Abstract

Various methods for simulating microstructure fibers have incorporated symmetry for improved efficiency and discrimination of nearly degenerate modes. A revision of the previously used symmetry-class implementations is proposed, with a more efficient partition of the degenerate classes. Advantages demonstrated using a multipole calculation should apply to finite-element and other simulation methods.

© 2004 Optical Society of America

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References

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  1. P. Kaiser and H. W. Astle, “Low-loss single-matrial fibers made from pure fused silica,” Bell Syst. Tech. J. 53, 1021–1039 (1974).
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  4. N. Venkataraman, M. T. Gallagher, C. M. Smith, D. Müller, J. A. West, K. W. Koch, and J. C. Fajardo, “Low loss (13 db/km) air core photonic band-gap fibre,” presented at the 28th European Conference on Optical Communication, Copenhagen, Denmark, September, 8–12, 2002.
  5. K. Tajima, J. Zhou, K. Kurokawa, and K. Nakajima, “Low water peak photonic crystal fibres,” presented at the 29th European Conference on Optical Communication, Rimini, Italy, September 22–24, 2003, paper Th4.1.6.
  6. S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, and J. L. Hall, “Direct link between microwave and optical frequencies with a 300 thz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
    [CrossRef] [PubMed]
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  8. D. Müller, D. C. Allan, N. F. Borrelli, K. T. Gahagan, M. T. Gallagher, C. M. Smith, N. Venkataraman, and K. W. Koch, “Measurement of photonic band-gap fiber transmission from 1 to 3 μm and impact of surface mode coupling,” in Quantum Electronics and Lases Science, Vol. 89 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), paper QTuL2.
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  11. A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, “Holey-fiber analysis through the finite-element method,” IEEE Photon. Technol. Lett. 14, 1530–1532 (2002).
    [CrossRef]
  12. A. Ferrando, E. Silvestre, J. J. Miret, and P. Andrés, “Full vector analysis of a realistic photonic crystal fiber,” Opt. Lett. 24, 276–278 (1999).
    [CrossRef]
  13. B. T. Kuhlmey, T. P. White, G. Renversez, D. Maystre, L. C. Botten, C. M. deSterke, and R. C. McPhedran, “Multipole methods for microstructured optical fibers. II. Implementation and results,” J. Opt. Soc. Am. B 19, 2331–2341 (2002).
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    [CrossRef]
  16. C. Vassalo, “Circular Fourier analysis of full Maxwell equations for arbitrarily shaped dielectric waveguides—application to gain factors of semiconductor laser waveguides,” J. Lightwave Technol. 8, 1723–1729 (1990).
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2003 (3)

2002 (2)

2001 (1)

2000 (1)

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, and J. L. Hall, “Direct link between microwave and optical frequencies with a 300 thz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[CrossRef] [PubMed]

1999 (2)

1997 (1)

1990 (1)

C. Vassalo, “Circular Fourier analysis of full Maxwell equations for arbitrarily shaped dielectric waveguides—application to gain factors of semiconductor laser waveguides,” J. Lightwave Technol. 8, 1723–1729 (1990).
[CrossRef]

1978 (1)

1975 (1)

P. R. McIsaac, “Symmetry-induced modal characteristics of uniform waveguides. I. Summary of results,” IEEE Trans. Microwave Theory Tech. 23, 421–429 (1975).
[CrossRef]

1974 (1)

P. Kaiser and H. W. Astle, “Low-loss single-matrial fibers made from pure fused silica,” Bell Syst. Tech. J. 53, 1021–1039 (1974).
[CrossRef]

Andrés, P.

Astle, H. W.

P. Kaiser and H. W. Astle, “Low-loss single-matrial fibers made from pure fused silica,” Bell Syst. Tech. J. 53, 1021–1039 (1974).
[CrossRef]

Bennett, P. J.

Berthelot, L.

Birks, T. A.

Botten, L. C.

Broderick, N. G. R.

Chartier, T.

Cucinotta, A.

A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, “Holey-fiber analysis through the finite-element method,” IEEE Photon. Technol. Lett. 14, 1530–1532 (2002).
[CrossRef]

Cundiff, S. T.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, and J. L. Hall, “Direct link between microwave and optical frequencies with a 300 thz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[CrossRef] [PubMed]

deSterke, C. M.

Diddams, S. A.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, and J. L. Hall, “Direct link between microwave and optical frequencies with a 300 thz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[CrossRef] [PubMed]

Ferrando, A.

Guan, N.

Habu, S.

Hall, J. L.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, and J. L. Hall, “Direct link between microwave and optical frequencies with a 300 thz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[CrossRef] [PubMed]

Hideur, A.

Himeno, K.

Issa, N. A.

Jones, D. J.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, and J. L. Hall, “Direct link between microwave and optical frequencies with a 300 thz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[CrossRef] [PubMed]

Kaiser, P.

P. Kaiser and H. W. Astle, “Low-loss single-matrial fibers made from pure fused silica,” Bell Syst. Tech. J. 53, 1021–1039 (1974).
[CrossRef]

Knight, J. C.

Kuhlmey, B. T.

Lempereur, S.

Marom, E.

Maystre, D.

McIsaac, P. R.

P. R. McIsaac, “Symmetry-induced modal characteristics of uniform waveguides. I. Summary of results,” IEEE Trans. Microwave Theory Tech. 23, 421–429 (1975).
[CrossRef]

McPhedran, R. C.

Mélin, G.

Miret, J. J.

Monro, T. M.

Pagnoux, D.

Peyrilloux, A.

Poladian, L.

Renversez, G.

Richardson, D. J.

Roy, P.

Russell, P. S. J.

Selleri, S.

A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, “Holey-fiber analysis through the finite-element method,” IEEE Photon. Technol. Lett. 14, 1530–1532 (2002).
[CrossRef]

Silvestre, E.

Steel, M. J.

Takenaga, K.

Vassalo, C.

C. Vassalo, “Circular Fourier analysis of full Maxwell equations for arbitrarily shaped dielectric waveguides—application to gain factors of semiconductor laser waveguides,” J. Lightwave Technol. 8, 1723–1729 (1990).
[CrossRef]

Vincetti, L.

A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, “Holey-fiber analysis through the finite-element method,” IEEE Photon. Technol. Lett. 14, 1530–1532 (2002).
[CrossRef]

Wada, A.

White, T. P.

Yariv, A.

Ye, J.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, and J. L. Hall, “Direct link between microwave and optical frequencies with a 300 thz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[CrossRef] [PubMed]

Yeh, P.

Zoboli, M.

A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, “Holey-fiber analysis through the finite-element method,” IEEE Photon. Technol. Lett. 14, 1530–1532 (2002).
[CrossRef]

Bell Syst. Tech. J. (1)

P. Kaiser and H. W. Astle, “Low-loss single-matrial fibers made from pure fused silica,” Bell Syst. Tech. J. 53, 1021–1039 (1974).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, “Holey-fiber analysis through the finite-element method,” IEEE Photon. Technol. Lett. 14, 1530–1532 (2002).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

P. R. McIsaac, “Symmetry-induced modal characteristics of uniform waveguides. I. Summary of results,” IEEE Trans. Microwave Theory Tech. 23, 421–429 (1975).
[CrossRef]

J. Lightwave Technol. (5)

J. Opt. Soc. Am. (1)

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

Opt. Lett. (3)

Phys. Rev. Lett. (1)

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, and J. L. Hall, “Direct link between microwave and optical frequencies with a 300 thz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[CrossRef] [PubMed]

Other (4)

D. Müller, D. C. Allan, N. F. Borrelli, K. T. Gahagan, M. T. Gallagher, C. M. Smith, N. Venkataraman, and K. W. Koch, “Measurement of photonic band-gap fiber transmission from 1 to 3 μm and impact of surface mode coupling,” in Quantum Electronics and Lases Science, Vol. 89 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), paper QTuL2.

N. Venkataraman, M. T. Gallagher, C. M. Smith, D. Müller, J. A. West, K. W. Koch, and J. C. Fajardo, “Low loss (13 db/km) air core photonic band-gap fibre,” presented at the 28th European Conference on Optical Communication, Copenhagen, Denmark, September, 8–12, 2002.

K. Tajima, J. Zhou, K. Kurokawa, and K. Nakajima, “Low water peak photonic crystal fibres,” presented at the 29th European Conference on Optical Communication, Rimini, Italy, September 22–24, 2003, paper Th4.1.6.

J. Jasapara, R. Bise, T. Her, and J. Nicholson, “Effect of mode cut-off on dispersion in photonic bandgap fibers,” Optical Fiber Communication Conference, Vol. 86 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), paper ThI3.

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Figures (4)

Fig. 1
Fig. 1

Mode lines of this air-core microstructure fiber are shown in the region of the λneff plot, where the bandgap (unshaded region) crosses neff=1. Mode structure is primarily dominated by unwanted glass-guided modes.

Fig. 2
Fig. 2

Calculated intensity profiles show two modes with neff0.98, a fundamental core mode at λ=1.44 (center), and a surface mode at λ=1.42, guided primarily in glass webs (right). Holes are shown dashed.

Fig. 3
Fig. 3

Determinant of the mode-condition matrix is plotted versus neff for three subspaces: class 8, class 4 quadrant, and class 4 rotation (l=1). The product relation is indicated by the agreement between ‘x’ symbols and the solid curve.

Fig. 4
Fig. 4

Simulated effective index of a typical microstructure fiber (left) is compared with the similar “satellite fiber” (right), demonstrating the applicability of the revised symmetry classes to fibers with no reflection symmetry. Both fibers have a two-ring cladding of air holes with spacing Λ=2 µm and diameter d=1.3 µm. The satellite fiber includes small high-index inclusions at the periphery of the core region (index 2.0, radius ≈0.1 µm). The inclusions act as waveguides at short wavelengths and perturbations at long wavelengths.

Tables (1)

Tables Icon

Table 1 Symmetry Relations Used to Obtain Compact Field Representations for Various Methods Outlineda

Equations (10)

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

E(r)=E(x, y)exp(ikzz),
H(r)=H(x, y)exp(ikzz).
(A-neff2B)b=0.
M(λ, neff)b=0.
b=Zbs.
E(Rπ/3r)=exp(ipπ/3)Rπ/3E(r).
Z*(A-neff2B)Zbs=(As-neff2Bs)bs=0,
Z*MZbs=Msbs=0.
Pl{E(r)}=1N n=1N-1 exp(-i2πnl/N)R2π/N-nE(R2π/Nnr),
Ez(Rπ/3r)=exp(±iπ/3)Ez(r)(l=±1mode).

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