Abstract

Multiple-beam Fizeau fringes are formed across a liquid silvered wedge when it is illuminated by a collimated beam of monochromatic light. Inserting the fiber into the liquid silvered wedge causes the fringes to shift across the fiber region with respect to the fringes at the liquid region. Fringe shift is a function in the geometry of the different regions of the fiber and the refractive index profile of the fiber. In this paper, theoretical models for the fringe shift across double-clad fibers (DCFs) with rectangular, elliptical, circular, and D-shaped inner cladding are developed. An algorithm to reconstruct the linear and nonlinear terms of the refractive index profile of the DCF is outlined. Numerical examples are provided and discussed.

© 2011 Optical Society of America

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References

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  1. http://en.wikipedia.org/wiki/Double-clad_fiber.
  2. http://www.rp-photonics.com/double_clad_fibers.html.
  3. D. Yelin, B. E. Bouma, S. H. Yun, and G. J. Tearney, “Double-clad fiber for endoscopy,” Opt. Lett. 29, 2408–2410 (2004).
    [CrossRef] [PubMed]
  4. N. Barakat, “Interferometric studies on fibers. Part I: Theory of interferometric determination of indices of fibers,” Textile Res. J. 41, 167–170 (1971).
    [CrossRef]
  5. N. Barakat and H. A. El-Hennawi, “Interferometric studies of fibers. Part II: Interferometric determination of the refractive indices and birefringence of acrylic fibers,” Textile Res. J. 41, 391–396 (1971).
    [CrossRef]
  6. M. J. Saunders and W. B. Gardner, “Nondestructive interferometric measurement of the delta and alpha of clad optical fibers,” Appl. Opt. 16, 2368–2371 (1977).
    [CrossRef] [PubMed]
  7. A. A. Hamza, T. Z. N. Sokkar, and M. A. Kabeel, “Multiple-beam interferometric studies on fibres with irregular transverse sections,” J. Phys. D 18, 1773–1780 (1985).
    [CrossRef]
  8. N. Barakat, A. A. Hamza, and A. S. Goneid, “Multiple-beam interference fringes applied to GRIN optical waveguides to determine fiber characteristics,” Appl. Opt. 24, 4383–4386(1985).
    [CrossRef] [PubMed]
  9. H. A. El-Hennawi, “A mathematical expression for the shape of multiple beam Fizeau fringes crossing a multilayer cylindrical fiber,” Egypt. J. Phys. 19, 91–100 (1988).
  10. N. Barakat and A. A. Hamza, Interferometry of Fibrous Materials (Hilger, 1990).
  11. N. Barakat, H. A. El-Hennawi, S. Y. El-Zaiat, and R. Hassan, “Estimation of the index profile parameters of a GRIN optical waveguide and fringe synthesis applying multiple beam interference,” Pure Appl. Opt. 5, 27–34 (1996).
    [CrossRef]
  12. N. Barakat, H. A. El-Hennawi, E. A. El-Ghafar, H. El-Ghandoor, R. Hassan, and F. El-Diasty, “Three-dimensional refractive index profile of a GRIN optical waveguide using multiple beam interference fringes,” Opt. Commun. 191, 39–47 (2001).
    [CrossRef]
  13. A. A. Hamza, T. Z. N. Sokkar, M. A. El-Morsy, and M. A. E. Nawareg, “Automatic determination of refractive index profile, sectional area, and shape of fibers having regular and/or irregular transverse sections,” Opt. Laser Technol. 40, 1082–1090 (2008).
    [CrossRef]
  14. F. El-Diasty and H. A. El-Hennawi, “Nonlinearity in bent optical fibers,” Appl. Opt. 48, 3818–3822 (2009).
    [CrossRef] [PubMed]
  15. M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
    [CrossRef]
  16. K. S. Kim, R. H. Stolen, W. A. Reed, and K. W. Quoi, “Measurement of the nonlinear index of silica-core and dispersion-shifted fibers,” Opt. Lett. 19, 257–259 (1994).
    [CrossRef] [PubMed]
  17. K. Li, Z. Xiong, G. D. Peng, and P. L. Chu, “Direct measurement of nonlinear refractive index with an all-fibre Sagnac interferometer,” Opt. Commun. 136, 223–226 (1997).
    [CrossRef]
  18. D. Milam and M. J. Weber, “Measurement of nonlinear refractive‐index coefficients using time‐resolved interferometry: application to optical materials for high‐power neodymium lasers,” J. Appl. Phys. 47, 2497–2501 (1976).
    [CrossRef]
  19. H. K. Lee, K. H. Kim, and E.-H. Lee, “Measurement of the nonlinear refractive index of fibers with a rotating nonlinear Sagnac interferometer,” Appl. Opt. 36, 5893–5897(1997).
    [CrossRef] [PubMed]
  20. C. Vinegoni, M. Wegmuller, and N. Gisin, “Measurements of the nonlinear coefficient of standard SMF, DSF, and DCF fibers using a self-aligned interferometer and a Faraday mirror,” IEEE Photon. Technol. Lett. 13, 1337–1339(2001).
    [CrossRef]
  21. R. A. Betts, T. Tjugiarto, Y. L. Xue, and P. L. Chu, “Nonlinear refractive index in erbium doped optical fiber: theory and experiment,” IEEE J. Quantum Electron. 27, 908–913(1991).
    [CrossRef]

2009 (1)

2008 (1)

A. A. Hamza, T. Z. N. Sokkar, M. A. El-Morsy, and M. A. E. Nawareg, “Automatic determination of refractive index profile, sectional area, and shape of fibers having regular and/or irregular transverse sections,” Opt. Laser Technol. 40, 1082–1090 (2008).
[CrossRef]

2004 (1)

2001 (2)

N. Barakat, H. A. El-Hennawi, E. A. El-Ghafar, H. El-Ghandoor, R. Hassan, and F. El-Diasty, “Three-dimensional refractive index profile of a GRIN optical waveguide using multiple beam interference fringes,” Opt. Commun. 191, 39–47 (2001).
[CrossRef]

C. Vinegoni, M. Wegmuller, and N. Gisin, “Measurements of the nonlinear coefficient of standard SMF, DSF, and DCF fibers using a self-aligned interferometer and a Faraday mirror,” IEEE Photon. Technol. Lett. 13, 1337–1339(2001).
[CrossRef]

1997 (2)

K. Li, Z. Xiong, G. D. Peng, and P. L. Chu, “Direct measurement of nonlinear refractive index with an all-fibre Sagnac interferometer,” Opt. Commun. 136, 223–226 (1997).
[CrossRef]

H. K. Lee, K. H. Kim, and E.-H. Lee, “Measurement of the nonlinear refractive index of fibers with a rotating nonlinear Sagnac interferometer,” Appl. Opt. 36, 5893–5897(1997).
[CrossRef] [PubMed]

1996 (1)

N. Barakat, H. A. El-Hennawi, S. Y. El-Zaiat, and R. Hassan, “Estimation of the index profile parameters of a GRIN optical waveguide and fringe synthesis applying multiple beam interference,” Pure Appl. Opt. 5, 27–34 (1996).
[CrossRef]

1994 (1)

1991 (1)

R. A. Betts, T. Tjugiarto, Y. L. Xue, and P. L. Chu, “Nonlinear refractive index in erbium doped optical fiber: theory and experiment,” IEEE J. Quantum Electron. 27, 908–913(1991).
[CrossRef]

1990 (1)

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

1988 (1)

H. A. El-Hennawi, “A mathematical expression for the shape of multiple beam Fizeau fringes crossing a multilayer cylindrical fiber,” Egypt. J. Phys. 19, 91–100 (1988).

1985 (2)

A. A. Hamza, T. Z. N. Sokkar, and M. A. Kabeel, “Multiple-beam interferometric studies on fibres with irregular transverse sections,” J. Phys. D 18, 1773–1780 (1985).
[CrossRef]

N. Barakat, A. A. Hamza, and A. S. Goneid, “Multiple-beam interference fringes applied to GRIN optical waveguides to determine fiber characteristics,” Appl. Opt. 24, 4383–4386(1985).
[CrossRef] [PubMed]

1977 (1)

1976 (1)

D. Milam and M. J. Weber, “Measurement of nonlinear refractive‐index coefficients using time‐resolved interferometry: application to optical materials for high‐power neodymium lasers,” J. Appl. Phys. 47, 2497–2501 (1976).
[CrossRef]

1971 (2)

N. Barakat, “Interferometric studies on fibers. Part I: Theory of interferometric determination of indices of fibers,” Textile Res. J. 41, 167–170 (1971).
[CrossRef]

N. Barakat and H. A. El-Hennawi, “Interferometric studies of fibers. Part II: Interferometric determination of the refractive indices and birefringence of acrylic fibers,” Textile Res. J. 41, 391–396 (1971).
[CrossRef]

Barakat, N.

N. Barakat, H. A. El-Hennawi, E. A. El-Ghafar, H. El-Ghandoor, R. Hassan, and F. El-Diasty, “Three-dimensional refractive index profile of a GRIN optical waveguide using multiple beam interference fringes,” Opt. Commun. 191, 39–47 (2001).
[CrossRef]

N. Barakat, H. A. El-Hennawi, S. Y. El-Zaiat, and R. Hassan, “Estimation of the index profile parameters of a GRIN optical waveguide and fringe synthesis applying multiple beam interference,” Pure Appl. Opt. 5, 27–34 (1996).
[CrossRef]

N. Barakat, A. A. Hamza, and A. S. Goneid, “Multiple-beam interference fringes applied to GRIN optical waveguides to determine fiber characteristics,” Appl. Opt. 24, 4383–4386(1985).
[CrossRef] [PubMed]

N. Barakat, “Interferometric studies on fibers. Part I: Theory of interferometric determination of indices of fibers,” Textile Res. J. 41, 167–170 (1971).
[CrossRef]

N. Barakat and H. A. El-Hennawi, “Interferometric studies of fibers. Part II: Interferometric determination of the refractive indices and birefringence of acrylic fibers,” Textile Res. J. 41, 391–396 (1971).
[CrossRef]

N. Barakat and A. A. Hamza, Interferometry of Fibrous Materials (Hilger, 1990).

Betts, R. A.

R. A. Betts, T. Tjugiarto, Y. L. Xue, and P. L. Chu, “Nonlinear refractive index in erbium doped optical fiber: theory and experiment,” IEEE J. Quantum Electron. 27, 908–913(1991).
[CrossRef]

Bouma, B. E.

Chu, P. L.

K. Li, Z. Xiong, G. D. Peng, and P. L. Chu, “Direct measurement of nonlinear refractive index with an all-fibre Sagnac interferometer,” Opt. Commun. 136, 223–226 (1997).
[CrossRef]

R. A. Betts, T. Tjugiarto, Y. L. Xue, and P. L. Chu, “Nonlinear refractive index in erbium doped optical fiber: theory and experiment,” IEEE J. Quantum Electron. 27, 908–913(1991).
[CrossRef]

El-Diasty, F.

F. El-Diasty and H. A. El-Hennawi, “Nonlinearity in bent optical fibers,” Appl. Opt. 48, 3818–3822 (2009).
[CrossRef] [PubMed]

N. Barakat, H. A. El-Hennawi, E. A. El-Ghafar, H. El-Ghandoor, R. Hassan, and F. El-Diasty, “Three-dimensional refractive index profile of a GRIN optical waveguide using multiple beam interference fringes,” Opt. Commun. 191, 39–47 (2001).
[CrossRef]

El-Ghafar, E. A.

N. Barakat, H. A. El-Hennawi, E. A. El-Ghafar, H. El-Ghandoor, R. Hassan, and F. El-Diasty, “Three-dimensional refractive index profile of a GRIN optical waveguide using multiple beam interference fringes,” Opt. Commun. 191, 39–47 (2001).
[CrossRef]

El-Ghandoor, H.

N. Barakat, H. A. El-Hennawi, E. A. El-Ghafar, H. El-Ghandoor, R. Hassan, and F. El-Diasty, “Three-dimensional refractive index profile of a GRIN optical waveguide using multiple beam interference fringes,” Opt. Commun. 191, 39–47 (2001).
[CrossRef]

El-Hennawi, H. A.

F. El-Diasty and H. A. El-Hennawi, “Nonlinearity in bent optical fibers,” Appl. Opt. 48, 3818–3822 (2009).
[CrossRef] [PubMed]

N. Barakat, H. A. El-Hennawi, E. A. El-Ghafar, H. El-Ghandoor, R. Hassan, and F. El-Diasty, “Three-dimensional refractive index profile of a GRIN optical waveguide using multiple beam interference fringes,” Opt. Commun. 191, 39–47 (2001).
[CrossRef]

N. Barakat, H. A. El-Hennawi, S. Y. El-Zaiat, and R. Hassan, “Estimation of the index profile parameters of a GRIN optical waveguide and fringe synthesis applying multiple beam interference,” Pure Appl. Opt. 5, 27–34 (1996).
[CrossRef]

H. A. El-Hennawi, “A mathematical expression for the shape of multiple beam Fizeau fringes crossing a multilayer cylindrical fiber,” Egypt. J. Phys. 19, 91–100 (1988).

N. Barakat and H. A. El-Hennawi, “Interferometric studies of fibers. Part II: Interferometric determination of the refractive indices and birefringence of acrylic fibers,” Textile Res. J. 41, 391–396 (1971).
[CrossRef]

El-Morsy, M. A.

A. A. Hamza, T. Z. N. Sokkar, M. A. El-Morsy, and M. A. E. Nawareg, “Automatic determination of refractive index profile, sectional area, and shape of fibers having regular and/or irregular transverse sections,” Opt. Laser Technol. 40, 1082–1090 (2008).
[CrossRef]

El-Zaiat, S. Y.

N. Barakat, H. A. El-Hennawi, S. Y. El-Zaiat, and R. Hassan, “Estimation of the index profile parameters of a GRIN optical waveguide and fringe synthesis applying multiple beam interference,” Pure Appl. Opt. 5, 27–34 (1996).
[CrossRef]

Gardner, W. B.

Gisin, N.

C. Vinegoni, M. Wegmuller, and N. Gisin, “Measurements of the nonlinear coefficient of standard SMF, DSF, and DCF fibers using a self-aligned interferometer and a Faraday mirror,” IEEE Photon. Technol. Lett. 13, 1337–1339(2001).
[CrossRef]

Goneid, A. S.

Hagan, D. J.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

Hamza, A. A.

A. A. Hamza, T. Z. N. Sokkar, M. A. El-Morsy, and M. A. E. Nawareg, “Automatic determination of refractive index profile, sectional area, and shape of fibers having regular and/or irregular transverse sections,” Opt. Laser Technol. 40, 1082–1090 (2008).
[CrossRef]

N. Barakat, A. A. Hamza, and A. S. Goneid, “Multiple-beam interference fringes applied to GRIN optical waveguides to determine fiber characteristics,” Appl. Opt. 24, 4383–4386(1985).
[CrossRef] [PubMed]

A. A. Hamza, T. Z. N. Sokkar, and M. A. Kabeel, “Multiple-beam interferometric studies on fibres with irregular transverse sections,” J. Phys. D 18, 1773–1780 (1985).
[CrossRef]

N. Barakat and A. A. Hamza, Interferometry of Fibrous Materials (Hilger, 1990).

Hassan, R.

N. Barakat, H. A. El-Hennawi, E. A. El-Ghafar, H. El-Ghandoor, R. Hassan, and F. El-Diasty, “Three-dimensional refractive index profile of a GRIN optical waveguide using multiple beam interference fringes,” Opt. Commun. 191, 39–47 (2001).
[CrossRef]

N. Barakat, H. A. El-Hennawi, S. Y. El-Zaiat, and R. Hassan, “Estimation of the index profile parameters of a GRIN optical waveguide and fringe synthesis applying multiple beam interference,” Pure Appl. Opt. 5, 27–34 (1996).
[CrossRef]

Kabeel, M. A.

A. A. Hamza, T. Z. N. Sokkar, and M. A. Kabeel, “Multiple-beam interferometric studies on fibres with irregular transverse sections,” J. Phys. D 18, 1773–1780 (1985).
[CrossRef]

Kim, K. H.

Kim, K. S.

Lee, E.-H.

Lee, H. K.

Li, K.

K. Li, Z. Xiong, G. D. Peng, and P. L. Chu, “Direct measurement of nonlinear refractive index with an all-fibre Sagnac interferometer,” Opt. Commun. 136, 223–226 (1997).
[CrossRef]

Milam, D.

D. Milam and M. J. Weber, “Measurement of nonlinear refractive‐index coefficients using time‐resolved interferometry: application to optical materials for high‐power neodymium lasers,” J. Appl. Phys. 47, 2497–2501 (1976).
[CrossRef]

Nawareg, M. A. E.

A. A. Hamza, T. Z. N. Sokkar, M. A. El-Morsy, and M. A. E. Nawareg, “Automatic determination of refractive index profile, sectional area, and shape of fibers having regular and/or irregular transverse sections,” Opt. Laser Technol. 40, 1082–1090 (2008).
[CrossRef]

Peng, G. D.

K. Li, Z. Xiong, G. D. Peng, and P. L. Chu, “Direct measurement of nonlinear refractive index with an all-fibre Sagnac interferometer,” Opt. Commun. 136, 223–226 (1997).
[CrossRef]

Quoi, K. W.

Reed, W. A.

Said, A. A.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

Saunders, M. J.

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

Sokkar, T. Z. N.

A. A. Hamza, T. Z. N. Sokkar, M. A. El-Morsy, and M. A. E. Nawareg, “Automatic determination of refractive index profile, sectional area, and shape of fibers having regular and/or irregular transverse sections,” Opt. Laser Technol. 40, 1082–1090 (2008).
[CrossRef]

A. A. Hamza, T. Z. N. Sokkar, and M. A. Kabeel, “Multiple-beam interferometric studies on fibres with irregular transverse sections,” J. Phys. D 18, 1773–1780 (1985).
[CrossRef]

Stolen, R. H.

Tearney, G. J.

Tjugiarto, T.

R. A. Betts, T. Tjugiarto, Y. L. Xue, and P. L. Chu, “Nonlinear refractive index in erbium doped optical fiber: theory and experiment,” IEEE J. Quantum Electron. 27, 908–913(1991).
[CrossRef]

Van Stryland, E. W.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

Vinegoni, C.

C. Vinegoni, M. Wegmuller, and N. Gisin, “Measurements of the nonlinear coefficient of standard SMF, DSF, and DCF fibers using a self-aligned interferometer and a Faraday mirror,” IEEE Photon. Technol. Lett. 13, 1337–1339(2001).
[CrossRef]

Weber, M. J.

D. Milam and M. J. Weber, “Measurement of nonlinear refractive‐index coefficients using time‐resolved interferometry: application to optical materials for high‐power neodymium lasers,” J. Appl. Phys. 47, 2497–2501 (1976).
[CrossRef]

Wegmuller, M.

C. Vinegoni, M. Wegmuller, and N. Gisin, “Measurements of the nonlinear coefficient of standard SMF, DSF, and DCF fibers using a self-aligned interferometer and a Faraday mirror,” IEEE Photon. Technol. Lett. 13, 1337–1339(2001).
[CrossRef]

Wei, T.-H.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

Xiong, Z.

K. Li, Z. Xiong, G. D. Peng, and P. L. Chu, “Direct measurement of nonlinear refractive index with an all-fibre Sagnac interferometer,” Opt. Commun. 136, 223–226 (1997).
[CrossRef]

Xue, Y. L.

R. A. Betts, T. Tjugiarto, Y. L. Xue, and P. L. Chu, “Nonlinear refractive index in erbium doped optical fiber: theory and experiment,” IEEE J. Quantum Electron. 27, 908–913(1991).
[CrossRef]

Yelin, D.

Yun, S. H.

Appl. Opt. (4)

Egypt. J. Phys. (1)

H. A. El-Hennawi, “A mathematical expression for the shape of multiple beam Fizeau fringes crossing a multilayer cylindrical fiber,” Egypt. J. Phys. 19, 91–100 (1988).

IEEE J. Quantum Electron. (2)

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

R. A. Betts, T. Tjugiarto, Y. L. Xue, and P. L. Chu, “Nonlinear refractive index in erbium doped optical fiber: theory and experiment,” IEEE J. Quantum Electron. 27, 908–913(1991).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

C. Vinegoni, M. Wegmuller, and N. Gisin, “Measurements of the nonlinear coefficient of standard SMF, DSF, and DCF fibers using a self-aligned interferometer and a Faraday mirror,” IEEE Photon. Technol. Lett. 13, 1337–1339(2001).
[CrossRef]

J. Appl. Phys. (1)

D. Milam and M. J. Weber, “Measurement of nonlinear refractive‐index coefficients using time‐resolved interferometry: application to optical materials for high‐power neodymium lasers,” J. Appl. Phys. 47, 2497–2501 (1976).
[CrossRef]

J. Phys. D (1)

A. A. Hamza, T. Z. N. Sokkar, and M. A. Kabeel, “Multiple-beam interferometric studies on fibres with irregular transverse sections,” J. Phys. D 18, 1773–1780 (1985).
[CrossRef]

Opt. Commun. (2)

K. Li, Z. Xiong, G. D. Peng, and P. L. Chu, “Direct measurement of nonlinear refractive index with an all-fibre Sagnac interferometer,” Opt. Commun. 136, 223–226 (1997).
[CrossRef]

N. Barakat, H. A. El-Hennawi, E. A. El-Ghafar, H. El-Ghandoor, R. Hassan, and F. El-Diasty, “Three-dimensional refractive index profile of a GRIN optical waveguide using multiple beam interference fringes,” Opt. Commun. 191, 39–47 (2001).
[CrossRef]

Opt. Laser Technol. (1)

A. A. Hamza, T. Z. N. Sokkar, M. A. El-Morsy, and M. A. E. Nawareg, “Automatic determination of refractive index profile, sectional area, and shape of fibers having regular and/or irregular transverse sections,” Opt. Laser Technol. 40, 1082–1090 (2008).
[CrossRef]

Opt. Lett. (2)

Pure Appl. Opt. (1)

N. Barakat, H. A. El-Hennawi, S. Y. El-Zaiat, and R. Hassan, “Estimation of the index profile parameters of a GRIN optical waveguide and fringe synthesis applying multiple beam interference,” Pure Appl. Opt. 5, 27–34 (1996).
[CrossRef]

Textile Res. J. (2)

N. Barakat, “Interferometric studies on fibers. Part I: Theory of interferometric determination of indices of fibers,” Textile Res. J. 41, 167–170 (1971).
[CrossRef]

N. Barakat and H. A. El-Hennawi, “Interferometric studies of fibers. Part II: Interferometric determination of the refractive indices and birefringence of acrylic fibers,” Textile Res. J. 41, 391–396 (1971).
[CrossRef]

Other (3)

http://en.wikipedia.org/wiki/Double-clad_fiber.

http://www.rp-photonics.com/double_clad_fibers.html.

N. Barakat and A. A. Hamza, Interferometry of Fibrous Materials (Hilger, 1990).

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Figures (19)

Fig. 1
Fig. 1

Cross section of the DCF with rectangular inner cladding.

Fig. 2
Fig. 2

Cross section of the DCF with elliptical inner cladding.

Fig. 3
Fig. 3

Cross section of the DCF with circular inner cladding.

Fig. 4
Fig. 4

Cross section of the DCF with D-shaped inner cladding.

Fig. 5
Fig. 5

Refractive index profile across the liquid and the DCF with rectangular inner cladding.

Fig. 6
Fig. 6

Refractive index profile across the liquid and the DCF with circular inner cladding. The core center is shifted by 15 μm .

Fig. 7
Fig. 7

Fringe shift across the DCF with rectangular inner cladding.

Fig. 8
Fig. 8

Fringe shift across the DCF with elliptical inner cladding.

Fig. 9
Fig. 9

Fringe shift across the DCF with circular inner cladding and shifted core ( 15 μm ).

Fig. 10
Fig. 10

Fringe shift across the DCF with circular inner cladding and centered core.

Fig. 11
Fig. 11

Fringe shift across the DCF with D-shaped inner cladding.

Fig. 12
Fig. 12

Difference in the fringe shift due to the contribution of the nonlinear refractive index across the DCF with rectangular inner cladding.

Fig. 13
Fig. 13

Difference in the fringe shift due to the contribution of the nonlinear refractive index across DCF with elliptical inner cladding.

Fig. 14
Fig. 14

Difference in the fringe shift due to the contribution of the nonlinear refractive index across the DCF with circular inner cladding with shifted core ( 15 μm ).

Fig. 15
Fig. 15

Difference in the fringe shift due to the contribution of the nonlinear refractive index across the DCF with circular inner cladding and centered core.

Fig. 16
Fig. 16

Difference in fringe shift due to the contribution of the nonlinear refractive index across the DCF with D-shaped inner cladding.

Fig. 17
Fig. 17

Fringe shift across the DCF with rectangular inner cladding (matching liquid).

Fig. 18
Fig. 18

Fringe shift across the DCF with circular cladding with shifted core (matching liquid).

Fig. 19
Fig. 19

Fringe shift across the DCF with D-shaped cladding (matching liquid).

Tables (1)

Tables Icon

Table 1 Geometrical Parameters and Refractive Indices for DCFs with Different Double-Cladding Geometries

Equations (47)

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

n C L 1 = n C L 1 ( E ) = n C L 1 , o + Δ n C L 1 , n ( E ) = n C L 1 , o + n C L 1 , n E ,
n C L 2 = n C L 2 ( E ) = n C L 2 , o + Δ n C L 2 , n ( E ) = n C L 2 , o + n C L 2 , n E ,
n c = n c ( E ) = n c , o + Δ n c , n ( E ) = n c , o + n c , n E ,
n L = n L ( E ) = n L , o + Δ n L , n ( E ) = n L , o + n L , n E ,
OPL I = ( t 2 y 3 , I ) n L + 2 y 3 , I n C L 1 .
y 3 , I = ( a c L 1 2 x I 2 ) 1 / 2 .
OPL I = n L t + 2 ( a C L 1 2 x I 2 ) 1 / 2 ( n C L 1 n L ) .
OPL I I = ( t 2 y 3 , I I ) n L + 2 ( y 3 , I I L ) n C L 1 + 2 L n C L 2 ,
y 3 , I I = ( a c L 1 2 x I I 2 ) 1 / 2 .
OPL I I = n L t + 2 ( a C L 1 2 x I I 2 ) 1 / 2 ( n C L 1 n L ) + 2 L ( n C L 2 n C L 1 ) .
OPL I I I = ( t 2 y 3 , I I I ) n L + 2 ( y 3 , I I I L ) n C L 1 + 2 ( L y 1 , I I I ) n C L 2 + 2 y 1 , I I I n c ,
y 1 , I I I = ( a c 2 x I I I 2 ) 1 / 2 , y 2 , I I I = ( a C L 2 2 x I I I 2 ) 1 / 2 , y 3 , I I I = ( a C L 1 2 x I I I 2 ) 1 / 2 .
OPL I I I = n L t + 2 ( a C L 1 2 x I I I 2 ) 1 / 2 ( n C L 1 n L ) + 2 L ( n C L 2 n C L 1 ) + ( a C 2 x I I I 2 ) 1 / 2 ( n c n C L 2 ) .
tan ε = δ t I δ Z I = δ t I I δ Z I I = δ t I I I δ Z I I I .
tan ε = λ 2 n L Δ Z .
δ Z I = 2 Δ Z λ n L δ t I , δ Z I I = 2 Δ Z λ n L δ t I I , δ Z I I I = 2 Δ Z λ n L δ t I I I .
OPL I = n L ( t + δ t I ) , OPL I I = n L ( t + δ t I I ) , OPL I I I = n L ( t + δ t I I I ) .
n L δ t I = 2 ( a C L 1 2 x I 2 ) 1 / 2 ( n C L 1 n L ) .
δ Z I = 4 Δ Z λ ( a C L 1 2 x I 2 ) 1 / 2 ( n C L 2 n L ) .
δ Z I I = 4 Δ Z λ [ ( a C L 1 2 x I I 2 ) 1 / 2 ( n C L 1 n L ) + L ( n C L 2 n C L 1 ) ] ,
δ Z I I I = 4 Δ Z λ [ ( a C L 1 2 x I I I 2 ) 1 / 2 ( n C L 1 n L ) + L ( n C L 2 n C L 1 ) + ( a C 2 x I I I 2 ) 1 / 2 ( n c n C L 2 ) ] .
x 2 A 2 + y 2 B 2 = 1 ,
OPL I = ( t 2 y 3 , I ) n L + 2 y 3 , I n C L 1 ,
y 3 , I = ( a c L 1 2 x I 2 ) 1 / 2 ,
OPL I = n t L + 2 ( a C L 1 2 x I 2 ) 1 / 2 ( n C L 1 n L ) .
OPL I I = ( t 2 y 3 , I I ) n L + 2 ( y 3 , I I y 2 , I I ) n C L 1 + 2 y 2 , I I n C L 2 ,
y 2 , I I = B ( 1 x I I 2 A 2 ) 1 / 2 , y 3 , I I = ( a C L 1 2 x I I 2 ) 1 / 2 ,
OPL I I = n L t + 2 ( a C L 1 2 x I I 2 ) 1 / 2 ( n C L 1 n L ) + 2 B ( 1 x I I 2 A 2 ) 1 / 2 ( n C L 2 n C L 1 ) .
OPL I I I = ( t 2 y 3 , I I I ) n L + 2 ( y 3 , I I I y 2 , I I I ) n C L 1 + 2 ( y 2 , I I I y 1 , I I I ) n C L 2 + 2 y 1 , I I I n c ,
y 1 , I I I = ( a c 2 ( x I I I η ) 2 ) 1 / 2 , y 2 , I I I = B ( 1 x I I I 2 A 2 ) 1 / 2 , y 3 , I I I = ( a C L 1 2 x I I I 2 ) 1 / 2 ,
OPL I I I = n L t + [ 2 ( a C L 1 2 x I I I 2 ) 1 / 2 ( n C L 1 n L ) + 2 B ( 1 x I I I 2 A 2 ) 1 / 2 ( n C L 2 n C L 1 ) + 2 ( a c 2 ( x I I I η ) 2 ) 1 / 2 ( n c n C L 2 ) ] .
δ Z I = 4 Δ Z λ ( a C L 1 2 x I 2 ) 1 / 2 ( n C L 1 n L ) ,
δ Z I I = 4 Δ Z λ [ ( a C L 1 2 x I I 2 ) 1 / 2 ( n C L 1 n L ) + B ( 1 x I I 2 A 2 ) 1 / 2 ( n C L 2 n C L 1 ) ] ,
δ Z I I I = 4 Δ Z λ [ ( a C L 1 2 x I I I 2 ) 1 / 2 ( n C L 1 n L ) + B ( 1 x I I I 2 A 2 ) 1 / 2 ( n C L 2 n C L 1 ) + ( a c 2 ( x I I I η ) 2 ) 1 / 2 ( n c n C L 2 ) ] .
δ Z I I I = 4 Δ Z λ [ ( a C L 1 2 x I I I 2 ) 1 / 2 ( n C L 1 n L ) + B ( 1 x I I I 2 A 2 ) 1 / 2 ( n C L 2 n C L 1 ) + ( a c 2 x I I I 2 ) 1 / 2 ( n c n C L 2 ) ] .
δ Z I = 4 Δ Z λ ( a C L 1 2 x I 2 ) 1 / 2 ( n C L I n L ) .
δ Z I I = 4 Δ Z λ [ ( a C L 1 2 x I I 2 ) 1 / 2 ( n C L 1 n L ) + ( a C L 2 2 x I I 2 ) 1 / 2 ( n C L 2 n C L 1 ) ] .
δ Z I I I = 4 Δ Z λ [ ( a C L 1 2 x I I I ) 1 / 2 ( n C L 1 n L ) + ( a C L 2 2 x I I I 2 ) 1 / 2 ( n C L 2 n C L 1 ) + ( a c 2 ( x I I I η ) 2 ) 1 / 2 ( n c n C L 2 ) ] .
OPL I = ( t 2 y 3 , I ) n L + 2 y 3 , I n C L 1 ,
OPL I I = ( t 2 y 3 , I I ) n L + 2 ( y 3 , I I y 2 , I I ) n C L 1 + 2 y 2 , I I n C L 2 ,
y 2 , I I = ( a C L 2 2 x I I 2 ) 1 / 2 , y 3 , I I = ( a c L 1 2 x I I 2 ) 1 / 2 ,
OPL I I I = ( t 2 y 3 , I I I ) n L + ( y 3 , I I I y 2 , I I I ) n C L 1 + ( y 2 , I I I + K ) n C L 2 + ( y 3 , I I I K ) n C L 1 ,
OPL I I I I = ( t 2 y 3 , I I I I ) n L + ( y 3 , I I I I y 2 , I I I I ) n C L 1 + ( y 2 , I I I I y 1 , I I I I ) n C L 2 + 2 y 1 , I I I I n c + ( K y 1 , I I I I ) n C L 2 + ( y 3 , I I I I K ) n C L 1 ,
δ Z I = 4 Δ Z λ ( a C L 1 2 x I 2 ) 1 / 2 ( n C L 1 n L ) ,
δ Z I I = 4 Δ Z λ [ ( a C L 1 2 x I I 2 ) 1 / 2 ( n C L 1 n L ) + ( a C L 2 2 x I I 2 ) 1 / 2 ( n C L 2 n C L 1 ) ] ,
δ Z I I I = 4 Δ Z λ [ ( a C L 1 2 x I I I 2 ) 1 / 2 ( n C L 1 n L ) + 1 2 ( a C L 2 2 x I I I 2 ) 1 / 2 ( n C L 2 n C L 1 ) + K 2 ( n C L 2 n C L 1 ) ] ,
δ Z I I I I = 4 Δ Z λ [ ( a C L 1 2 x I I I I 2 ) 1 / 2 ( n C L 1 n L ) + 1 2 ( a C L 2 2 x I I I I 2 ) 1 / 2 ( n C L 2 n C L 1 ) + ( a c 2 x I I I I 2 ) 1 / 2 ( n c n C L 2 ) + K 2 ( n C L 2 n C L 1 ) ] .

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