Abstract

We study the applicability of the weakly guiding approximation (WGA) to the modal analysis of an M-type optical fiber in which a ring-shaped core lies between two uniform cladding layers. Besides being dependent on the refractive indices, the accuracy of the approximation is shown to be substantially affected by the transverse dimensions of the core. The accuracy is characterized by calculating an overlap integral between the exact and WGA-approximated modal fields. Fibers that have an inner cladding similar to the outer cladding, or similar to vacuum, are considered in detail. The feasibility of the WGA in determining the fiber parameters for single-mode guidance is also discussed.

© 2005 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  3. R. G. Dall, M. D. Hoogerland, D. Tierney, K. G. H. Baldwin, S. J. Buckman, “Single-mode hollow optical fibres for atom guiding,” Appl. Phys. B: Lasers Opt. 74, 11–18 (2002).
    [CrossRef]
  4. S. H. Yoo, C. Won, J.-A. Kim, K. Kim, U. Shim, K. Oh, U.-C. Paek, W. Jhe, “Diffracted near field of hollow optical fibre for a novel atomic funnel,” J. Opt. B: Quantum Semiclassical Opt. 1, 364–370 (1999).
    [CrossRef]
  5. Y.-I. Shin, M. Heo, J.-W. Kim, W. Shim, H.-R. Noh, W. Jhe, “Diffraction-limited optical dipole trap with a hollow optical fiber,” J. Opt. Soc. Am. B 20, 937–941 (2003).
    [CrossRef]
  6. P. Glas, M. Naumann, A. Schirrmacher, Th. Pertsch, “A neodymium doped hollow optical fiber laser for applications in sensing and laser guided atoms,” Opt. Commun. 166, 71–78 (1999).
    [CrossRef]
  7. P. Glas, M. Naumann, A. Schirrmacher, S. Unger, Th. Pertsch, “Short-length 10-W cw neodymium-doped M-profile fiber laser,” Appl. Opt. 37, 8434–8437 (1998).
    [CrossRef]
  8. A. Nürenberg, G. Schweiger, “Excitation and recording of morphology-dependent resonances in spherical micro- resonators by hollow light guiding fibers,” Appl. Phys. Lett. 84, 2043–2045 (2004).
    [CrossRef]
  9. S. Choi, T. J. Eom, J. W. Yu, B. H. Lee, K. Oh, “Novel all-fiber bandpass filter based on hollow optical fiber,” IEEE Photonics Technol. Lett. 14, 1701–1703 (2002).
    [CrossRef]
  10. S. Choi, K. Oh, W. Shin, C. S. Park, U. C. Paek, K. J. Park, Y. C. Chung, G. Y. Kim, Y. G. Lee, “Novel mode converter based on hollow optical fiber for gigabit LAN communication,” IEEE Photonics Technol. Lett. 14, 248–250 (2002).
    [CrossRef]
  11. S. Choi, K. Oh, “A new LP02 mode dispersion compensation scheme based on mode converter using hollow optical fiber,” Opt. Commun. 221, 307–312 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. P. K. Choudhury, R. A. Lessard, “An estimation of power transmission through a doubly clad optical fiber with an annular core,” Microwave Opt. Technol. Lett. 29, 402–405 (2001).
    [CrossRef]
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    [CrossRef]
  17. A. P. Napartovich, D. V. Vysotsky, “Phase-locking of multicore fibre laser due to Talbot self-reproduction,” J. Mod. Opt. 50, 2715–2725 (2003).
    [CrossRef]
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    [CrossRef]
  20. I. V. Neves, A. S. C. Fernandes, “Modal characteristics for A-type and V-type dielectric profile fibers,” Microwave Opt. Technol. Lett. 16, 164–169 (1997).
    [CrossRef]
  21. I. V. Neves, A. S. C. Fernandes, “Modal characteristics for W-type and M-type dielectric profile fibers,” Microwave Opt. Technol. Lett. 22, 398–405 (1999).
    [CrossRef]
  22. H. Ito, K. Sakaki, T. Nakata, W. Jhe, M. Ohtsu, “Optical guidance of neutral atoms using evanescent waves in a cylindrical-core hollow fiber: theoretical approach,” Ultramicroscopy 61, 91–97 (1995).
    [CrossRef]
  23. A. W. Snyder, J. D. Love, Optical Waveguide Theory, 1st ed. (Chapman & Hall, London, 1983).
  24. D. Marcuse, Theory of Dielectric Optical Waveguides, 1st ed. (Academic, New York, 1974).
  25. G. B. Arfken, H. J. Weber, Mathematical Methods for Physicists, 4th ed. (Academic, San Diego, Calif., 1995).
  26. Y. Ni, N. Liu, J. Yin, “Diffracted field distributions from the HE11 mode in a hollow optical fibre for an atomic funnel,” J. Opt. B: Quantum Semiclassical Opt. 5, 300–308 (2003).
    [CrossRef]

2004 (1)

A. Nürenberg, G. Schweiger, “Excitation and recording of morphology-dependent resonances in spherical micro- resonators by hollow light guiding fibers,” Appl. Phys. Lett. 84, 2043–2045 (2004).
[CrossRef]

2003 (6)

S. Choi, K. Oh, “A new LP02 mode dispersion compensation scheme based on mode converter using hollow optical fiber,” Opt. Commun. 221, 307–312 (2003).
[CrossRef]

J. Marcou, S. Février, “Comments on ‘On the analysis of a weakly guiding doubly clad dielectric optical fiber with an annular core’,” Microwave Opt. Technol. Lett. 38, 249–254 (2003).
[CrossRef]

A. P. Napartovich, D. V. Vysotsky, “Phase-locking of multicore fibre laser due to Talbot self-reproduction,” J. Mod. Opt. 50, 2715–2725 (2003).
[CrossRef]

P. R. Chaudhuri, C. Lu, W. Xiaoyan, “Scalar model and exact vectorial description for the design analysis of hollow optical fiber components,” Opt. Commun. 228, 285–293 (2003).
[CrossRef]

Y. Ni, N. Liu, J. Yin, “Diffracted field distributions from the HE11 mode in a hollow optical fibre for an atomic funnel,” J. Opt. B: Quantum Semiclassical Opt. 5, 300–308 (2003).
[CrossRef]

Y.-I. Shin, M. Heo, J.-W. Kim, W. Shim, H.-R. Noh, W. Jhe, “Diffraction-limited optical dipole trap with a hollow optical fiber,” J. Opt. Soc. Am. B 20, 937–941 (2003).
[CrossRef]

2002 (5)

M. Wrage, P. Glas, D. Fischer, M. Leitner, N. N. Elkin, D. V. Vysotsky, A. P. Napartovich, V. N. Troshchieva, “Phase-locking of a multicore fiber laser by wave propagation through an annular waveguide,” Opt. Commun. 205, 367–375 (2002).
[CrossRef]

S. Choi, T. J. Eom, J. W. Yu, B. H. Lee, K. Oh, “Novel all-fiber bandpass filter based on hollow optical fiber,” IEEE Photonics Technol. Lett. 14, 1701–1703 (2002).
[CrossRef]

S. Choi, K. Oh, W. Shin, C. S. Park, U. C. Paek, K. J. Park, Y. C. Chung, G. Y. Kim, Y. G. Lee, “Novel mode converter based on hollow optical fiber for gigabit LAN communication,” IEEE Photonics Technol. Lett. 14, 248–250 (2002).
[CrossRef]

H. -R. Noh, W. Jhe, “Atom optics with hollow optical systems,” Phys. Rep. 372, 269–317 (2002).
[CrossRef]

R. G. Dall, M. D. Hoogerland, D. Tierney, K. G. H. Baldwin, S. J. Buckman, “Single-mode hollow optical fibres for atom guiding,” Appl. Phys. B: Lasers Opt. 74, 11–18 (2002).
[CrossRef]

2001 (2)

B. C. Sarkar, P. K. Choudhury, T. Yoshino, “On the analysis of a weakly guiding doubly clad dielectric optical fiber with an annular core,” Microwave Opt. Technol. Lett. 31, 435–439 (2001).
[CrossRef]

P. K. Choudhury, R. A. Lessard, “An estimation of power transmission through a doubly clad optical fiber with an annular core,” Microwave Opt. Technol. Lett. 29, 402–405 (2001).
[CrossRef]

1999 (3)

I. V. Neves, A. S. C. Fernandes, “Modal characteristics for W-type and M-type dielectric profile fibers,” Microwave Opt. Technol. Lett. 22, 398–405 (1999).
[CrossRef]

S. H. Yoo, C. Won, J.-A. Kim, K. Kim, U. Shim, K. Oh, U.-C. Paek, W. Jhe, “Diffracted near field of hollow optical fibre for a novel atomic funnel,” J. Opt. B: Quantum Semiclassical Opt. 1, 364–370 (1999).
[CrossRef]

P. Glas, M. Naumann, A. Schirrmacher, Th. Pertsch, “A neodymium doped hollow optical fiber laser for applications in sensing and laser guided atoms,” Opt. Commun. 166, 71–78 (1999).
[CrossRef]

1998 (1)

1997 (1)

I. V. Neves, A. S. C. Fernandes, “Modal characteristics for A-type and V-type dielectric profile fibers,” Microwave Opt. Technol. Lett. 16, 164–169 (1997).
[CrossRef]

1995 (2)

H. Ito, K. Sakaki, T. Nakata, W. Jhe, M. Ohtsu, “Optical potential for atom guidance in a cylindrical-core hollow fiber,” Opt. Commun. 115, 57–64 (1995).
[CrossRef]

H. Ito, K. Sakaki, T. Nakata, W. Jhe, M. Ohtsu, “Optical guidance of neutral atoms using evanescent waves in a cylindrical-core hollow fiber: theoretical approach,” Ultramicroscopy 61, 91–97 (1995).
[CrossRef]

1989 (1)

1971 (1)

Arfken, G. B.

G. B. Arfken, H. J. Weber, Mathematical Methods for Physicists, 4th ed. (Academic, San Diego, Calif., 1995).

Baldwin, K. G. H.

R. G. Dall, M. D. Hoogerland, D. Tierney, K. G. H. Baldwin, S. J. Buckman, “Single-mode hollow optical fibres for atom guiding,” Appl. Phys. B: Lasers Opt. 74, 11–18 (2002).
[CrossRef]

Buckman, S. J.

R. G. Dall, M. D. Hoogerland, D. Tierney, K. G. H. Baldwin, S. J. Buckman, “Single-mode hollow optical fibres for atom guiding,” Appl. Phys. B: Lasers Opt. 74, 11–18 (2002).
[CrossRef]

Chaudhuri, P. R.

P. R. Chaudhuri, C. Lu, W. Xiaoyan, “Scalar model and exact vectorial description for the design analysis of hollow optical fiber components,” Opt. Commun. 228, 285–293 (2003).
[CrossRef]

Choi, S.

S. Choi, K. Oh, “A new LP02 mode dispersion compensation scheme based on mode converter using hollow optical fiber,” Opt. Commun. 221, 307–312 (2003).
[CrossRef]

S. Choi, T. J. Eom, J. W. Yu, B. H. Lee, K. Oh, “Novel all-fiber bandpass filter based on hollow optical fiber,” IEEE Photonics Technol. Lett. 14, 1701–1703 (2002).
[CrossRef]

S. Choi, K. Oh, W. Shin, C. S. Park, U. C. Paek, K. J. Park, Y. C. Chung, G. Y. Kim, Y. G. Lee, “Novel mode converter based on hollow optical fiber for gigabit LAN communication,” IEEE Photonics Technol. Lett. 14, 248–250 (2002).
[CrossRef]

Choudhury, P. K.

B. C. Sarkar, P. K. Choudhury, T. Yoshino, “On the analysis of a weakly guiding doubly clad dielectric optical fiber with an annular core,” Microwave Opt. Technol. Lett. 31, 435–439 (2001).
[CrossRef]

P. K. Choudhury, R. A. Lessard, “An estimation of power transmission through a doubly clad optical fiber with an annular core,” Microwave Opt. Technol. Lett. 29, 402–405 (2001).
[CrossRef]

Chung, Y. C.

S. Choi, K. Oh, W. Shin, C. S. Park, U. C. Paek, K. J. Park, Y. C. Chung, G. Y. Kim, Y. G. Lee, “Novel mode converter based on hollow optical fiber for gigabit LAN communication,” IEEE Photonics Technol. Lett. 14, 248–250 (2002).
[CrossRef]

Dall, R. G.

R. G. Dall, M. D. Hoogerland, D. Tierney, K. G. H. Baldwin, S. J. Buckman, “Single-mode hollow optical fibres for atom guiding,” Appl. Phys. B: Lasers Opt. 74, 11–18 (2002).
[CrossRef]

Elkin, N. N.

M. Wrage, P. Glas, D. Fischer, M. Leitner, N. N. Elkin, D. V. Vysotsky, A. P. Napartovich, V. N. Troshchieva, “Phase-locking of a multicore fiber laser by wave propagation through an annular waveguide,” Opt. Commun. 205, 367–375 (2002).
[CrossRef]

Eom, T. J.

S. Choi, T. J. Eom, J. W. Yu, B. H. Lee, K. Oh, “Novel all-fiber bandpass filter based on hollow optical fiber,” IEEE Photonics Technol. Lett. 14, 1701–1703 (2002).
[CrossRef]

Fernandes, A. S. C.

I. V. Neves, A. S. C. Fernandes, “Modal characteristics for W-type and M-type dielectric profile fibers,” Microwave Opt. Technol. Lett. 22, 398–405 (1999).
[CrossRef]

I. V. Neves, A. S. C. Fernandes, “Modal characteristics for A-type and V-type dielectric profile fibers,” Microwave Opt. Technol. Lett. 16, 164–169 (1997).
[CrossRef]

Février, S.

J. Marcou, S. Février, “Comments on ‘On the analysis of a weakly guiding doubly clad dielectric optical fiber with an annular core’,” Microwave Opt. Technol. Lett. 38, 249–254 (2003).
[CrossRef]

Fischer, D.

M. Wrage, P. Glas, D. Fischer, M. Leitner, N. N. Elkin, D. V. Vysotsky, A. P. Napartovich, V. N. Troshchieva, “Phase-locking of a multicore fiber laser by wave propagation through an annular waveguide,” Opt. Commun. 205, 367–375 (2002).
[CrossRef]

Gambling, W. A.

Glas, P.

M. Wrage, P. Glas, D. Fischer, M. Leitner, N. N. Elkin, D. V. Vysotsky, A. P. Napartovich, V. N. Troshchieva, “Phase-locking of a multicore fiber laser by wave propagation through an annular waveguide,” Opt. Commun. 205, 367–375 (2002).
[CrossRef]

P. Glas, M. Naumann, A. Schirrmacher, Th. Pertsch, “A neodymium doped hollow optical fiber laser for applications in sensing and laser guided atoms,” Opt. Commun. 166, 71–78 (1999).
[CrossRef]

P. Glas, M. Naumann, A. Schirrmacher, S. Unger, Th. Pertsch, “Short-length 10-W cw neodymium-doped M-profile fiber laser,” Appl. Opt. 37, 8434–8437 (1998).
[CrossRef]

Gloge, D.

Heo, M.

Hoogerland, M. D.

R. G. Dall, M. D. Hoogerland, D. Tierney, K. G. H. Baldwin, S. J. Buckman, “Single-mode hollow optical fibres for atom guiding,” Appl. Phys. B: Lasers Opt. 74, 11–18 (2002).
[CrossRef]

Ito, H.

H. Ito, K. Sakaki, T. Nakata, W. Jhe, M. Ohtsu, “Optical potential for atom guidance in a cylindrical-core hollow fiber,” Opt. Commun. 115, 57–64 (1995).
[CrossRef]

H. Ito, K. Sakaki, T. Nakata, W. Jhe, M. Ohtsu, “Optical guidance of neutral atoms using evanescent waves in a cylindrical-core hollow fiber: theoretical approach,” Ultramicroscopy 61, 91–97 (1995).
[CrossRef]

Jhe, W.

Y.-I. Shin, M. Heo, J.-W. Kim, W. Shim, H.-R. Noh, W. Jhe, “Diffraction-limited optical dipole trap with a hollow optical fiber,” J. Opt. Soc. Am. B 20, 937–941 (2003).
[CrossRef]

H. -R. Noh, W. Jhe, “Atom optics with hollow optical systems,” Phys. Rep. 372, 269–317 (2002).
[CrossRef]

S. H. Yoo, C. Won, J.-A. Kim, K. Kim, U. Shim, K. Oh, U.-C. Paek, W. Jhe, “Diffracted near field of hollow optical fibre for a novel atomic funnel,” J. Opt. B: Quantum Semiclassical Opt. 1, 364–370 (1999).
[CrossRef]

H. Ito, K. Sakaki, T. Nakata, W. Jhe, M. Ohtsu, “Optical potential for atom guidance in a cylindrical-core hollow fiber,” Opt. Commun. 115, 57–64 (1995).
[CrossRef]

H. Ito, K. Sakaki, T. Nakata, W. Jhe, M. Ohtsu, “Optical guidance of neutral atoms using evanescent waves in a cylindrical-core hollow fiber: theoretical approach,” Ultramicroscopy 61, 91–97 (1995).
[CrossRef]

Kim, G. Y.

S. Choi, K. Oh, W. Shin, C. S. Park, U. C. Paek, K. J. Park, Y. C. Chung, G. Y. Kim, Y. G. Lee, “Novel mode converter based on hollow optical fiber for gigabit LAN communication,” IEEE Photonics Technol. Lett. 14, 248–250 (2002).
[CrossRef]

Kim, J.-A.

S. H. Yoo, C. Won, J.-A. Kim, K. Kim, U. Shim, K. Oh, U.-C. Paek, W. Jhe, “Diffracted near field of hollow optical fibre for a novel atomic funnel,” J. Opt. B: Quantum Semiclassical Opt. 1, 364–370 (1999).
[CrossRef]

Kim, J.-W.

Kim, K.

S. H. Yoo, C. Won, J.-A. Kim, K. Kim, U. Shim, K. Oh, U.-C. Paek, W. Jhe, “Diffracted near field of hollow optical fibre for a novel atomic funnel,” J. Opt. B: Quantum Semiclassical Opt. 1, 364–370 (1999).
[CrossRef]

Lee, B. H.

S. Choi, T. J. Eom, J. W. Yu, B. H. Lee, K. Oh, “Novel all-fiber bandpass filter based on hollow optical fiber,” IEEE Photonics Technol. Lett. 14, 1701–1703 (2002).
[CrossRef]

Lee, Y. G.

S. Choi, K. Oh, W. Shin, C. S. Park, U. C. Paek, K. J. Park, Y. C. Chung, G. Y. Kim, Y. G. Lee, “Novel mode converter based on hollow optical fiber for gigabit LAN communication,” IEEE Photonics Technol. Lett. 14, 248–250 (2002).
[CrossRef]

Leitner, M.

M. Wrage, P. Glas, D. Fischer, M. Leitner, N. N. Elkin, D. V. Vysotsky, A. P. Napartovich, V. N. Troshchieva, “Phase-locking of a multicore fiber laser by wave propagation through an annular waveguide,” Opt. Commun. 205, 367–375 (2002).
[CrossRef]

Lessard, R. A.

P. K. Choudhury, R. A. Lessard, “An estimation of power transmission through a doubly clad optical fiber with an annular core,” Microwave Opt. Technol. Lett. 29, 402–405 (2001).
[CrossRef]

Liu, N.

Y. Ni, N. Liu, J. Yin, “Diffracted field distributions from the HE11 mode in a hollow optical fibre for an atomic funnel,” J. Opt. B: Quantum Semiclassical Opt. 5, 300–308 (2003).
[CrossRef]

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory, 1st ed. (Chapman & Hall, London, 1983).

Lu, C.

P. R. Chaudhuri, C. Lu, W. Xiaoyan, “Scalar model and exact vectorial description for the design analysis of hollow optical fiber components,” Opt. Commun. 228, 285–293 (2003).
[CrossRef]

Marcou, J.

J. Marcou, S. Février, “Comments on ‘On the analysis of a weakly guiding doubly clad dielectric optical fiber with an annular core’,” Microwave Opt. Technol. Lett. 38, 249–254 (2003).
[CrossRef]

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides, 1st ed. (Academic, New York, 1974).

Nakata, T.

H. Ito, K. Sakaki, T. Nakata, W. Jhe, M. Ohtsu, “Optical guidance of neutral atoms using evanescent waves in a cylindrical-core hollow fiber: theoretical approach,” Ultramicroscopy 61, 91–97 (1995).
[CrossRef]

H. Ito, K. Sakaki, T. Nakata, W. Jhe, M. Ohtsu, “Optical potential for atom guidance in a cylindrical-core hollow fiber,” Opt. Commun. 115, 57–64 (1995).
[CrossRef]

Napartovich, A. P.

A. P. Napartovich, D. V. Vysotsky, “Phase-locking of multicore fibre laser due to Talbot self-reproduction,” J. Mod. Opt. 50, 2715–2725 (2003).
[CrossRef]

M. Wrage, P. Glas, D. Fischer, M. Leitner, N. N. Elkin, D. V. Vysotsky, A. P. Napartovich, V. N. Troshchieva, “Phase-locking of a multicore fiber laser by wave propagation through an annular waveguide,” Opt. Commun. 205, 367–375 (2002).
[CrossRef]

Naumann, M.

P. Glas, M. Naumann, A. Schirrmacher, Th. Pertsch, “A neodymium doped hollow optical fiber laser for applications in sensing and laser guided atoms,” Opt. Commun. 166, 71–78 (1999).
[CrossRef]

P. Glas, M. Naumann, A. Schirrmacher, S. Unger, Th. Pertsch, “Short-length 10-W cw neodymium-doped M-profile fiber laser,” Appl. Opt. 37, 8434–8437 (1998).
[CrossRef]

Neves, I. V.

I. V. Neves, A. S. C. Fernandes, “Modal characteristics for W-type and M-type dielectric profile fibers,” Microwave Opt. Technol. Lett. 22, 398–405 (1999).
[CrossRef]

I. V. Neves, A. S. C. Fernandes, “Modal characteristics for A-type and V-type dielectric profile fibers,” Microwave Opt. Technol. Lett. 16, 164–169 (1997).
[CrossRef]

Ni, Y.

Y. Ni, N. Liu, J. Yin, “Diffracted field distributions from the HE11 mode in a hollow optical fibre for an atomic funnel,” J. Opt. B: Quantum Semiclassical Opt. 5, 300–308 (2003).
[CrossRef]

Noh, H. -R.

H. -R. Noh, W. Jhe, “Atom optics with hollow optical systems,” Phys. Rep. 372, 269–317 (2002).
[CrossRef]

Noh, H.-R.

Nürenberg, A.

A. Nürenberg, G. Schweiger, “Excitation and recording of morphology-dependent resonances in spherical micro- resonators by hollow light guiding fibers,” Appl. Phys. Lett. 84, 2043–2045 (2004).
[CrossRef]

Oh, K.

S. Choi, K. Oh, “A new LP02 mode dispersion compensation scheme based on mode converter using hollow optical fiber,” Opt. Commun. 221, 307–312 (2003).
[CrossRef]

S. Choi, T. J. Eom, J. W. Yu, B. H. Lee, K. Oh, “Novel all-fiber bandpass filter based on hollow optical fiber,” IEEE Photonics Technol. Lett. 14, 1701–1703 (2002).
[CrossRef]

S. Choi, K. Oh, W. Shin, C. S. Park, U. C. Paek, K. J. Park, Y. C. Chung, G. Y. Kim, Y. G. Lee, “Novel mode converter based on hollow optical fiber for gigabit LAN communication,” IEEE Photonics Technol. Lett. 14, 248–250 (2002).
[CrossRef]

S. H. Yoo, C. Won, J.-A. Kim, K. Kim, U. Shim, K. Oh, U.-C. Paek, W. Jhe, “Diffracted near field of hollow optical fibre for a novel atomic funnel,” J. Opt. B: Quantum Semiclassical Opt. 1, 364–370 (1999).
[CrossRef]

Ohtsu, M.

H. Ito, K. Sakaki, T. Nakata, W. Jhe, M. Ohtsu, “Optical potential for atom guidance in a cylindrical-core hollow fiber,” Opt. Commun. 115, 57–64 (1995).
[CrossRef]

H. Ito, K. Sakaki, T. Nakata, W. Jhe, M. Ohtsu, “Optical guidance of neutral atoms using evanescent waves in a cylindrical-core hollow fiber: theoretical approach,” Ultramicroscopy 61, 91–97 (1995).
[CrossRef]

Paek, U. C.

S. Choi, K. Oh, W. Shin, C. S. Park, U. C. Paek, K. J. Park, Y. C. Chung, G. Y. Kim, Y. G. Lee, “Novel mode converter based on hollow optical fiber for gigabit LAN communication,” IEEE Photonics Technol. Lett. 14, 248–250 (2002).
[CrossRef]

Paek, U.-C.

S. H. Yoo, C. Won, J.-A. Kim, K. Kim, U. Shim, K. Oh, U.-C. Paek, W. Jhe, “Diffracted near field of hollow optical fibre for a novel atomic funnel,” J. Opt. B: Quantum Semiclassical Opt. 1, 364–370 (1999).
[CrossRef]

Park, C. S.

S. Choi, K. Oh, W. Shin, C. S. Park, U. C. Paek, K. J. Park, Y. C. Chung, G. Y. Kim, Y. G. Lee, “Novel mode converter based on hollow optical fiber for gigabit LAN communication,” IEEE Photonics Technol. Lett. 14, 248–250 (2002).
[CrossRef]

Park, K. J.

S. Choi, K. Oh, W. Shin, C. S. Park, U. C. Paek, K. J. Park, Y. C. Chung, G. Y. Kim, Y. G. Lee, “Novel mode converter based on hollow optical fiber for gigabit LAN communication,” IEEE Photonics Technol. Lett. 14, 248–250 (2002).
[CrossRef]

Payne, D. N.

Pertsch, Th.

P. Glas, M. Naumann, A. Schirrmacher, Th. Pertsch, “A neodymium doped hollow optical fiber laser for applications in sensing and laser guided atoms,” Opt. Commun. 166, 71–78 (1999).
[CrossRef]

P. Glas, M. Naumann, A. Schirrmacher, S. Unger, Th. Pertsch, “Short-length 10-W cw neodymium-doped M-profile fiber laser,” Appl. Opt. 37, 8434–8437 (1998).
[CrossRef]

Sakaki, K.

H. Ito, K. Sakaki, T. Nakata, W. Jhe, M. Ohtsu, “Optical guidance of neutral atoms using evanescent waves in a cylindrical-core hollow fiber: theoretical approach,” Ultramicroscopy 61, 91–97 (1995).
[CrossRef]

H. Ito, K. Sakaki, T. Nakata, W. Jhe, M. Ohtsu, “Optical potential for atom guidance in a cylindrical-core hollow fiber,” Opt. Commun. 115, 57–64 (1995).
[CrossRef]

Sarkar, B. C.

B. C. Sarkar, P. K. Choudhury, T. Yoshino, “On the analysis of a weakly guiding doubly clad dielectric optical fiber with an annular core,” Microwave Opt. Technol. Lett. 31, 435–439 (2001).
[CrossRef]

Schirrmacher, A.

P. Glas, M. Naumann, A. Schirrmacher, Th. Pertsch, “A neodymium doped hollow optical fiber laser for applications in sensing and laser guided atoms,” Opt. Commun. 166, 71–78 (1999).
[CrossRef]

P. Glas, M. Naumann, A. Schirrmacher, S. Unger, Th. Pertsch, “Short-length 10-W cw neodymium-doped M-profile fiber laser,” Appl. Opt. 37, 8434–8437 (1998).
[CrossRef]

Schweiger, G.

A. Nürenberg, G. Schweiger, “Excitation and recording of morphology-dependent resonances in spherical micro- resonators by hollow light guiding fibers,” Appl. Phys. Lett. 84, 2043–2045 (2004).
[CrossRef]

Shim, U.

S. H. Yoo, C. Won, J.-A. Kim, K. Kim, U. Shim, K. Oh, U.-C. Paek, W. Jhe, “Diffracted near field of hollow optical fibre for a novel atomic funnel,” J. Opt. B: Quantum Semiclassical Opt. 1, 364–370 (1999).
[CrossRef]

Shim, W.

Shin, W.

S. Choi, K. Oh, W. Shin, C. S. Park, U. C. Paek, K. J. Park, Y. C. Chung, G. Y. Kim, Y. G. Lee, “Novel mode converter based on hollow optical fiber for gigabit LAN communication,” IEEE Photonics Technol. Lett. 14, 248–250 (2002).
[CrossRef]

Shin, Y.-I.

Snyder, A. W.

A. W. Snyder, J. D. Love, Optical Waveguide Theory, 1st ed. (Chapman & Hall, London, 1983).

Tierney, D.

R. G. Dall, M. D. Hoogerland, D. Tierney, K. G. H. Baldwin, S. J. Buckman, “Single-mode hollow optical fibres for atom guiding,” Appl. Phys. B: Lasers Opt. 74, 11–18 (2002).
[CrossRef]

Troshchieva, V. N.

M. Wrage, P. Glas, D. Fischer, M. Leitner, N. N. Elkin, D. V. Vysotsky, A. P. Napartovich, V. N. Troshchieva, “Phase-locking of a multicore fiber laser by wave propagation through an annular waveguide,” Opt. Commun. 205, 367–375 (2002).
[CrossRef]

Tsao, C. Y. H.

Unger, S.

Vysotsky, D. V.

A. P. Napartovich, D. V. Vysotsky, “Phase-locking of multicore fibre laser due to Talbot self-reproduction,” J. Mod. Opt. 50, 2715–2725 (2003).
[CrossRef]

M. Wrage, P. Glas, D. Fischer, M. Leitner, N. N. Elkin, D. V. Vysotsky, A. P. Napartovich, V. N. Troshchieva, “Phase-locking of a multicore fiber laser by wave propagation through an annular waveguide,” Opt. Commun. 205, 367–375 (2002).
[CrossRef]

Weber, H. J.

G. B. Arfken, H. J. Weber, Mathematical Methods for Physicists, 4th ed. (Academic, San Diego, Calif., 1995).

Won, C.

S. H. Yoo, C. Won, J.-A. Kim, K. Kim, U. Shim, K. Oh, U.-C. Paek, W. Jhe, “Diffracted near field of hollow optical fibre for a novel atomic funnel,” J. Opt. B: Quantum Semiclassical Opt. 1, 364–370 (1999).
[CrossRef]

Wrage, M.

M. Wrage, P. Glas, D. Fischer, M. Leitner, N. N. Elkin, D. V. Vysotsky, A. P. Napartovich, V. N. Troshchieva, “Phase-locking of a multicore fiber laser by wave propagation through an annular waveguide,” Opt. Commun. 205, 367–375 (2002).
[CrossRef]

Xiaoyan, W.

P. R. Chaudhuri, C. Lu, W. Xiaoyan, “Scalar model and exact vectorial description for the design analysis of hollow optical fiber components,” Opt. Commun. 228, 285–293 (2003).
[CrossRef]

Yin, J.

Y. Ni, N. Liu, J. Yin, “Diffracted field distributions from the HE11 mode in a hollow optical fibre for an atomic funnel,” J. Opt. B: Quantum Semiclassical Opt. 5, 300–308 (2003).
[CrossRef]

Yoo, S. H.

S. H. Yoo, C. Won, J.-A. Kim, K. Kim, U. Shim, K. Oh, U.-C. Paek, W. Jhe, “Diffracted near field of hollow optical fibre for a novel atomic funnel,” J. Opt. B: Quantum Semiclassical Opt. 1, 364–370 (1999).
[CrossRef]

Yoshino, T.

B. C. Sarkar, P. K. Choudhury, T. Yoshino, “On the analysis of a weakly guiding doubly clad dielectric optical fiber with an annular core,” Microwave Opt. Technol. Lett. 31, 435–439 (2001).
[CrossRef]

Yu, J. W.

S. Choi, T. J. Eom, J. W. Yu, B. H. Lee, K. Oh, “Novel all-fiber bandpass filter based on hollow optical fiber,” IEEE Photonics Technol. Lett. 14, 1701–1703 (2002).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. B: Lasers Opt. (1)

R. G. Dall, M. D. Hoogerland, D. Tierney, K. G. H. Baldwin, S. J. Buckman, “Single-mode hollow optical fibres for atom guiding,” Appl. Phys. B: Lasers Opt. 74, 11–18 (2002).
[CrossRef]

Appl. Phys. Lett. (1)

A. Nürenberg, G. Schweiger, “Excitation and recording of morphology-dependent resonances in spherical micro- resonators by hollow light guiding fibers,” Appl. Phys. Lett. 84, 2043–2045 (2004).
[CrossRef]

IEEE Photonics Technol. Lett. (2)

S. Choi, T. J. Eom, J. W. Yu, B. H. Lee, K. Oh, “Novel all-fiber bandpass filter based on hollow optical fiber,” IEEE Photonics Technol. Lett. 14, 1701–1703 (2002).
[CrossRef]

S. Choi, K. Oh, W. Shin, C. S. Park, U. C. Paek, K. J. Park, Y. C. Chung, G. Y. Kim, Y. G. Lee, “Novel mode converter based on hollow optical fiber for gigabit LAN communication,” IEEE Photonics Technol. Lett. 14, 248–250 (2002).
[CrossRef]

J. Mod. Opt. (1)

A. P. Napartovich, D. V. Vysotsky, “Phase-locking of multicore fibre laser due to Talbot self-reproduction,” J. Mod. Opt. 50, 2715–2725 (2003).
[CrossRef]

J. Opt. B: Quantum Semiclassical Opt. (2)

Y. Ni, N. Liu, J. Yin, “Diffracted field distributions from the HE11 mode in a hollow optical fibre for an atomic funnel,” J. Opt. B: Quantum Semiclassical Opt. 5, 300–308 (2003).
[CrossRef]

S. H. Yoo, C. Won, J.-A. Kim, K. Kim, U. Shim, K. Oh, U.-C. Paek, W. Jhe, “Diffracted near field of hollow optical fibre for a novel atomic funnel,” J. Opt. B: Quantum Semiclassical Opt. 1, 364–370 (1999).
[CrossRef]

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

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

Microwave Opt. Technol. Lett. (5)

B. C. Sarkar, P. K. Choudhury, T. Yoshino, “On the analysis of a weakly guiding doubly clad dielectric optical fiber with an annular core,” Microwave Opt. Technol. Lett. 31, 435–439 (2001).
[CrossRef]

J. Marcou, S. Février, “Comments on ‘On the analysis of a weakly guiding doubly clad dielectric optical fiber with an annular core’,” Microwave Opt. Technol. Lett. 38, 249–254 (2003).
[CrossRef]

P. K. Choudhury, R. A. Lessard, “An estimation of power transmission through a doubly clad optical fiber with an annular core,” Microwave Opt. Technol. Lett. 29, 402–405 (2001).
[CrossRef]

I. V. Neves, A. S. C. Fernandes, “Modal characteristics for A-type and V-type dielectric profile fibers,” Microwave Opt. Technol. Lett. 16, 164–169 (1997).
[CrossRef]

I. V. Neves, A. S. C. Fernandes, “Modal characteristics for W-type and M-type dielectric profile fibers,” Microwave Opt. Technol. Lett. 22, 398–405 (1999).
[CrossRef]

Opt. Commun. (5)

H. Ito, K. Sakaki, T. Nakata, W. Jhe, M. Ohtsu, “Optical potential for atom guidance in a cylindrical-core hollow fiber,” Opt. Commun. 115, 57–64 (1995).
[CrossRef]

M. Wrage, P. Glas, D. Fischer, M. Leitner, N. N. Elkin, D. V. Vysotsky, A. P. Napartovich, V. N. Troshchieva, “Phase-locking of a multicore fiber laser by wave propagation through an annular waveguide,” Opt. Commun. 205, 367–375 (2002).
[CrossRef]

P. R. Chaudhuri, C. Lu, W. Xiaoyan, “Scalar model and exact vectorial description for the design analysis of hollow optical fiber components,” Opt. Commun. 228, 285–293 (2003).
[CrossRef]

P. Glas, M. Naumann, A. Schirrmacher, Th. Pertsch, “A neodymium doped hollow optical fiber laser for applications in sensing and laser guided atoms,” Opt. Commun. 166, 71–78 (1999).
[CrossRef]

S. Choi, K. Oh, “A new LP02 mode dispersion compensation scheme based on mode converter using hollow optical fiber,” Opt. Commun. 221, 307–312 (2003).
[CrossRef]

Phys. Rep. (1)

H. -R. Noh, W. Jhe, “Atom optics with hollow optical systems,” Phys. Rep. 372, 269–317 (2002).
[CrossRef]

Ultramicroscopy (1)

H. Ito, K. Sakaki, T. Nakata, W. Jhe, M. Ohtsu, “Optical guidance of neutral atoms using evanescent waves in a cylindrical-core hollow fiber: theoretical approach,” Ultramicroscopy 61, 91–97 (1995).
[CrossRef]

Other (3)

A. W. Snyder, J. D. Love, Optical Waveguide Theory, 1st ed. (Chapman & Hall, London, 1983).

D. Marcuse, Theory of Dielectric Optical Waveguides, 1st ed. (Academic, New York, 1974).

G. B. Arfken, H. J. Weber, Mathematical Methods for Physicists, 4th ed. (Academic, San Diego, Calif., 1995).

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Figures (5)

Fig. 1
Fig. 1

(a) Schematic cross section of an M-type fiber, as defined here, with an inner and outer radius a and b of the core, respectively. Below are shown the refractive-index profiles of an annular-core fiber (ACF) and a hollow optical fiber (HOF) for which the inner claddings have the refractive index of that of the outer cladding (of infinite extent) and of vacuum, respectively. The step-index profile of a conventional optical fiber can be obtained on taking the limit a 0 . (b) Transverse intensity profiles of the two lowest-order LP m , p modes calculated for a = 2 μ m , b = 6 μ m , n 1 = 1.46 , n 2 = 1.45 , and wavelength λ = 1.55 μ m .

Fig. 2
Fig. 2

Effect of the inner radius of the core on the polarization and amplitude of the fundamental mode. The fiber parameters are Δ n 1 , 2 = 1.00 % and b = 10 μ m and the wavelength is λ = 780 nm . The core boundaries are shown by dashed circles. (a) HE 1 , 1 or LP 0 , 1 mode in a conventional step-index fiber. (b) HE 1 , 1 mode in an HOF with an inner radius of a = 8 μ m . (c) LP 0 , 1 mode of the fiber in Fig. 2b calculated by use of the WGA.

Fig. 3
Fig. 3

Accuracy W 2 of the WGA in describing the HE 1 , 1 mode (a) in an ACF at λ = 1.55 μ m and (b) in an HOF at λ = 780 nm with n 2 = 1.45 as a function of the inner radius a of the core. Three different outer radii b of the core, denoted by vertical dotted lines, are considered in both plots. The curves correspond to refractive-index differences increasing from top to down, as indicated.

Fig. 4
Fig. 4

Correspondence between LP 1 , 1 mode with the superposition of odd HE 2 , 1 and TE 0 , 1 (solid curves) and even HE 2 , 1 and TM 0 , 1 (dashed curves) modes in terms of the quantity W 2 as a function of the inner radius a of the core. The different outer radii b of the core, the wavelengths, and the refractive indices are as in Fig. 3. Second-order modes do not exist for b = 3 μ m with Δ n 1 , 2 = 0.25 % ; thus only three pairs of curves are given.

Fig. 5
Fig. 5

Ratio of cutoff wavelengths λ ̃ c (WGA) and λ c (exact) of the fundamental mode as a function of the refractive index n 0 of the inner cladding for different ratios between the inner and outer radii, a and b, respectively, of the core. The fixed refractive indices are n 1 = 1.4525 and n 2 = 1.45 .

Equations (18)

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F ( r , θ ) = { C 1 I l ( v r ) sin ( l θ + ϕ ) , r a [ C 2 J l ( u r ) + C 3 N l ( u r ) ] sin ( l θ + ϕ ) , a < r < b C 4 K l ( w r ) sin ( l θ + ϕ ) , b r .
E t ( r , θ ) = i β 2 k 2 n j 2 [ β t E z ( r , θ ) μ j ω u z × t H z ( r , θ ) ] ,
H t ( r , θ ) = i β 2 k 2 n j 2 [ β t H z ( r , θ ) + ϵ j ω u z × t E z ( r , θ ) ] ,
E r ( r , θ ) = E r ( r ) sin ( l θ + ϕ ) ,
E θ ( r , θ ) = E θ ( r ) cos ( l θ + ϕ ) ,
H r ( r , θ ) = H r ( r ) cos ( l θ + ϕ ) ,
H θ ( r , θ ) = H θ ( r ) sin ( l θ + ϕ ) .
A = [ I l ( v a ) J l ( u a ) N l ( u a ) 0 0 0 0 0 l β a v 2 I l ( v a ) l β a u 2 J l ( u a ) l β a u 2 N l ( u a ) 0 ω μ v I l ( v a ) ω μ u J l ( u a ) ω μ u N l ( u a ) 0 0 0 0 0 I l ( v a ) J l ( u a ) N l ( u a ) 0 ω ϵ 0 v I l ( v a ) ω ϵ 0 u J l ( u a ) ω ϵ 0 u N l ( u a ) 0 l β a v 2 I l ( v a ) l β a u 2 J l ( u a ) l β a u 2 N l ( u a ) 0 0 J l ( u b ) N l ( u a ) K l ( w b ) 0 0 0 0 0 l β b u 2 J l ( u b ) l β b u 2 N l ( u b ) l β b w 2 K l ( w b ) 0 ω μ u J l ( u b ) ω μ u N l ( u b ) ω μ w K l ( w b ) 0 0 0 0 0 J l ( u b ) N l ( u b ) K l ( w b ) 0 ω ϵ 1 u J l ( u b ) ω ϵ 1 u N l ( u b ) ω ϵ 2 w K l ( w b ) 0 l β b u 2 J l ( u b ) l β b u 2 N l ( u b ) l β b w 2 K l ( w b ) ] .
v ̃ I m ( v ̃ a ) I m ( v ̃ a ) u ̃ C ̃ 2 J m ( u ̃ a ) + u ̃ C ̃ 3 N m ( u ̃ a ) C ̃ 2 J m ( u ̃ a ) + C ̃ 3 N m ( u ̃ a ) = 0 ,
w ̃ K m ( w ̃ b ) K m ( w ̃ b ) u ̃ C ̃ 2 J m ( u ̃ b ) + u ̃ C ̃ 3 N m ( u ̃ b ) C ̃ 2 J m ( u ̃ b ) + C ̃ 3 N m ( u ̃ b ) = 0 .
E ̃ x ( r , θ ) E r ( r ) sin [ ( m 1 ) θ ] cos θ E θ ( r ) cos [ ( m 1 ) θ ] sin θ + E r + ( r ) sin [ ( m + 1 ) θ ] cos θ E θ + ( r ) cos [ ( m + 1 ) θ ] sin θ ,
E ̃ y ( r , θ ) E r ( r ) sin [ ( m 1 ) θ ] sin θ + E θ ( r ) cos [ ( m 1 ) θ ] cos θ + E r + ( r ) sin [ ( m + 1 ) θ ] sin θ + E θ + ( r ) cos [ ( m + 1 ) θ ] cos θ ,
E ̃ y ( r , θ ) = 2 E ̂ ( r ) sin ( m θ + π 2 ) ,
W = 0 0 2 π [ E ( r , θ ) + E + ( r , θ ) ] * E ̃ ( r , θ ) r d r d θ ,
{ [ 1 u N l ( u a ) + 1 v I l ( v a ) I l ( v a ) N l ( u a ) ] J l ( u b ) [ 1 u J l ( u a ) + 1 v I l ( v a ) I l ( v a ) J l ( u a ) ] N l ( u b ) } { [ n 1 2 u N l ( u a ) + n 0 2 v I l ( v a ) I l ( v a ) N l ( u a ) ] J l ( u b ) [ n 1 2 u J l ( u a ) + n 0 2 v I l ( v a ) I l ( v a ) J l ( u a ) ] N l ( u b ) } ( n 2 l a ) 2 ( 1 u 2 + 1 v 2 ) 2
[ J l ( u a ) N l ( u b ) J l ( u b ) N l ( u a ) ] 2 = 0 .
[ 1 u ̃ N m ( u ̃ a ) + 1 v ̃ I m ( v ̃ a ) I m 1 ( v ̃ a ) N m 1 ( u ̃ a ) ] J m 1 ( u ̃ b ) [ 1 u ̃ J m ( u ̃ a ) + 1 v ̃ I m ( v ̃ a ) I m 1 ( v ̃ a ) J m 1 ( u ̃ a ) ] N m 1 ( u ̃ b ) = 0 .
n 0 , c [ n 1 2 ( b a ) 2 ( n 1 2 n 2 2 ) ] 1 2 ,

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