Abstract

Microstructured or “air-clad” fibers, with air holes surrounding a large core, have recently demonstrated much wider light-acceptance angles than conventional fibers. An original and accurate method is presented for determining the numerical aperture of such fibers using leaky modes. The dependence on length, wavelength, and various microstructure dimensions are evaluated for the first time for a class of fibers that exhibit exceptionally high numerical apertures. These results show excellent agreement with published measurements on similar fibers and verify that bridge thicknesses much smaller than the wavelength are required for high numerical apertures.

© 2004 Optical Society of America

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References

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  1. C. P. Achenbach, J. H. Cobb, “Computational studies of light acceptance and propagation in straight and curved multimode active fibers,” J. Opt. A 5, 239–249 (2003).
    [CrossRef]
  2. E. Mediavilla, S. Arribas, F. Watson, Fiber Optics in Astronomy (Astronomical Society of the Pacific, San Francisco, Calif., 1998), Vol. 3.
  3. J. K. Sahu, C. C. Renaud, K. Furusawa, R. Selvas, J. A. Alvarez-Chavez, D. J. Richardson, J. Nilsson, “Jacketed air-clad cladding pumped ytterbium-doped fiber laser with wide tuning range,” Electron. Lett. 37, 1116–1117 (2001).
    [CrossRef]
  4. N. A. Mortensen, M. Stach, J. Broeng, A. Petersson, H. R. Simonsen, R. Michalzik, “Multi-mode photonic crystal fibers for VCSEL based data transmission,” Opt. Express 11, 1953–1959 (2003).
    [CrossRef] [PubMed]
  5. D. Feuermann, J. M. Gordon, M. Huleihil, “Light leakage in optical fibers: experimental results, modeling and the consequences for solar collectors,” Solar Energy 72, 195–204 (2002).
    [CrossRef]
  6. W. J. Wadsworth, R. M. Percival, G. Bouwmans, J. C. Knight, P. St. J. Russell, “High power air-clad photonic crystal fiber laser,” Opt. Express 11, 48–53 (2003).
    [CrossRef] [PubMed]
  7. G. Bouwmans, R. M. Percival, W. J. Wadsworth, J. C. Knight, P. St. J. Russell, “High-power Er:Yb fiber laser with very high numerical aperture pump-cladding waveguide,” Appl. Phys. Lett. 83, 817–818 (2003).
    [CrossRef]
  8. W. J. Wadsworth, R. M. Percival, G. Bouwmans, J. C. Knight, T. A. Birks, T. D. Hedley, P. St. J. Russell, “Very high numerical aperture fibers,” IEEE Photon. Technol. Lett. 16, 843–845 (2004).
    [CrossRef]
  9. K. Furusawa, A. Malinowski, J. H. V. Price, T. M. Monro, J. K. Sahu, J. Nilsson, D. J. Richardson, “Cladding pumped ytterbium-doped fiber laser with holey inner and outer cladding,” Opt. Express 9, 714–720 (2001).
    [CrossRef] [PubMed]
  10. J. Limpert, T. Schreiber, A. Liem, S. Nolte, H. Zellmer, T. Peschel, V. Guyenot, A. Tünnermann, “Thermo-optical properties of air-clad photonic crystal fiber lasers in high power operation,” Opt. Express. 11, 2982–2990 (2003).
    [CrossRef] [PubMed]
  11. E. A. J. Marcatili, “Air clad optical fiber waveguide,” U.S. patent3,712,705 (23January1973).
  12. R. J. Potter, “Transmission properties of optical fibers,” J. Opt. Soc. Am. 51, 1079–1089 (1961).
    [CrossRef]
  13. N. A. Mortensen, J. R. Folkenberg, P. M. W. Skovgaard, J. Broeng, “Numerical aperture of single-mode photonic crystal fibers,” IEEE Photon. Technol. Lett. 14, 1094–1096 (2002).
    [CrossRef]
  14. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman Hall, London, 1983), Chap. 24.
  15. R. Sammut, A. W. Snyder, “Leaky modes on a dielectric waveguide: orthogonality and excitation,” Appl. Opt. 15, 1040–1044 (1976).
    [CrossRef] [PubMed]
  16. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman Hall, London, 1983), Chaps. 4 and 20.
  17. J. A. Buck, “Fundamentals of optical fibers,” (Wiley, New York, 1995), pp. 49–51.
  18. R. L. Gallawa, “On the definition of fiber numerical aperture,” Electro-Opt. Syst. Des. 14, 46–54 (1982).
  19. N. A. Issa, L. Poladian, “Vector wave expansion method for leaky modes of microstructured optical fibers,” J. Lightwave Technol. 21, 1005–1012 (2003).
    [CrossRef]
  20. K. Sakoda, Optical Properties of Photonic Crystals (Springer, Berlin, 2001), pp. 21–23.
  21. E. Hecht, Optics, 3rd ed. (Addison-Wesley, Reading, Mass., 1998), pp. 419–420.

2004 (1)

W. J. Wadsworth, R. M. Percival, G. Bouwmans, J. C. Knight, T. A. Birks, T. D. Hedley, P. St. J. Russell, “Very high numerical aperture fibers,” IEEE Photon. Technol. Lett. 16, 843–845 (2004).
[CrossRef]

2003 (6)

J. Limpert, T. Schreiber, A. Liem, S. Nolte, H. Zellmer, T. Peschel, V. Guyenot, A. Tünnermann, “Thermo-optical properties of air-clad photonic crystal fiber lasers in high power operation,” Opt. Express. 11, 2982–2990 (2003).
[CrossRef] [PubMed]

C. P. Achenbach, J. H. Cobb, “Computational studies of light acceptance and propagation in straight and curved multimode active fibers,” J. Opt. A 5, 239–249 (2003).
[CrossRef]

G. Bouwmans, R. M. Percival, W. J. Wadsworth, J. C. Knight, P. St. J. Russell, “High-power Er:Yb fiber laser with very high numerical aperture pump-cladding waveguide,” Appl. Phys. Lett. 83, 817–818 (2003).
[CrossRef]

W. J. Wadsworth, R. M. Percival, G. Bouwmans, J. C. Knight, P. St. J. Russell, “High power air-clad photonic crystal fiber laser,” Opt. Express 11, 48–53 (2003).
[CrossRef] [PubMed]

N. A. Issa, L. Poladian, “Vector wave expansion method for leaky modes of microstructured optical fibers,” J. Lightwave Technol. 21, 1005–1012 (2003).
[CrossRef]

N. A. Mortensen, M. Stach, J. Broeng, A. Petersson, H. R. Simonsen, R. Michalzik, “Multi-mode photonic crystal fibers for VCSEL based data transmission,” Opt. Express 11, 1953–1959 (2003).
[CrossRef] [PubMed]

2002 (2)

D. Feuermann, J. M. Gordon, M. Huleihil, “Light leakage in optical fibers: experimental results, modeling and the consequences for solar collectors,” Solar Energy 72, 195–204 (2002).
[CrossRef]

N. A. Mortensen, J. R. Folkenberg, P. M. W. Skovgaard, J. Broeng, “Numerical aperture of single-mode photonic crystal fibers,” IEEE Photon. Technol. Lett. 14, 1094–1096 (2002).
[CrossRef]

2001 (2)

J. K. Sahu, C. C. Renaud, K. Furusawa, R. Selvas, J. A. Alvarez-Chavez, D. J. Richardson, J. Nilsson, “Jacketed air-clad cladding pumped ytterbium-doped fiber laser with wide tuning range,” Electron. Lett. 37, 1116–1117 (2001).
[CrossRef]

K. Furusawa, A. Malinowski, J. H. V. Price, T. M. Monro, J. K. Sahu, J. Nilsson, D. J. Richardson, “Cladding pumped ytterbium-doped fiber laser with holey inner and outer cladding,” Opt. Express 9, 714–720 (2001).
[CrossRef] [PubMed]

1982 (1)

R. L. Gallawa, “On the definition of fiber numerical aperture,” Electro-Opt. Syst. Des. 14, 46–54 (1982).

1976 (1)

1961 (1)

Achenbach, C. P.

C. P. Achenbach, J. H. Cobb, “Computational studies of light acceptance and propagation in straight and curved multimode active fibers,” J. Opt. A 5, 239–249 (2003).
[CrossRef]

Alvarez-Chavez, J. A.

J. K. Sahu, C. C. Renaud, K. Furusawa, R. Selvas, J. A. Alvarez-Chavez, D. J. Richardson, J. Nilsson, “Jacketed air-clad cladding pumped ytterbium-doped fiber laser with wide tuning range,” Electron. Lett. 37, 1116–1117 (2001).
[CrossRef]

Arribas, S.

E. Mediavilla, S. Arribas, F. Watson, Fiber Optics in Astronomy (Astronomical Society of the Pacific, San Francisco, Calif., 1998), Vol. 3.

Birks, T. A.

W. J. Wadsworth, R. M. Percival, G. Bouwmans, J. C. Knight, T. A. Birks, T. D. Hedley, P. St. J. Russell, “Very high numerical aperture fibers,” IEEE Photon. Technol. Lett. 16, 843–845 (2004).
[CrossRef]

Bouwmans, G.

W. J. Wadsworth, R. M. Percival, G. Bouwmans, J. C. Knight, T. A. Birks, T. D. Hedley, P. St. J. Russell, “Very high numerical aperture fibers,” IEEE Photon. Technol. Lett. 16, 843–845 (2004).
[CrossRef]

W. J. Wadsworth, R. M. Percival, G. Bouwmans, J. C. Knight, P. St. J. Russell, “High power air-clad photonic crystal fiber laser,” Opt. Express 11, 48–53 (2003).
[CrossRef] [PubMed]

G. Bouwmans, R. M. Percival, W. J. Wadsworth, J. C. Knight, P. St. J. Russell, “High-power Er:Yb fiber laser with very high numerical aperture pump-cladding waveguide,” Appl. Phys. Lett. 83, 817–818 (2003).
[CrossRef]

Broeng, J.

N. A. Mortensen, M. Stach, J. Broeng, A. Petersson, H. R. Simonsen, R. Michalzik, “Multi-mode photonic crystal fibers for VCSEL based data transmission,” Opt. Express 11, 1953–1959 (2003).
[CrossRef] [PubMed]

N. A. Mortensen, J. R. Folkenberg, P. M. W. Skovgaard, J. Broeng, “Numerical aperture of single-mode photonic crystal fibers,” IEEE Photon. Technol. Lett. 14, 1094–1096 (2002).
[CrossRef]

Buck, J. A.

J. A. Buck, “Fundamentals of optical fibers,” (Wiley, New York, 1995), pp. 49–51.

Cobb, J. H.

C. P. Achenbach, J. H. Cobb, “Computational studies of light acceptance and propagation in straight and curved multimode active fibers,” J. Opt. A 5, 239–249 (2003).
[CrossRef]

Feuermann, D.

D. Feuermann, J. M. Gordon, M. Huleihil, “Light leakage in optical fibers: experimental results, modeling and the consequences for solar collectors,” Solar Energy 72, 195–204 (2002).
[CrossRef]

Folkenberg, J. R.

N. A. Mortensen, J. R. Folkenberg, P. M. W. Skovgaard, J. Broeng, “Numerical aperture of single-mode photonic crystal fibers,” IEEE Photon. Technol. Lett. 14, 1094–1096 (2002).
[CrossRef]

Furusawa, K.

K. Furusawa, A. Malinowski, J. H. V. Price, T. M. Monro, J. K. Sahu, J. Nilsson, D. J. Richardson, “Cladding pumped ytterbium-doped fiber laser with holey inner and outer cladding,” Opt. Express 9, 714–720 (2001).
[CrossRef] [PubMed]

J. K. Sahu, C. C. Renaud, K. Furusawa, R. Selvas, J. A. Alvarez-Chavez, D. J. Richardson, J. Nilsson, “Jacketed air-clad cladding pumped ytterbium-doped fiber laser with wide tuning range,” Electron. Lett. 37, 1116–1117 (2001).
[CrossRef]

Gallawa, R. L.

R. L. Gallawa, “On the definition of fiber numerical aperture,” Electro-Opt. Syst. Des. 14, 46–54 (1982).

Gordon, J. M.

D. Feuermann, J. M. Gordon, M. Huleihil, “Light leakage in optical fibers: experimental results, modeling and the consequences for solar collectors,” Solar Energy 72, 195–204 (2002).
[CrossRef]

Guyenot, V.

J. Limpert, T. Schreiber, A. Liem, S. Nolte, H. Zellmer, T. Peschel, V. Guyenot, A. Tünnermann, “Thermo-optical properties of air-clad photonic crystal fiber lasers in high power operation,” Opt. Express. 11, 2982–2990 (2003).
[CrossRef] [PubMed]

Hecht, E.

E. Hecht, Optics, 3rd ed. (Addison-Wesley, Reading, Mass., 1998), pp. 419–420.

Hedley, T. D.

W. J. Wadsworth, R. M. Percival, G. Bouwmans, J. C. Knight, T. A. Birks, T. D. Hedley, P. St. J. Russell, “Very high numerical aperture fibers,” IEEE Photon. Technol. Lett. 16, 843–845 (2004).
[CrossRef]

Huleihil, M.

D. Feuermann, J. M. Gordon, M. Huleihil, “Light leakage in optical fibers: experimental results, modeling and the consequences for solar collectors,” Solar Energy 72, 195–204 (2002).
[CrossRef]

Issa, N. A.

Knight, J. C.

W. J. Wadsworth, R. M. Percival, G. Bouwmans, J. C. Knight, T. A. Birks, T. D. Hedley, P. St. J. Russell, “Very high numerical aperture fibers,” IEEE Photon. Technol. Lett. 16, 843–845 (2004).
[CrossRef]

W. J. Wadsworth, R. M. Percival, G. Bouwmans, J. C. Knight, P. St. J. Russell, “High power air-clad photonic crystal fiber laser,” Opt. Express 11, 48–53 (2003).
[CrossRef] [PubMed]

G. Bouwmans, R. M. Percival, W. J. Wadsworth, J. C. Knight, P. St. J. Russell, “High-power Er:Yb fiber laser with very high numerical aperture pump-cladding waveguide,” Appl. Phys. Lett. 83, 817–818 (2003).
[CrossRef]

Liem, A.

J. Limpert, T. Schreiber, A. Liem, S. Nolte, H. Zellmer, T. Peschel, V. Guyenot, A. Tünnermann, “Thermo-optical properties of air-clad photonic crystal fiber lasers in high power operation,” Opt. Express. 11, 2982–2990 (2003).
[CrossRef] [PubMed]

Limpert, J.

J. Limpert, T. Schreiber, A. Liem, S. Nolte, H. Zellmer, T. Peschel, V. Guyenot, A. Tünnermann, “Thermo-optical properties of air-clad photonic crystal fiber lasers in high power operation,” Opt. Express. 11, 2982–2990 (2003).
[CrossRef] [PubMed]

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman Hall, London, 1983), Chap. 24.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman Hall, London, 1983), Chaps. 4 and 20.

Malinowski, A.

Marcatili, E. A. J.

E. A. J. Marcatili, “Air clad optical fiber waveguide,” U.S. patent3,712,705 (23January1973).

Mediavilla, E.

E. Mediavilla, S. Arribas, F. Watson, Fiber Optics in Astronomy (Astronomical Society of the Pacific, San Francisco, Calif., 1998), Vol. 3.

Michalzik, R.

Monro, T. M.

Mortensen, N. A.

N. A. Mortensen, M. Stach, J. Broeng, A. Petersson, H. R. Simonsen, R. Michalzik, “Multi-mode photonic crystal fibers for VCSEL based data transmission,” Opt. Express 11, 1953–1959 (2003).
[CrossRef] [PubMed]

N. A. Mortensen, J. R. Folkenberg, P. M. W. Skovgaard, J. Broeng, “Numerical aperture of single-mode photonic crystal fibers,” IEEE Photon. Technol. Lett. 14, 1094–1096 (2002).
[CrossRef]

Nilsson, J.

K. Furusawa, A. Malinowski, J. H. V. Price, T. M. Monro, J. K. Sahu, J. Nilsson, D. J. Richardson, “Cladding pumped ytterbium-doped fiber laser with holey inner and outer cladding,” Opt. Express 9, 714–720 (2001).
[CrossRef] [PubMed]

J. K. Sahu, C. C. Renaud, K. Furusawa, R. Selvas, J. A. Alvarez-Chavez, D. J. Richardson, J. Nilsson, “Jacketed air-clad cladding pumped ytterbium-doped fiber laser with wide tuning range,” Electron. Lett. 37, 1116–1117 (2001).
[CrossRef]

Nolte, S.

J. Limpert, T. Schreiber, A. Liem, S. Nolte, H. Zellmer, T. Peschel, V. Guyenot, A. Tünnermann, “Thermo-optical properties of air-clad photonic crystal fiber lasers in high power operation,” Opt. Express. 11, 2982–2990 (2003).
[CrossRef] [PubMed]

Percival, R. M.

W. J. Wadsworth, R. M. Percival, G. Bouwmans, J. C. Knight, T. A. Birks, T. D. Hedley, P. St. J. Russell, “Very high numerical aperture fibers,” IEEE Photon. Technol. Lett. 16, 843–845 (2004).
[CrossRef]

W. J. Wadsworth, R. M. Percival, G. Bouwmans, J. C. Knight, P. St. J. Russell, “High power air-clad photonic crystal fiber laser,” Opt. Express 11, 48–53 (2003).
[CrossRef] [PubMed]

G. Bouwmans, R. M. Percival, W. J. Wadsworth, J. C. Knight, P. St. J. Russell, “High-power Er:Yb fiber laser with very high numerical aperture pump-cladding waveguide,” Appl. Phys. Lett. 83, 817–818 (2003).
[CrossRef]

Peschel, T.

J. Limpert, T. Schreiber, A. Liem, S. Nolte, H. Zellmer, T. Peschel, V. Guyenot, A. Tünnermann, “Thermo-optical properties of air-clad photonic crystal fiber lasers in high power operation,” Opt. Express. 11, 2982–2990 (2003).
[CrossRef] [PubMed]

Petersson, A.

Poladian, L.

Potter, R. J.

Price, J. H. V.

Renaud, C. C.

J. K. Sahu, C. C. Renaud, K. Furusawa, R. Selvas, J. A. Alvarez-Chavez, D. J. Richardson, J. Nilsson, “Jacketed air-clad cladding pumped ytterbium-doped fiber laser with wide tuning range,” Electron. Lett. 37, 1116–1117 (2001).
[CrossRef]

Richardson, D. J.

J. K. Sahu, C. C. Renaud, K. Furusawa, R. Selvas, J. A. Alvarez-Chavez, D. J. Richardson, J. Nilsson, “Jacketed air-clad cladding pumped ytterbium-doped fiber laser with wide tuning range,” Electron. Lett. 37, 1116–1117 (2001).
[CrossRef]

K. Furusawa, A. Malinowski, J. H. V. Price, T. M. Monro, J. K. Sahu, J. Nilsson, D. J. Richardson, “Cladding pumped ytterbium-doped fiber laser with holey inner and outer cladding,” Opt. Express 9, 714–720 (2001).
[CrossRef] [PubMed]

Sahu, J. K.

K. Furusawa, A. Malinowski, J. H. V. Price, T. M. Monro, J. K. Sahu, J. Nilsson, D. J. Richardson, “Cladding pumped ytterbium-doped fiber laser with holey inner and outer cladding,” Opt. Express 9, 714–720 (2001).
[CrossRef] [PubMed]

J. K. Sahu, C. C. Renaud, K. Furusawa, R. Selvas, J. A. Alvarez-Chavez, D. J. Richardson, J. Nilsson, “Jacketed air-clad cladding pumped ytterbium-doped fiber laser with wide tuning range,” Electron. Lett. 37, 1116–1117 (2001).
[CrossRef]

Sakoda, K.

K. Sakoda, Optical Properties of Photonic Crystals (Springer, Berlin, 2001), pp. 21–23.

Sammut, R.

Schreiber, T.

J. Limpert, T. Schreiber, A. Liem, S. Nolte, H. Zellmer, T. Peschel, V. Guyenot, A. Tünnermann, “Thermo-optical properties of air-clad photonic crystal fiber lasers in high power operation,” Opt. Express. 11, 2982–2990 (2003).
[CrossRef] [PubMed]

Selvas, R.

J. K. Sahu, C. C. Renaud, K. Furusawa, R. Selvas, J. A. Alvarez-Chavez, D. J. Richardson, J. Nilsson, “Jacketed air-clad cladding pumped ytterbium-doped fiber laser with wide tuning range,” Electron. Lett. 37, 1116–1117 (2001).
[CrossRef]

Simonsen, H. R.

Skovgaard, P. M. W.

N. A. Mortensen, J. R. Folkenberg, P. M. W. Skovgaard, J. Broeng, “Numerical aperture of single-mode photonic crystal fibers,” IEEE Photon. Technol. Lett. 14, 1094–1096 (2002).
[CrossRef]

Snyder, A. W.

R. Sammut, A. W. Snyder, “Leaky modes on a dielectric waveguide: orthogonality and excitation,” Appl. Opt. 15, 1040–1044 (1976).
[CrossRef] [PubMed]

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman Hall, London, 1983), Chaps. 4 and 20.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman Hall, London, 1983), Chap. 24.

St. J. Russell, P.

W. J. Wadsworth, R. M. Percival, G. Bouwmans, J. C. Knight, T. A. Birks, T. D. Hedley, P. St. J. Russell, “Very high numerical aperture fibers,” IEEE Photon. Technol. Lett. 16, 843–845 (2004).
[CrossRef]

W. J. Wadsworth, R. M. Percival, G. Bouwmans, J. C. Knight, P. St. J. Russell, “High power air-clad photonic crystal fiber laser,” Opt. Express 11, 48–53 (2003).
[CrossRef] [PubMed]

G. Bouwmans, R. M. Percival, W. J. Wadsworth, J. C. Knight, P. St. J. Russell, “High-power Er:Yb fiber laser with very high numerical aperture pump-cladding waveguide,” Appl. Phys. Lett. 83, 817–818 (2003).
[CrossRef]

Stach, M.

Tünnermann, A.

J. Limpert, T. Schreiber, A. Liem, S. Nolte, H. Zellmer, T. Peschel, V. Guyenot, A. Tünnermann, “Thermo-optical properties of air-clad photonic crystal fiber lasers in high power operation,” Opt. Express. 11, 2982–2990 (2003).
[CrossRef] [PubMed]

Wadsworth, W. J.

W. J. Wadsworth, R. M. Percival, G. Bouwmans, J. C. Knight, T. A. Birks, T. D. Hedley, P. St. J. Russell, “Very high numerical aperture fibers,” IEEE Photon. Technol. Lett. 16, 843–845 (2004).
[CrossRef]

W. J. Wadsworth, R. M. Percival, G. Bouwmans, J. C. Knight, P. St. J. Russell, “High power air-clad photonic crystal fiber laser,” Opt. Express 11, 48–53 (2003).
[CrossRef] [PubMed]

G. Bouwmans, R. M. Percival, W. J. Wadsworth, J. C. Knight, P. St. J. Russell, “High-power Er:Yb fiber laser with very high numerical aperture pump-cladding waveguide,” Appl. Phys. Lett. 83, 817–818 (2003).
[CrossRef]

Watson, F.

E. Mediavilla, S. Arribas, F. Watson, Fiber Optics in Astronomy (Astronomical Society of the Pacific, San Francisco, Calif., 1998), Vol. 3.

Zellmer, H.

J. Limpert, T. Schreiber, A. Liem, S. Nolte, H. Zellmer, T. Peschel, V. Guyenot, A. Tünnermann, “Thermo-optical properties of air-clad photonic crystal fiber lasers in high power operation,” Opt. Express. 11, 2982–2990 (2003).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

G. Bouwmans, R. M. Percival, W. J. Wadsworth, J. C. Knight, P. St. J. Russell, “High-power Er:Yb fiber laser with very high numerical aperture pump-cladding waveguide,” Appl. Phys. Lett. 83, 817–818 (2003).
[CrossRef]

Electro-Opt. Syst. Des. (1)

R. L. Gallawa, “On the definition of fiber numerical aperture,” Electro-Opt. Syst. Des. 14, 46–54 (1982).

Electron. Lett. (1)

J. K. Sahu, C. C. Renaud, K. Furusawa, R. Selvas, J. A. Alvarez-Chavez, D. J. Richardson, J. Nilsson, “Jacketed air-clad cladding pumped ytterbium-doped fiber laser with wide tuning range,” Electron. Lett. 37, 1116–1117 (2001).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

W. J. Wadsworth, R. M. Percival, G. Bouwmans, J. C. Knight, T. A. Birks, T. D. Hedley, P. St. J. Russell, “Very high numerical aperture fibers,” IEEE Photon. Technol. Lett. 16, 843–845 (2004).
[CrossRef]

N. A. Mortensen, J. R. Folkenberg, P. M. W. Skovgaard, J. Broeng, “Numerical aperture of single-mode photonic crystal fibers,” IEEE Photon. Technol. Lett. 14, 1094–1096 (2002).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. A (1)

C. P. Achenbach, J. H. Cobb, “Computational studies of light acceptance and propagation in straight and curved multimode active fibers,” J. Opt. A 5, 239–249 (2003).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Express (3)

Opt. Express. (1)

J. Limpert, T. Schreiber, A. Liem, S. Nolte, H. Zellmer, T. Peschel, V. Guyenot, A. Tünnermann, “Thermo-optical properties of air-clad photonic crystal fiber lasers in high power operation,” Opt. Express. 11, 2982–2990 (2003).
[CrossRef] [PubMed]

Solar Energy (1)

D. Feuermann, J. M. Gordon, M. Huleihil, “Light leakage in optical fibers: experimental results, modeling and the consequences for solar collectors,” Solar Energy 72, 195–204 (2002).
[CrossRef]

Other (7)

E. Mediavilla, S. Arribas, F. Watson, Fiber Optics in Astronomy (Astronomical Society of the Pacific, San Francisco, Calif., 1998), Vol. 3.

E. A. J. Marcatili, “Air clad optical fiber waveguide,” U.S. patent3,712,705 (23January1973).

K. Sakoda, Optical Properties of Photonic Crystals (Springer, Berlin, 2001), pp. 21–23.

E. Hecht, Optics, 3rd ed. (Addison-Wesley, Reading, Mass., 1998), pp. 419–420.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman Hall, London, 1983), Chap. 24.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman Hall, London, 1983), Chaps. 4 and 20.

J. A. Buck, “Fundamentals of optical fibers,” (Wiley, New York, 1995), pp. 49–51.

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Figures (6)

Fig. 1
Fig. 1

(a) Cross section along optical fiber axis. The core refractive index, n co = 1.45, is assumed equal to the index of the infinite jacket. Both are lossless. (b) Fresnel reflection at fiber end faces for TE and TM polarized light. Total internal reflection (TIR) occurs at the fiber end faces when n eff ≤ (n co 2 - 1)1/2 or θin ≥ arcsin(1/n co). (c) Schematic of air-clad fiber geometry studied here.

Fig. 2
Fig. 2

Typical far-field transmission calculation for a core surrounded by a continuous air ring. L = 10 m.

Fig. 3
Fig. 3

Example transmission for bridged air-clad fiber. δ/λ = 0.2, N = 75, w/λ = 8, and L/ D = 10 m/D o. (a) Total loss, -10 log[T(θ)], as a function of n eff for three mode classes, n b is the effective index of the fundamental bridge mode, calculated for the equivalent slab waveguide of thickness 0.2. It is a TE mode with respect to the orientation of the slab. n b* is the effective index of the second bridge mode, which is a TM mode with respect to the orientation of the slab. (b) Typical transmission curve. Partial transmission after the first sharp drop is due to low-loss TE-like modes and is neglected when measuring the 5% level.

Fig. 4
Fig. 4

Numerical aperture of a circular core with continuous air ring of radial width w. Results are obtained by a leaky-mode analysis (points) and the local-plane-wave approach (solid curves). Both show strong length dependence.

Fig. 5
Fig. 5

Example intensity plots of sample core modes in regions I (n eff r ≃ 1.175 > n b, TM-like mode), II (n eff r ≃ 1.1412 ≃ n b, TM-like mode), III (n eff r ≃ 1.1 < n b, TE-like mode) and IV (n eff r ≃ 1.1 < n b, TM-like mode).

Fig. 6
Fig. 6

Full calculation of NA and comparison with measured values. The vertical bar through experimental data indicates the range of measured values for different fiber lengths (when quoted). Shown are L/ D = 1 m/D o, 10 m/D o, 100 m/D o, and 1000 m/D o for w/λ = 8. Calculations for N = 50, 75, and 100 are nearly indistinguishable. The NA˜ = nco2 - nb21/2curve is obtained from the fundamental bridge mode.

Equations (6)

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NA=sinθmax,
θ=sin-1nco2-neffr 2,
Pθ=A 02πθ-Δθ/2θ+Δθ/2 Iθsinθdθdϕ2πAIθsinθΔθ,
TθPθFTEθ+FTMθ22αθ2πA sinθΔθ=IθFTEθ+FTMθ22αθ,
αθ=1Mm=1Mexp-2neffimkL,
Tθ1ncodθindθ IθinFTEθ+FTMθ2αθ,

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