Abstract

We numerically and theoretically investigate the core modes of two-dimensional solid-core photonic bandgap (PBG) fibers based on hexagonal arrays of high-index circular rods. Such fibers guide light in discrete bandgaps, and the number of core-guided modes depends on the order of the bandgap as well as the position within the bandgap. We first classify the different core-guided modes in such fibers and we discuss the links among band structure, losses, and number and type of modes. We demonstrate that, similar to the case of bandgapless Kagome and ring-based fibers, solid-core bandgap fibers can have core-guided modes that are within photonic bands of the cladding. We discuss the classification of core modes in such fibers, and highlight analogies and differences with that of index-guiding fibers. Through an asymptotic expansion of an analytic model of a fiber’s photonic bands, we show that, in the limit of higher-order gaps (i.e., short wavelengths), the number of modes in the middle of gaps tends to a constant that is independent of refractive index contrast, as is the case for index-guiding photonic crystal fibers. We also discuss the evolution of the effectively single-mode propagation regime with geometrical parameters of structures having constant or variable band diagrams. For small- and large-core PBG fibers, we compute the exact number of core-guided modes within the center of the transmission band. We discuss their evolution with gap orders and coupling strength between high-index inclusions in the cladding. We find good agreement of the core-guided mode number in the center of the gaps computed with our theoretical model and with a numerical method for short wavelengths.

© 2012 Optical Society of America

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2012 (2)

2011 (2)

V. Pureur and J. M. Dudley, “Design of solid core photonic bandgap fibers for visible supercontinuum generation,” Opt. Commun. 284, 1661–1668 (2011).
[CrossRef]

B. Ward, “Solid-core photonic bandgap fibers for cladding-pumped Raman amplification,” Opt. Express 19, 11852–11866 (2011).
[CrossRef]

2010 (4)

2009 (2)

B. T. Kuhlmey, B. J. Eggleton, and D. K. C. Wu, “Fluid-filled solid-core photonic bandgap fibers,” J. Lightwave Technol. 27, 1617–1630 (2009).
[CrossRef]

V. Pureur, A. Bétourné, G. Bouwmans, L. Bigot, A. Kudlinski, K. Delplace, A. Le Rouge, Y. Quiquempois, and M. Douay, “Overview on solid core photonic bandgap fibers,” Fiber Integr. Opt. 28, 27–50 (2009).
[CrossRef]

2008 (5)

2007 (2)

A. Argyros and J. Pla, “Hollow-core polymer fibres with a kagome lattice: potential for transmission in the infrared,” Opt. Express 15, 7713–7719 (2007).
[CrossRef]

F. Couny, F. Benabid, P. J. Roberts, P. S. Light, and M. G. Raymer, “Generation and photonic guidance of multioctave optical-frequency combs,” Science 318, 1118–1121 (2007).
[CrossRef]

2006 (4)

2005 (5)

2004 (2)

2003 (1)

2002 (3)

2001 (2)

1999 (1)

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allen, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
[CrossRef]

1997 (1)

1996 (1)

1975 (1)

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

Abeeluck, A. K.

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1965).

Allen, D. C.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allen, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
[CrossRef]

Argyros, A.

Atkin, D.

Bang, O.

Benabid, F.

F. Couny, F. Benabid, P. J. Roberts, P. S. Light, and M. G. Raymer, “Generation and photonic guidance of multioctave optical-frequency combs,” Science 318, 1118–1121 (2007).
[CrossRef]

Bétourné, A.

Y. Ould-Agha, A. Bétourné, O. Vanvincq, G. Bouwmans, and Y. Quiquempois, “Broadband bandgap guidance and mode filtering in radially hybrid photonic crystal fiber,” Opt. Express 20, 6746–6760 (2012).
[CrossRef]

V. Pureur, A. Bétourné, G. Bouwmans, L. Bigot, A. Kudlinski, K. Delplace, A. Le Rouge, Y. Quiquempois, and M. Douay, “Overview on solid core photonic bandgap fibers,” Fiber Integr. Opt. 28, 27–50 (2009).
[CrossRef]

Bigot, L.

V. Pureur, A. Bétourné, G. Bouwmans, L. Bigot, A. Kudlinski, K. Delplace, A. Le Rouge, Y. Quiquempois, and M. Douay, “Overview on solid core photonic bandgap fibers,” Fiber Integr. Opt. 28, 27–50 (2009).
[CrossRef]

V. Pureur, L. Bigot, G. Bouwmans, Y. Quiquempois, M. Douay, and Y. Jaouen, “Ytterbium-doped solid core photonic bandgap fiber for laser operation around 980 nm,” Appl. Phys. Lett. 92, 061113 (2008).
[CrossRef]

V. Pureur, L. Bigot, G. Bouwmans, Y. Quiquempois, M. Douay, and Y. Jaouen, “Ytterbium-doped solid core photonic bandgap fiber for laser operation around 980 nm,” Appl. Phys. Lett. 92, 061113 (2008).
[CrossRef]

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 13, 8452–8459 (2005).
[CrossRef]

Bird, D. M.

Biriukov, A. S.

Birks, T.

Birks, T. A.

Bjarklev, A.

Bordas, F.

Botten, L.

Botten, L. C.

Bouwmans, G.

Y. Ould-Agha, A. Bétourné, O. Vanvincq, G. Bouwmans, and Y. Quiquempois, “Broadband bandgap guidance and mode filtering in radially hybrid photonic crystal fiber,” Opt. Express 20, 6746–6760 (2012).
[CrossRef]

V. Pureur, A. Bétourné, G. Bouwmans, L. Bigot, A. Kudlinski, K. Delplace, A. Le Rouge, Y. Quiquempois, and M. Douay, “Overview on solid core photonic bandgap fibers,” Fiber Integr. Opt. 28, 27–50 (2009).
[CrossRef]

V. Pureur, L. Bigot, G. Bouwmans, Y. Quiquempois, M. Douay, and Y. Jaouen, “Ytterbium-doped solid core photonic bandgap fiber for laser operation around 980 nm,” Appl. Phys. Lett. 92, 061113 (2008).
[CrossRef]

V. Pureur, L. Bigot, G. Bouwmans, Y. Quiquempois, M. Douay, and Y. Jaouen, “Ytterbium-doped solid core photonic bandgap fiber for laser operation around 980 nm,” Appl. Phys. Lett. 92, 061113 (2008).
[CrossRef]

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 13, 8452–8459 (2005).
[CrossRef]

Broeng, J.

Chen, M.

Coen, S.

Couny, F.

F. Couny, F. Benabid, P. J. Roberts, P. S. Light, and M. G. Raymer, “Generation and photonic guidance of multioctave optical-frequency combs,” Science 318, 1118–1121 (2007).
[CrossRef]

Cregan, R. F.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allen, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
[CrossRef]

de Sterke, C. M.

de Sterke, C. Martijn

Delplace, K.

V. Pureur, A. Bétourné, G. Bouwmans, L. Bigot, A. Kudlinski, K. Delplace, A. Le Rouge, Y. Quiquempois, and M. Douay, “Overview on solid core photonic bandgap fibers,” Fiber Integr. Opt. 28, 27–50 (2009).
[CrossRef]

Denisov, A. N.

Dianov, E. M.

Digonnet, M. J. F.

Docherty, A.

Douay, M.

V. Pureur, A. Bétourné, G. Bouwmans, L. Bigot, A. Kudlinski, K. Delplace, A. Le Rouge, Y. Quiquempois, and M. Douay, “Overview on solid core photonic bandgap fibers,” Fiber Integr. Opt. 28, 27–50 (2009).
[CrossRef]

V. Pureur, L. Bigot, G. Bouwmans, Y. Quiquempois, M. Douay, and Y. Jaouen, “Ytterbium-doped solid core photonic bandgap fiber for laser operation around 980 nm,” Appl. Phys. Lett. 92, 061113 (2008).
[CrossRef]

V. Pureur, L. Bigot, G. Bouwmans, Y. Quiquempois, M. Douay, and Y. Jaouen, “Ytterbium-doped solid core photonic bandgap fiber for laser operation around 980 nm,” Appl. Phys. Lett. 92, 061113 (2008).
[CrossRef]

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 13, 8452–8459 (2005).
[CrossRef]

Dudley, J. M.

V. Pureur and J. M. Dudley, “Design of solid core photonic bandgap fibers for visible supercontinuum generation,” Opt. Commun. 284, 1661–1668 (2011).
[CrossRef]

V. Pureur and J. M. Dudley, “Nonlinear spectral broadening of femtosecond pulses in solid-core photonic bandgap fibers,” Opt. Lett. 35, 2813–2815 (2010).
[CrossRef]

Eggleton, B. J.

Egorova, O. N.

Engeness, T.

Fan, S.

Fink, Y.

Fujimaki, M.

Gaponov, D. A.

George, A. K.

Grujic, T.

Guobin, R.

Gurianov, A. N.

Hansen, K. P.

Headley, C.

Hedley, T. D.

Ibanescu, M.

Isomäki, A.

Jacobs, S.

Jaouen, Y.

V. Pureur, L. Bigot, G. Bouwmans, Y. Quiquempois, M. Douay, and Y. Jaouen, “Ytterbium-doped solid core photonic bandgap fiber for laser operation around 980 nm,” Appl. Phys. Lett. 92, 061113 (2008).
[CrossRef]

V. Pureur, L. Bigot, G. Bouwmans, Y. Quiquempois, M. Douay, and Y. Jaouen, “Ytterbium-doped solid core photonic bandgap fiber for laser operation around 980 nm,” Appl. Phys. Lett. 92, 061113 (2008).
[CrossRef]

Joannopoulos, J.

Joannopoulos, J. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Johnson, S.

Johnson, S. G.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Kashiwagi, M.

Khopin, V. F.

Kim, H. K.

Kino, G. S.

Knight, J.

Knight, J. C.

Koshiba, M.

Kosolapov, A. F.

Kudlinski, A.

V. Pureur, A. Bétourné, G. Bouwmans, L. Bigot, A. Kudlinski, K. Delplace, A. Le Rouge, Y. Quiquempois, and M. Douay, “Overview on solid core photonic bandgap fibers,” Fiber Integr. Opt. 28, 27–50 (2009).
[CrossRef]

Kuhlmey, B. T.

T. Grujic, B. T. Kuhlmey, A. Argyros, S. Coen, and C. M. de Sterke, “Solid-core fiber with ultra-wide bandwidth transmission window due to inhibited coupling,” Opt. Express 18, 25556–25566 (2010).
[CrossRef]

V. Pureur, J. C. Knight, and B. T. Kuhlmey, “Higher order guided mode propagation in solid-core photonic bandgap fibers,” Opt. Express 18, 8906–8915 (2010).
[CrossRef]

B. T. Kuhlmey, B. J. Eggleton, and D. K. C. Wu, “Fluid-filled solid-core photonic bandgap fibers,” J. Lightwave Technol. 27, 1617–1630 (2009).
[CrossRef]

P. Steinvurzel, C. Martijn de Sterke, M. J. Steel, B. T. Kuhlmey, and B. J. Eggleton, “Single scatterer Fano resonances in solid core photonic band gap fibers,” Opt. Express 14, 8797–8811 (2006).
[CrossRef]

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).
[CrossRef]

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Opt. Soc. Am. B 19, 2322–2330 (2002).
[CrossRef]

B. T. Kuhlmey, R. C. McPhedran, and C. M. de Sterke, “Modal cutoff in microstructured optical fibers,” Opt. Lett. 27, 1684–1686 (2002).
[CrossRef]

B. T. Kuhlmey, “Theoretical and numerical investigation of the physics of microstructured optical fibres,” Ph.D. dissertation (University of Sydney and Université Aix-Marseille III, 2003), http://hdl.handle.net/2123/560 .

Kuksenkov, D. V.

Lægsgaard, J.

Le Rouge, A.

V. Pureur, A. Bétourné, G. Bouwmans, L. Bigot, A. Kudlinski, K. Delplace, A. Le Rouge, Y. Quiquempois, and M. Douay, “Overview on solid core photonic bandgap fibers,” Fiber Integr. Opt. 28, 27–50 (2009).
[CrossRef]

Leon-Saval, S. G.

Light, P. S.

F. Couny, F. Benabid, P. J. Roberts, P. S. Light, and M. G. Raymer, “Generation and photonic guidance of multioctave optical-frequency combs,” Science 318, 1118–1121 (2007).
[CrossRef]

Litchinitser, N. M.

Lopez, F.

Love, J.

A. Snyder and J. Love, Optical Waveguide Theory (Kluwer Academic, 1983).

Luan, F.

Lyngs, J. K.

Mangan, B. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allen, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
[CrossRef]

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, 1991).

Matsuo, S.

Maystre, D.

McIsaac, P. R.

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

McPhedran, R.

McPhedran, R. C.

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Mortensen, N. A.

Okhotnikov, O. G.

Olausson, C. B.

Ould-Agha, Y.

Pearce, G. J.

Pla, J.

Provino, L.

Pryamikov, A. D.

Pureur, V.

V. Pureur and J. M. Dudley, “Design of solid core photonic bandgap fibers for visible supercontinuum generation,” Opt. Commun. 284, 1661–1668 (2011).
[CrossRef]

V. Pureur, J. C. Knight, and B. T. Kuhlmey, “Higher order guided mode propagation in solid-core photonic bandgap fibers,” Opt. Express 18, 8906–8915 (2010).
[CrossRef]

V. Pureur and J. M. Dudley, “Nonlinear spectral broadening of femtosecond pulses in solid-core photonic bandgap fibers,” Opt. Lett. 35, 2813–2815 (2010).
[CrossRef]

V. Pureur, A. Bétourné, G. Bouwmans, L. Bigot, A. Kudlinski, K. Delplace, A. Le Rouge, Y. Quiquempois, and M. Douay, “Overview on solid core photonic bandgap fibers,” Fiber Integr. Opt. 28, 27–50 (2009).
[CrossRef]

V. Pureur, L. Bigot, G. Bouwmans, Y. Quiquempois, M. Douay, and Y. Jaouen, “Ytterbium-doped solid core photonic bandgap fiber for laser operation around 980 nm,” Appl. Phys. Lett. 92, 061113 (2008).
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V. Pureur, L. Bigot, G. Bouwmans, Y. Quiquempois, M. Douay, and Y. Jaouen, “Ytterbium-doped solid core photonic bandgap fiber for laser operation around 980 nm,” Appl. Phys. Lett. 92, 061113 (2008).
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Y. Ould-Agha, A. Bétourné, O. Vanvincq, G. Bouwmans, and Y. Quiquempois, “Broadband bandgap guidance and mode filtering in radially hybrid photonic crystal fiber,” Opt. Express 20, 6746–6760 (2012).
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V. Pureur, A. Bétourné, G. Bouwmans, L. Bigot, A. Kudlinski, K. Delplace, A. Le Rouge, Y. Quiquempois, and M. Douay, “Overview on solid core photonic bandgap fibers,” Fiber Integr. Opt. 28, 27–50 (2009).
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V. Pureur, L. Bigot, G. Bouwmans, Y. Quiquempois, M. Douay, and Y. Jaouen, “Ytterbium-doped solid core photonic bandgap fiber for laser operation around 980 nm,” Appl. Phys. Lett. 92, 061113 (2008).
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V. Pureur, L. Bigot, G. Bouwmans, Y. Quiquempois, M. Douay, and Y. Jaouen, “Ytterbium-doped solid core photonic bandgap fiber for laser operation around 980 nm,” Appl. Phys. Lett. 92, 061113 (2008).
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V. Pureur, L. Bigot, G. Bouwmans, Y. Quiquempois, M. Douay, and Y. Jaouen, “Ytterbium-doped solid core photonic bandgap fiber for laser operation around 980 nm,” Appl. Phys. Lett. 92, 061113 (2008).
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V. Pureur, L. Bigot, G. Bouwmans, Y. Quiquempois, M. Douay, and Y. Jaouen, “Ytterbium-doped solid core photonic bandgap fiber for laser operation around 980 nm,” Appl. Phys. Lett. 92, 061113 (2008).
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A. Isomäki and O. G. Okhotnikov, “Femtosecond soliton mode-locked laser based on ytterbium-doped photonic bandgap fiber,” Opt. Express 14, 9238–9243 (2006).
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Y. Ould-Agha, A. Bétourné, O. Vanvincq, G. Bouwmans, and Y. Quiquempois, “Broadband bandgap guidance and mode filtering in radially hybrid photonic crystal fiber,” Opt. Express 20, 6746–6760 (2012).
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F. Couny, F. Benabid, P. J. Roberts, P. S. Light, and M. G. Raymer, “Generation and photonic guidance of multioctave optical-frequency combs,” Science 318, 1118–1121 (2007).
[CrossRef]

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allen, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999).
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A. Snyder and J. Love, Optical Waveguide Theory (Kluwer Academic, 1983).

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M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1965).

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