, M. A. El-Morsy, “Refractive index profile of polyethylene fiber using interactive multiple-beam Fizeau fringe analysis,” J. Appl. Polym. Sci. 77, 3090–3106 (2000).
[CrossRef]

A. A. Hamza, T. Z. N. Sokkar, K. A. El-Farahaty, H. M. El-Dessouky, “Comparative study on interferometric techniques for measurement of the optical properties of a fiber,” J. Opt. 1, 41–50 (1999).

A. A. Hamza, A. M. Nasr, “Interferometric studies on multi-mode step-index optical fibres,” Pure Appl. Opt. 7, 449–456 (1998).
[CrossRef]

Hassan, R.

H. El-Ghandoor, E. A. El-Ghafar, R. Hassan, “Refractive index profiling of a GRIN optical fiber using a modulated speckled sheet of light,” Opt. Laser Technol. 31, 481–488 (1999).
[CrossRef]

Hori, N.

Hui, Z.

M. Hai, X. Jianping, Z. Hui, S. Yuensheng, C. Nong, “Measuring abberations of a gradient-index rod lens with holographic shearing interferometry,” Int. J. Optoelectron. 7, 53–56 (1992).

Huntington, S. T.

S. T. Huntington, A. Roberts, K. A. Nugent, P. Mulvaney, M. Bazylenko, “Fibre and waveguide refractive index measurements with AFM resolution,” Jpn. J. Appl. Phys. 37, 62–64 (1998).

S. T. Huntington, P. Mulvaney, A. Roberts, K. A. Nugent, M. Bazylenko, “Atomic force microscopy for the determination of refractive index profiles of optical fibers and waveguides: a quantitative study,” J. Appl. Phys. 820, 2730–2734 (1997).
[CrossRef]

Huttner, B.

Ishigure, T.

Iwamura, K.

Jianping, X.

M. Hai, X. Jianping, Z. Hui, S. Yuensheng, C. Nong, “Measuring abberations of a gradient-index rod lens with holographic shearing interferometry,” Int. J. Optoelectron. 7, 53–56 (1992).

Kinoshita, T.

A. Tagaya, Y. Koike, T. Kinoshita, E. Nihei, T. Yamamoto, K. Sasaki, “Polymer optical fiber amplifier,” Appl. Phys. Lett. 63, 883–884 (1993).
[CrossRef]

Koike, Y.

E. Nihei, T. Ishigure, Y. Koike, “High-bandwidth, graded-index polymer optical fiber for near-infrared use,” Appl. Opt. 35, 7085–7090 (1996).
[CrossRef] [PubMed]

A. Tagaya, Y. Koike, T. Kinoshita, E. Nihei, T. Yamamoto, K. Sasaki, “Polymer optical fiber amplifier,” Appl. Phys. Lett. 63, 883–884 (1993).
[CrossRef]

Y. Ohtsuka, E. Nihei, Y. Koike, “Graded-index optical fibers of methyl methacrylate—vinyl benzoate copolymer with low loss and high bandwidth,” Appl. Phys. Lett. 57, 120–122 (1990).
[CrossRef]

Kuzyk, M. G.

S. R. Vigil, Z. Zhou, B. K. Canfield, J. Tostenrude, M. G. Kuzyk, “Dual-core single-mode polymer fiber coupler,” J. Opt. Soc. Am. B 15, 895–900 (1998).
[CrossRef]

D. W. Garvey, K. Zimmerman, P. Young, J. Tostenrude, J. S. Townsend, Z. Zhou, M. Lobel, M. Dayton, R. Wittorf, M. G. Kuzyk, “Single-mode nonlinear-optical polymer fibers,” J. Opt. Soc. Am. B 13, 2017–2023 (1996).
[CrossRef]

D. W. Garvey, Q. Li, M. G. Kuzyk, C. W. Dirk, S. Martinez, “Sagnac interferometric intensity-dependent refractive-index measurements of polymer optical fiber,” Opt. Lett. 21, 104–106 (1996).
[CrossRef] [PubMed]

D. J. Welker, M. G. Kuzyk, “All-optical switching in a dye-doped polymer fiber Fabry–Perot waveguide,” Appl. Phys. Lett. 69, 1835–1836 (1996).
[CrossRef]

D. J. Welker, M. G. Kuzyk, “Optical and mechanical multistability in a dye-doped polymer fiber Fabry–Perot waveguide,” Appl. Phys. Lett. 66, 2792–2794 (1995).
[CrossRef]

D. J. Welker, M. G. Kuzyk, “Photomechanical stabilization in a polymer fiber-based all-optical circuit,” Appl. Phys. Lett. 64, 809–811 (1994).
[CrossRef]

M. G. Kuzyk, U. C. Paek, C. W. Dirk, “Guest-host polymer fibers for nonlinear optics,” Appl. Phys. Lett. 59, 902–904 (1991).
[CrossRef]

Li, Q.

Lobel, M.

Mabrouk, M. A.

A. A. Hamza, T. Z. N. Sokkar, M. A. Mabrouk, M. A. El-Morsy, “Refractive index profile of polyethylene fiber using interactive multiple-beam Fizeau fringe analysis,” J. Appl. Polym. Sci. 77, 3090–3106 (2000).
[CrossRef]

T. Z. N. Sokkar, M. A. Mabrouk, H. F. El-Bawab, “Refractive-index profile of GRIN optical fiber considering the area under the interference fringe shift: II. The mismatching case,” J. Opt. A 1, 64–72 (1999).
[CrossRef]

M. A. Mabrouk, H. F. El-Bawab, “Refractive index profile of GRIN optical fibre considering the area under the interference fringe shift. I. The matching case,” Pure Appl. Opt. 6, 247–256 (1997).
[CrossRef]

Mansour, I.

F. Gonella, A. Quaranta, A. Sambo, F. Caccavale, I. Mansour, “Construction of glass waveguide refractive index profiles by the effective-index finite-difference method,” Opt. Mat. 5, 321–326 (1996).
[CrossRef]

I. Mansour, F. Caccavale, “An improved procedure to calculate the refractive index profile from the measured near-field intensity,” J. Lightwave Technol. 14, 423–428 (1996).
[CrossRef]

Marcuse, D.

Martinez, S.

Miller, M.

P. Skok, M. Miller, “Spatial filtering method of oblique slit for measurement of refractive-index profile of optical-fibre preforms,” Electron. Lett. 23, 859–860 (1987).
[CrossRef]

Montaldo, G.

J. A. Ferrari, E. Frins, A. Rondoni, G. Montaldo, “Retrieval algorithm for refractive-index profile of fibers from transverse interferograms,” Opt. Commun. 117, 25–30 (1995).
[CrossRef]

Müller, T.

T. Müller, “Resolution improvement in refracted near-field index measurement by a lens-shaped liquid cell,” Electron. Lett. 19, 580–582 (1983).
[CrossRef]

Mulvaney, P.

S. T. Huntington, A. Roberts, K. A. Nugent, P. Mulvaney, M. Bazylenko, “Fibre and waveguide refractive index measurements with AFM resolution,” Jpn. J. Appl. Phys. 37, 62–64 (1998).

S. T. Huntington, P. Mulvaney, A. Roberts, K. A. Nugent, M. Bazylenko, “Atomic force microscopy for the determination of refractive index profiles of optical fibers and waveguides: a quantitative study,” J. Appl. Phys. 820, 2730–2734 (1997).
[CrossRef]

Nagano, S.

Nasr, A. M.

A. A. Hamza, A. M. Nasr, “Interferometric studies on multi-mode step-index optical fibres,” Pure Appl. Opt. 7, 449–456 (1998).
[CrossRef]

Nihei, E.

E. Nihei, T. Ishigure, Y. Koike, “High-bandwidth, graded-index polymer optical fiber for near-infrared use,” Appl. Opt. 35, 7085–7090 (1996).
[CrossRef] [PubMed]

A. Tagaya, Y. Koike, T. Kinoshita, E. Nihei, T. Yamamoto, K. Sasaki, “Polymer optical fiber amplifier,” Appl. Phys. Lett. 63, 883–884 (1993).
[CrossRef]

Y. Ohtsuka, E. Nihei, Y. Koike, “Graded-index optical fibers of methyl methacrylate—vinyl benzoate copolymer with low loss and high bandwidth,” Appl. Phys. Lett. 57, 120–122 (1990).
[CrossRef]

Nong, C.

M. Hai, X. Jianping, Z. Hui, S. Yuensheng, C. Nong, “Measuring abberations of a gradient-index rod lens with holographic shearing interferometry,” Int. J. Optoelectron. 7, 53–56 (1992).

Nugent, K. A.

S. T. Huntington, A. Roberts, K. A. Nugent, P. Mulvaney, M. Bazylenko, “Fibre and waveguide refractive index measurements with AFM resolution,” Jpn. J. Appl. Phys. 37, 62–64 (1998).

S. T. Huntington, P. Mulvaney, A. Roberts, K. A. Nugent, M. Bazylenko, “Atomic force microscopy for the determination of refractive index profiles of optical fibers and waveguides: a quantitative study,” J. Appl. Phys. 820, 2730–2734 (1997).
[CrossRef]

Oberson, P.

Ohtsuka, Y.

Y. Ohtsuka, E. Nihei, Y. Koike, “Graded-index optical fibers of methyl methacrylate—vinyl benzoate copolymer with low loss and high bandwidth,” Appl. Phys. Lett. 57, 120–122 (1990).
[CrossRef]

Oven, R.

S. Batchelor, R. Oven, D. G. Ashworth, “Reconstruction of refractive index profiles from multiple wavelength mode indices,” Opt. Commun. 131, 31–36 (1996).
[CrossRef]

R. Oven, S. Batchelor, D. G. Ashworth, D. Gelder, J. M. Bradshaw, “Iterative refinement technique for reconstructing refractive index profiles from mode indices,” Electron. Lett. 31, 229–231 (1995).
[CrossRef]

Paek, U. C.

M. G. Kuzyk, U. C. Paek, C. W. Dirk, “Guest-host polymer fibers for nonlinear optics,” Appl. Phys. Lett. 59, 902–904 (1991).
[CrossRef]

Passy, R.

Peng, G. D.

Z. Xiong, G. D. Peng, P. L. Chu, “Nonlinear coupling and optical switching in a β-carotene-doped twin-core polymer optical fiber,” Opt. Eng. 39, 624–627 (2000).
[CrossRef]

Peri, D.

D. Peri, P. L. Chu, “Measurement of refractive-index profile of optical-fibre preform by means of spatial filtering,” Electron. Lett. 17, 371–372 (1981).
[CrossRef]

Philips, L.

Pietraszkiewicz, K.

W. Urbanczyk, K. Pietraszkiewicz, W. A. Wozniak, “Novel bifunctional systems for measuring the refractive index profile and residual stress birefringence in optical fibers and preforms,” Opt. Eng. 31, 491–499 (1992).
[CrossRef]

Posey, R.

Quaranta, A.

F. Gonella, A. Quaranta, A. Sambo, F. Caccavale, I. Mansour, “Construction of glass waveguide refractive index profiles by the effective-index finite-difference method,” Opt. Mat. 5, 321–326 (1996).
[CrossRef]

Rivory, J.

Roberts, A.

S. T. Huntington, A. Roberts, K. A. Nugent, P. Mulvaney, M. Bazylenko, “Fibre and waveguide refractive index measurements with AFM resolution,” Jpn. J. Appl. Phys. 37, 62–64 (1998).

S. T. Huntington, P. Mulvaney, A. Roberts, K. A. Nugent, M. Bazylenko, “Atomic force microscopy for the determination of refractive index profiles of optical fibers and waveguides: a quantitative study,” J. Appl. Phys. 820, 2730–2734 (1997).
[CrossRef]

Rondoni, A.

J. A. Ferrari, E. Frins, A. Rondoni, G. Montaldo, “Retrieval algorithm for refractive-index profile of fibers from transverse interferograms,” Opt. Commun. 117, 25–30 (1995).
[CrossRef]

Saekeang, C.

Sambo, A.

F. Gonella, A. Quaranta, A. Sambo, F. Caccavale, I. Mansour, “Construction of glass waveguide refractive index profiles by the effective-index finite-difference method,” Opt. Mat. 5, 321–326 (1996).
[CrossRef]

Sasaki, K.

A. Tagaya, Y. Koike, T. Kinoshita, E. Nihei, T. Yamamoto, K. Sasaki, “Polymer optical fiber amplifier,” Appl. Phys. Lett. 63, 883–884 (1993).
[CrossRef]

Saunders, M. J.

Sawa, S.

T. Yabu, S. Sawa, M. Geshiro, “Measurement of refractive index distribution of optical waveguides by the propagation mode near-field method employing an improved inverse analysis,” Electron. Commun. Jpn. 79, 21–29 (1996).

Sharma, A.

Skok, P.

P. Skok, M. Miller, “Spatial filtering method of oblique slit for measurement of refractive-index profile of optical-fibre preforms,” Electron. Lett. 23, 859–860 (1987).
[CrossRef]

Sochacki, J.

J. Sochacki, M. Sochaka, C. Gomez-Reino, “Reconstruction of axially nonsymmetric refractive index profiles from ray deflection by means of the Abel integral transform,” Opt. Commun. 71, 20–22 (1989).
[CrossRef]

J. Sochacki, “Accurate reconstruction of the refractive-index profile of fibers and preform rods from transverse interferometric data,” Appl. Opt. 25, 3473–3482 (1986).
[CrossRef] [PubMed]

Sochaka, M.

J. Sochacki, M. Sochaka, C. Gomez-Reino, “Reconstruction of axially nonsymmetric refractive index profiles from ray deflection by means of the Abel integral transform,” Opt. Commun. 71, 20–22 (1989).
[CrossRef]

Sokkar, T. Z. N.

A. A. Hamza, T. Z. N. Sokkar, M. A. Mabrouk, M. A. El-Morsy, “Refractive index profile of polyethylene fiber using interactive multiple-beam Fizeau fringe analysis,” J. Appl. Polym. Sci. 77, 3090–3106 (2000).
[CrossRef]

T. Z. N. Sokkar, M. A. Mabrouk, H. F. El-Bawab, “Refractive-index profile of GRIN optical fiber considering the area under the interference fringe shift: II. The mismatching case,” J. Opt. A 1, 64–72 (1999).
[CrossRef]

A. A. Hamza, T. Z. N. Sokkar, K. A. El-Farahaty, H. M. El-Dessouky, “Comparative study on interferometric techniques for measurement of the optical properties of a fiber,” J. Opt. 1, 41–50 (1999).

Stamp, P.

Stewart, W. J.

W. J. Stewart, “Optical fiber and preform profiling technology,” IEEE J. Quantum Electron. 18, 1451–1465 (1982).
[CrossRef]

Tagaya, A.

A. Tagaya, Y. Koike, T. Kinoshita, E. Nihei, T. Yamamoto, K. Sasaki, “Polymer optical fiber amplifier,” Appl. Phys. Lett. 63, 883–884 (1993).
[CrossRef]

Tostenrude, J.

Townsend, J. S.

Urbanczyk, W.

W. Urbanczyk, K. Pietraszkiewicz, W. A. Wozniak, “Novel bifunctional systems for measuring the refractive index profile and residual stress birefringence in optical fibers and preforms,” Opt. Eng. 31, 491–499 (1992).
[CrossRef]

Van, V. N.

Vigil, S. R.

Vuye, G.

Wang, Y.

Welker, D. J.

D. J. Welker, M. G. Kuzyk, “All-optical switching in a dye-doped polymer fiber Fabry–Perot waveguide,” Appl. Phys. Lett. 69, 1835–1836 (1996).
[CrossRef]

D. J. Welker, M. G. Kuzyk, “Optical and mechanical multistability in a dye-doped polymer fiber Fabry–Perot waveguide,” Appl. Phys. Lett. 66, 2792–2794 (1995).
[CrossRef]

D. J. Welker, M. G. Kuzyk, “Photomechanical stabilization in a polymer fiber-based all-optical circuit,” Appl. Phys. Lett. 64, 809–811 (1994).
[CrossRef]

White, K. I.

K. I. White, “Practical application of the refracted near-field technique for the measurement of optical fibre refractive index profiles,” Opt. Quant. Electron. 11, 185–196 (1978).
[CrossRef]

Wittorf, R.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon Press, Oxford, UK1980).

Wozniak, W. A.

W. Urbanczyk, K. Pietraszkiewicz, W. A. Wozniak, “Novel bifunctional systems for measuring the refractive index profile and residual stress birefringence in optical fibers and preforms,” Opt. Eng. 31, 491–499 (1992).
[CrossRef]

Wu, Z. Z.

Z. Z. Wu, H. Davis, S. K. Batra, “Correct ray-tracing analysis for interference microscopy of fibers,” Proc. R. Soc. London Ser. A 450, 23–36 (1995).
[CrossRef]

Xiong, Z.

Z. Xiong, G. D. Peng, P. L. Chu, “Nonlinear coupling and optical switching in a β-carotene-doped twin-core polymer optical fiber,” Opt. Eng. 39, 624–627 (2000).
[CrossRef]

Yabu, T.

T. Yabu, S. Sawa, M. Geshiro, “Measurement of refractive index distribution of optical waveguides by the propagation mode near-field method employing an improved inverse analysis,” Electron. Commun. Jpn. 79, 21–29 (1996).

Yamamoto, T.

A. Tagaya, Y. Koike, T. Kinoshita, E. Nihei, T. Yamamoto, K. Sasaki, “Polymer optical fiber amplifier,” Appl. Phys. Lett. 63, 883–884 (1993).
[CrossRef]

Young, M.

Young, P.

Yuensheng, S.

M. Hai, X. Jianping, Z. Hui, S. Yuensheng, C. Nong, “Measuring abberations of a gradient-index rod lens with holographic shearing interferometry,” Int. J. Optoelectron. 7, 53–56 (1992).

Zbinden, H.

B. Groebil, B. Gisin, N. Gisin, H. Zbinden, “Measuring refractive index profiles of integrated LiNbO3 waveguides,” Opt. Eng. 34, 2309–3214 (1995).
[CrossRef]

Zhou, Z.

Zimmerman, K.

Appl. Opt. (9)

E. Nihei, T. Ishigure, Y. Koike, “High-bandwidth, graded-index polymer optical fiber for near-infrared use,” Appl. Opt. 35, 7085–7090 (1996).
[CrossRef] [PubMed]

V. N. Van, A. Brunet-Bruneau, S. Fisson, J. M. Frigerio, G. Vuye, Y. Wang, F. Abelès, J. Rivory, M. Berger, P. Chaton, “Determination of refractive-index profiles by a combination of visible and infrared ellipsometry measurements,” Appl. Opt. 35, 5540–5544 (1996).
[CrossRef]

D. Marcuse, “Refractive index determination by the focusing method,” Appl. Opt. 18, 9–13 (1979).
[CrossRef] [PubMed]

J. Sochacki, “Accurate reconstruction of the refractive-index profile of fibers and preform rods from transverse interferometric data,” Appl. Opt. 25, 3473–3482 (1986).
[CrossRef] [PubMed]

M. Young, “Calibration technique for refracted near-field scanning of optical fibers,” Appl. Opt. 19, 2479–2480 (1980).
[CrossRef] [PubMed]

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

N. Gisin, R. Passy, P. Stamp, N. Hori, S. Nagano, “New optical configuration for nondestructive measurements of refractive-index profiles of LiNbO3 waveguides,” Appl. Opt. 33, 1726–1731 (1994).
[CrossRef] [PubMed]

P. Oberson, B. Gisin, B. Huttner, N. Gisin, “Refracted near-field measurements of refractive index and geometry of silica-on-silicon integrated optical waveguides,” Appl. Opt. 37, 7268–7272 (1998).
[CrossRef]

M. J. Saunders, “Optical fiber profiles using the refracted near-field technique: A comparison with other methods,” Appl. Opt. 20, 1645–1651 (1981).
[CrossRef] [PubMed]

Appl. Phys. Lett. (6)

Y. Ohtsuka, E. Nihei, Y. Koike, “Graded-index optical fibers of methyl methacrylate—vinyl benzoate copolymer with low loss and high bandwidth,” Appl. Phys. Lett. 57, 120–122 (1990).
[CrossRef]

M. G. Kuzyk, U. C. Paek, C. W. Dirk, “Guest-host polymer fibers for nonlinear optics,” Appl. Phys. Lett. 59, 902–904 (1991).
[CrossRef]

A. Tagaya, Y. Koike, T. Kinoshita, E. Nihei, T. Yamamoto, K. Sasaki, “Polymer optical fiber amplifier,” Appl. Phys. Lett. 63, 883–884 (1993).
[CrossRef]

D. J. Welker, M. G. Kuzyk, “All-optical switching in a dye-doped polymer fiber Fabry–Perot waveguide,” Appl. Phys. Lett. 69, 1835–1836 (1996).
[CrossRef]

D. J. Welker, M. G. Kuzyk, “Photomechanical stabilization in a polymer fiber-based all-optical circuit,” Appl. Phys. Lett. 64, 809–811 (1994).
[CrossRef]

D. J. Welker, M. G. Kuzyk, “Optical and mechanical multistability in a dye-doped polymer fiber Fabry–Perot waveguide,” Appl. Phys. Lett. 66, 2792–2794 (1995).
[CrossRef]

Electron. Commun. Jpn. (1)

T. Yabu, S. Sawa, M. Geshiro, “Measurement of refractive index distribution of optical waveguides by the propagation mode near-field method employing an improved inverse analysis,” Electron. Commun. Jpn. 79, 21–29 (1996).

Electron. Lett. (5)

P. Skok, M. Miller, “Spatial filtering method of oblique slit for measurement of refractive-index profile of optical-fibre preforms,” Electron. Lett. 23, 859–860 (1987).
[CrossRef]

P. L. Chu, “Nondestructive measurement of index profile of an optical-fibre preform,” Electron. Lett. 13, 736–738 (1977).
[CrossRef]

D. Peri, P. L. Chu, “Measurement of refractive-index profile of optical-fibre preform by means of spatial filtering,” Electron. Lett. 17, 371–372 (1981).
[CrossRef]

T. Müller, “Resolution improvement in refracted near-field index measurement by a lens-shaped liquid cell,” Electron. Lett. 19, 580–582 (1983).
[CrossRef]

R. Oven, S. Batchelor, D. G. Ashworth, D. Gelder, J. M. Bradshaw, “Iterative refinement technique for reconstructing refractive index profiles from mode indices,” Electron. Lett. 31, 229–231 (1995).
[CrossRef]

IEEE J. Quantum Electron. (1)

W. J. Stewart, “Optical fiber and preform profiling technology,” IEEE J. Quantum Electron. 18, 1451–1465 (1982).
[CrossRef]

Int. J. Optoelectron. (1)

M. Hai, X. Jianping, Z. Hui, S. Yuensheng, C. Nong, “Measuring abberations of a gradient-index rod lens with holographic shearing interferometry,” Int. J. Optoelectron. 7, 53–56 (1992).

J. Appl. Phys. (1)

S. T. Huntington, P. Mulvaney, A. Roberts, K. A. Nugent, M. Bazylenko, “Atomic force microscopy for the determination of refractive index profiles of optical fibers and waveguides: a quantitative study,” J. Appl. Phys. 820, 2730–2734 (1997).
[CrossRef]

J. Appl. Polym. Sci. (1)

A. A. Hamza, T. Z. N. Sokkar, M. A. Mabrouk, M. A. El-Morsy, “Refractive index profile of polyethylene fiber using interactive multiple-beam Fizeau fringe analysis,” J. Appl. Polym. Sci. 77, 3090–3106 (2000).
[CrossRef]

J. Lightwave Technol. (1)

I. Mansour, F. Caccavale, “An improved procedure to calculate the refractive index profile from the measured near-field intensity,” J. Lightwave Technol. 14, 423–428 (1996).
[CrossRef]

J. Opt. (1)

A. A. Hamza, T. Z. N. Sokkar, K. A. El-Farahaty, H. M. El-Dessouky, “Comparative study on interferometric techniques for measurement of the optical properties of a fiber,” J. Opt. 1, 41–50 (1999).

J. Opt. A (1)

T. Z. N. Sokkar, M. A. Mabrouk, H. F. El-Bawab, “Refractive-index profile of GRIN optical fiber considering the area under the interference fringe shift: II. The mismatching case,” J. Opt. A 1, 64–72 (1999).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (2)

Jpn. J. Appl. Phys. (1)

S. T. Huntington, A. Roberts, K. A. Nugent, P. Mulvaney, M. Bazylenko, “Fibre and waveguide refractive index measurements with AFM resolution,” Jpn. J. Appl. Phys. 37, 62–64 (1998).

Opt. Commun. (4)

J. Sochacki, M. Sochaka, C. Gomez-Reino, “Reconstruction of axially nonsymmetric refractive index profiles from ray deflection by means of the Abel integral transform,” Opt. Commun. 71, 20–22 (1989).
[CrossRef]

J. A. Ferrari, E. Frins, A. Rondoni, G. Montaldo, “Retrieval algorithm for refractive-index profile of fibers from transverse interferograms,” Opt. Commun. 117, 25–30 (1995).
[CrossRef]

S. Batchelor, R. Oven, D. G. Ashworth, “Reconstruction of refractive index profiles from multiple wavelength mode indices,” Opt. Commun. 131, 31–36 (1996).
[CrossRef]

N. Gisin, “Correcting refracted near field refractive index profile measurements for Gaussian intensity distributions,” Opt. Commun. 83, 295–299 (1991).
[CrossRef]

Opt. Eng. (3)

B. Groebil, B. Gisin, N. Gisin, H. Zbinden, “Measuring refractive index profiles of integrated LiNbO3 waveguides,” Opt. Eng. 34, 2309–3214 (1995).
[CrossRef]

Z. Xiong, G. D. Peng, P. L. Chu, “Nonlinear coupling and optical switching in a β-carotene-doped twin-core polymer optical fiber,” Opt. Eng. 39, 624–627 (2000).
[CrossRef]

W. Urbanczyk, K. Pietraszkiewicz, W. A. Wozniak, “Novel bifunctional systems for measuring the refractive index profile and residual stress birefringence in optical fibers and preforms,” Opt. Eng. 31, 491–499 (1992).
[CrossRef]

Opt. Laser Technol. (1)

H. El-Ghandoor, E. A. El-Ghafar, R. Hassan, “Refractive index profiling of a GRIN optical fiber using a modulated speckled sheet of light,” Opt. Laser Technol. 31, 481–488 (1999).
[CrossRef]

Opt. Lett. (2)

Opt. Mat. (1)

F. Gonella, A. Quaranta, A. Sambo, F. Caccavale, I. Mansour, “Construction of glass waveguide refractive index profiles by the effective-index finite-difference method,” Opt. Mat. 5, 321–326 (1996).
[CrossRef]

Opt. Quant. Electron. (1)

K. I. White, “Practical application of the refracted near-field technique for the measurement of optical fibre refractive index profiles,” Opt. Quant. Electron. 11, 185–196 (1978).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

Z. Z. Wu, H. Davis, S. K. Batra, “Correct ray-tracing analysis for interference microscopy of fibers,” Proc. R. Soc. London Ser. A 450, 23–36 (1995).
[CrossRef]

Pure Appl. Opt. (2)

M. A. Mabrouk, H. F. El-Bawab, “Refractive index profile of GRIN optical fibre considering the area under the interference fringe shift. I. The matching case,” Pure Appl. Opt. 6, 247–256 (1997).
[CrossRef]

A. A. Hamza, A. M. Nasr, “Interferometric studies on multi-mode step-index optical fibres,” Pure Appl. Opt. 7, 449–456 (1998).
[CrossRef]

Other (1)

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon Press, Oxford, UK1980).

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Figures (10)

Fig. 1
Fig. 1

Graded-index preform fabrication by interfacial gel polymerization.

Fig. 2
Fig. 2

Step-index preform fabrication.

Fig. 3
Fig. 3

Profiling method geometry.

Fig. 4
Fig. 4

DDM experimental setup.

Fig. 5
Fig. 5

Vector field plots showing refractive index gradient: (a) original data, (b) wedge-corrected data.

Fig. 6
Fig. 6

Coordinate system and angle definitions.

Fig. 7
Fig. 7

One-dimensional GRIN preform refractive index profile. Top graph shows original biased data and linear fit; middle graph shows wedge-corrected data and paraboloid bias fit; bottom graph shows final corrected profile and parabolic profile fit.

Fig. 8
Fig. 8

Three-dimensional GRIN preform profile.

Fig. 9
Fig. 9

Raw deflection magnitude data for a step-index preform.

Fig. 10
Fig. 10

One-dimensional step-index preform profile.

Equations (10)

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ρ=1|Logn|=n|n|,
ρ2=t2+ρ-Δy2.
Δy=t22ρ.
θ=t2ρ,
θ=αn,
|n|=2αt.
n=2αrt.
nr2-nr1=2ztr1r2 frαˆ · dr.
erfcN=k -Nexp-ax2dx,
ΔnR, C  nR, C-nR, 1=2drztj=1C fR, jcosϕR, jcosαR, j,

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