Abstract

We describe a zoned microstructure fiber that exhibits low dispersion and virtually zero spherical aberration because of its optimized piecewise Gaussian index profile. We present results of a nine-zone design that has an average refractive index of 2.3, a refractive-index contrast of 0.1, a first zone radius of 1.67 µm, and a maximum core radius of 5 µm. It has an in-fiber focal length of 8.88 µm and can focus light to a spot size of radius 315 nm, facilitating efficient coupling between single-mode fiber and photonic crystals.

© 2004 Optical Society of America

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References

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  1. P. Yeh, A. Yariv, and E. Marom, J. Opt. Soc. Am. 68, 1196 (1978).
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    [CrossRef]
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    [CrossRef]
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  6. J. C. Knight, Nature 424, 847 (2003).
    [CrossRef] [PubMed]
  7. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), pp. 109–132.
    [CrossRef]
  8. D. W. Berreman, Bell Syst. Tech. J. 44, 2117 (1965).
    [CrossRef]
  9. P. Petropoulos, H. Ebendorff-Heidepriem, V. Finazzi, R. C. Moore, K. Frampton, D. J. Richardson, and T. M. Monro, Opt. Express 11, 3568 (2003), http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  10. J. Wilson and J. F. B. Hawkes, Optoelectronics: an Introduction, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J., 1989), pp. 329–332.

2003 (3)

M. Ibanescu, S. G. Johnson, M. Solijacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, Phys. Rev. E 67, 046608 (2003).
[CrossRef]

J. C. Knight, Nature 424, 847 (2003).
[CrossRef] [PubMed]

P. Petropoulos, H. Ebendorff-Heidepriem, V. Finazzi, R. C. Moore, K. Frampton, D. J. Richardson, and T. M. Monro, Opt. Express 11, 3568 (2003), http://www.opticsexpress.org .
[CrossRef] [PubMed]

2002 (1)

J. Canning, Opt. Commun. 207, 35 (2002).
[CrossRef]

1996 (1)

1978 (1)

1965 (1)

D. W. Berreman, Bell Syst. Tech. J. 44, 2117 (1965).
[CrossRef]

Atkin, D. M.

Berreman, D. W.

D. W. Berreman, Bell Syst. Tech. J. 44, 2117 (1965).
[CrossRef]

Birks, T. A.

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), pp. 109–132.
[CrossRef]

Canning, J.

J. Canning, Opt. Commun. 207, 35 (2002).
[CrossRef]

Ebendorff-Heidepriem, H.

Engeness, T. D.

M. Ibanescu, S. G. Johnson, M. Solijacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, Phys. Rev. E 67, 046608 (2003).
[CrossRef]

Finazzi, V.

Fink, Y.

M. Ibanescu, S. G. Johnson, M. Solijacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, Phys. Rev. E 67, 046608 (2003).
[CrossRef]

Frampton, K.

Hawkes, J. F. B.

J. Wilson and J. F. B. Hawkes, Optoelectronics: an Introduction, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J., 1989), pp. 329–332.

Hisatomi, M.

M. Hisatomi, M. C. Parker, and S. D. Walker, in Proceedings of IEEE/LEOS Summer Topical Meetings (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2003), pp. 43–44.

Ibanescu, M.

M. Ibanescu, S. G. Johnson, M. Solijacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, Phys. Rev. E 67, 046608 (2003).
[CrossRef]

Jacobs, S. A.

M. Ibanescu, S. G. Johnson, M. Solijacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, Phys. Rev. E 67, 046608 (2003).
[CrossRef]

Joannopoulos, J. D.

M. Ibanescu, S. G. Johnson, M. Solijacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, Phys. Rev. E 67, 046608 (2003).
[CrossRef]

Johnson, S. G.

M. Ibanescu, S. G. Johnson, M. Solijacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, Phys. Rev. E 67, 046608 (2003).
[CrossRef]

Knight, J. C.

Marom, E.

Monro, T. M.

Moore, R. C.

Parker, M. C.

M. Hisatomi, M. C. Parker, and S. D. Walker, in Proceedings of IEEE/LEOS Summer Topical Meetings (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2003), pp. 43–44.

Petropoulos, P.

Richardson, D. J.

Russell, P. St. J.

Skorobogatiy, M.

M. Ibanescu, S. G. Johnson, M. Solijacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, Phys. Rev. E 67, 046608 (2003).
[CrossRef]

Solijacic, M.

M. Ibanescu, S. G. Johnson, M. Solijacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, Phys. Rev. E 67, 046608 (2003).
[CrossRef]

Walker, S. D.

M. Hisatomi, M. C. Parker, and S. D. Walker, in Proceedings of IEEE/LEOS Summer Topical Meetings (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2003), pp. 43–44.

Weisberg, O.

M. Ibanescu, S. G. Johnson, M. Solijacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, Phys. Rev. E 67, 046608 (2003).
[CrossRef]

Wilson, J.

J. Wilson and J. F. B. Hawkes, Optoelectronics: an Introduction, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J., 1989), pp. 329–332.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), pp. 109–132.
[CrossRef]

Yariv, A.

Yeh, P.

Bell Syst. Tech. J. (1)

D. W. Berreman, Bell Syst. Tech. J. 44, 2117 (1965).
[CrossRef]

J. Opt. Soc. Am. (1)

Nature (1)

J. C. Knight, Nature 424, 847 (2003).
[CrossRef] [PubMed]

Opt. Commun. (1)

J. Canning, Opt. Commun. 207, 35 (2002).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. E (1)

M. Ibanescu, S. G. Johnson, M. Solijacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, Phys. Rev. E 67, 046608 (2003).
[CrossRef]

Other (3)

M. Hisatomi, M. C. Parker, and S. D. Walker, in Proceedings of IEEE/LEOS Summer Topical Meetings (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2003), pp. 43–44.

J. Wilson and J. F. B. Hawkes, Optoelectronics: an Introduction, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J., 1989), pp. 329–332.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), pp. 109–132.
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic of GZ MSF waveguide, (b) piecewise GZ RI profile nr.

Fig. 2
Fig. 2

(a) Trajectories for Gaussian GRIN fiber, (b) zoomed-in on-axis diagram.

Fig. 3
Fig. 3

(a) Trajectories for parabolic (Fresnel) zoned fiber, (b) zoomed-in on-axis diagram.

Fig. 4
Fig. 4

(a) Trajectories for GZ MSF, (b) zoomed-in on-axis diagram.

Tables (1)

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Table 1 Optimized Values for rm, κm, and Δnm

Equations (5)

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ddtnxdxdt=nx,
d2rdz2=1nrdndr.
d2rdz2=-κ12r.
nmr=n1 exp-κm2r2/2+Δnm,
d2rdz2=-κm2r1+Δnm/n1expκm2r2/2-κ˜12r.

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