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Antiresonant reflecting optical waveguide microstructured fibers revisited: a new analysis based on leaky mode coupling

Gilles Renversez, Philippe Boyer, and Angelo Sagrini

Open Access Open Access

Abstract

Using two different modal methods, the multipole method and the more recent fast Fourier factorization method, we exhibit and explain a core mode transition induced by avoided crossing between a core localized leaky mode and an high-index cylinder leaky mode in anti-resonant reflecting optical waveguide microstructured optical fibers (ARROW MOFs). Due to its wavelength selectivity and to the leaky nature of the involved modes, this transition does not seem to have already been described in detail and analyzed as done in this work in spite of several already published studies on core mode dispersion properties. The main properties of this transition are also described. We also revisit the already mentioned cut-off phenomena limiting the transmission band in ARROW MOFs in terms of mode coupling between the core mode and one or several high-index cylinder modes.

©2006 Optical Society of America

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References

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  1. N.M. Lichinitser, S. C. Dunn, P. E. Steinwuzel, B. J. Eggleton, T. P. White, R. C. McPhedran, and C.M. de Sterke. “Application of an ARROWmodel for designing tunable photonic devices,” Opt. Express 12:1540–1550 (2004).
    [Crossref]
  2. A. Argyros, T. A. Birks, S. G. Leon-Saval, C. M. B. Cordeiro, F. Luan, and P. St. Russell. “Photonic bandgap with an index step of one percent,” Opt. Express,  13309–314 (2005).
    [Crossref] [PubMed]
  3. G. Bouwmans, L. Bigot, Y. Quiquempois, F. Lopez, L. Provino, and M. Douay. “Fabrication and characterization of an all solid 2D photonic bandgap fiber with a low-loss region (<20 dB/km) around 1550 nm,” Opt. Express,  138452–8459 (2005).
    [Crossref] [PubMed]
  4. T. P. White, R. C. McPhedran, C. M. de Sterke, N. M. Lichinitser, and B. J. Eggleton. “Resonance and scaterring in microstructured optical fibers,” Opt. Lett. 27, 1977–1979 (2002).
    [Crossref]
  5. J. Laegsgaard. “Gap formation and guided modes in photonic bandgap fibres with high-index rods,” J. Opt. A: Pure Appl. Opt. 6, 798–804 (2004).
    [Crossref]
  6. A. Sagrini, G. Renversez, and P. Boyer. “Transition de délocalisation du mode de coeur des fibres microstructurées anti-résonantes par anticroisement des modes à pertes,” in Journées Nationales d’Optique Guidée (Société Française d’Optique, Chambéry, France, November2005), 183–185.
  7. B. Kuhlmey, T. P. White, G. Renversez, D. Maystre, L.C. Botten, C. Martijn de Sterke, and R. C. McPhedran. “Multipole method for microstructured optical fibers II: implementation and results,” J. Opt. Soc. Am. B 10, 2331–2340 (2002).
    [Crossref]
  8. F. Zolla, G. Renversez, A. Nicolet, B. Kuhlmey, S. Guenneau, and D. Felbacq. Foundations of Photonic Crystal Fibres, (Imperial College Press, London, 2005).
    [Crossref]
  9. P. Boyer, M. Nevière, E. Popov, and G. Renversez. “Diffraction theory : Application of the fast Fourier factorization method to cylindrical devices with arbitrary cross section lighted in conical mounting,” J. Opt. Soc. Am. A 23, 1146–1158 (2006).
    [Crossref]
  10. D. Marcuse. Theory of Dielectric Optical Waveguides, (Academic Press, San Diego, 2nd edition, 1991).
  11. T. D. Engeness, M. Ibanescu, S. G. Johnson, O. Weisberg, M. Skorobogatiy, S. Jacobs, and Y. Fink. “Dispersion tailoring and compensation by modal interactions in omniguide fibers,” Opt. Express 11, 1175–1196 (2003).
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  13. G. Renversez, F. Bordas, and B. T. Kuhlmey. “Second mode transition in microstructured optical fibers: determination of the critical geometrical parameter and study of the matrix refractive index and effects of cladding size,” Opt. Lett. 30, 1264–1266 (2005).
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2006 (1)

2005 (3)

2004 (3)

2003 (2)

2002 (2)

Argyros, A.

Bigot, L.

Bird, D. M.

Birks, T. A.

Bordas, F.

Botten, L.C.

Bouwmans, G.

Boyer, P.

P. Boyer, M. Nevière, E. Popov, and G. Renversez. “Diffraction theory : Application of the fast Fourier factorization method to cylindrical devices with arbitrary cross section lighted in conical mounting,” J. Opt. Soc. Am. A 23, 1146–1158 (2006).
[Crossref]

A. Sagrini, G. Renversez, and P. Boyer. “Transition de délocalisation du mode de coeur des fibres microstructurées anti-résonantes par anticroisement des modes à pertes,” in Journées Nationales d’Optique Guidée (Société Française d’Optique, Chambéry, France, November2005), 183–185.

Cordeiro, C. M. B.

de Sterke, C. M.

de Sterke, C.M.

Douay, M.

Dunn, S. C.

Eggleton, B. J.

Engeness, T. D.

Felbacq, D.

F. Zolla, G. Renversez, A. Nicolet, B. Kuhlmey, S. Guenneau, and D. Felbacq. Foundations of Photonic Crystal Fibres, (Imperial College Press, London, 2005).
[Crossref]

Fink, Y.

Guenneau, S.

F. Zolla, G. Renversez, A. Nicolet, B. Kuhlmey, S. Guenneau, and D. Felbacq. Foundations of Photonic Crystal Fibres, (Imperial College Press, London, 2005).
[Crossref]

Hedley, T. D.

Ibanescu, M.

Jacobs, S.

Johnson, S. G.

Koshiba, M.

Kuhlmey, B.

Kuhlmey, B. T.

Laegsgaard, J.

J. Laegsgaard. “Gap formation and guided modes in photonic bandgap fibres with high-index rods,” J. Opt. A: Pure Appl. Opt. 6, 798–804 (2004).
[Crossref]

Leon-Saval, S. G.

Lichinitser, N. M.

Lichinitser, N.M.

Lopez, F.

Luan, F.

Marcuse, D.

D. Marcuse. Theory of Dielectric Optical Waveguides, (Academic Press, San Diego, 2nd edition, 1991).

Martijn de Sterke, C.

Maystre, D.

McPhedran, R. C.

Mortensen, N. A.

Nevière, M.

Nicolet, A.

F. Zolla, G. Renversez, A. Nicolet, B. Kuhlmey, S. Guenneau, and D. Felbacq. Foundations of Photonic Crystal Fibres, (Imperial College Press, London, 2005).
[Crossref]

Popov, E.

Pottage, J. M.

Provino, L.

Quiquempois, Y.

Renversez, G.

Russell, P. S.

Russell, P. St.

Sagrini, A.

A. Sagrini, G. Renversez, and P. Boyer. “Transition de délocalisation du mode de coeur des fibres microstructurées anti-résonantes par anticroisement des modes à pertes,” in Journées Nationales d’Optique Guidée (Société Française d’Optique, Chambéry, France, November2005), 183–185.

Saitoh, K.

Skorobogatiy, M.

Steinwuzel, P. E.

Weisberg, O.

White, T. P.

Zolla, F.

F. Zolla, G. Renversez, A. Nicolet, B. Kuhlmey, S. Guenneau, and D. Felbacq. Foundations of Photonic Crystal Fibres, (Imperial College Press, London, 2005).
[Crossref]

J. Opt. A: Pure Appl. Opt. (1)

J. Laegsgaard. “Gap formation and guided modes in photonic bandgap fibres with high-index rods,” J. Opt. A: Pure Appl. Opt. 6, 798–804 (2004).
[Crossref]

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

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

Opt. Express (5)

Opt. Lett. (3)

Other (3)

F. Zolla, G. Renversez, A. Nicolet, B. Kuhlmey, S. Guenneau, and D. Felbacq. Foundations of Photonic Crystal Fibres, (Imperial College Press, London, 2005).
[Crossref]

A. Sagrini, G. Renversez, and P. Boyer. “Transition de délocalisation du mode de coeur des fibres microstructurées anti-résonantes par anticroisement des modes à pertes,” in Journées Nationales d’Optique Guidée (Société Française d’Optique, Chambéry, France, November2005), 183–185.

D. Marcuse. Theory of Dielectric Optical Waveguides, (Academic Press, San Diego, 2nd edition, 1991).

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Figures (4)
Fig. 1.
Fig. 1. Normalized real part of the effective index, ℜe(n eff), of the ARROW MOF core mode versus the wavelength around the transition. The asymptot for the core mode curves A and B is the real part of n eff for leaky mode EH33 of the isolated high-index cylinder. The imaginary part, ℑm(n eff), of the core modes A and B is also given (thin curves, right y-scale). Inset: overall view of the dispersion curve (without the discontinuities) in the corresponding transmission band.

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Fig. 2.
Fig. 2. Modulus distribution of the z-component of the Poynting vector across the transition of core mode A. (a) λ=0.8654 µm, (b) λ=0.8666 µm, (c) λ=0.8668 µm, (d) λ=0.8669 µm, (e) λ=0.8672 µm (see Fig. 1 for their respective positions in the ℜe(n eff)(λ) dispersion curve), (f) Modulus distribution of the z-component of the Poynting vector for the leaky mode EH33 of an isolated high-index inclusion (border shown by the black circle), n eff =1.438142+i 9.121 10-7 and λ=0.867µm.

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Fig. 3.
Fig. 3. Avoided crossings between the structure core mode and leaky modes of high refractive index cylinder (EH14, HE53, EH33) ; the cylinder parameters and the refractive indices are the same as the ones used previously. Dispersion curves for two smaller values of the pitch Λ are also given. HOCLM means higher order core localized mode. Due to its sharpness, the avoided crossing for Λ=5,64µm with the HE53 mode is not well resolved in this plot.

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Fig. 4.
Fig. 4. |𝓡|/Λ2 (as defined in the text) versus the wavelength for core modes A and B for three pitch values around the avoided crossing with leaky mode EH33 (d is kept constant). The influence of the refractive index contrast is also given. The curves for n mat =1.5 and 1.6 have been translated along the x-axis to make them visible.

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