Abstract

We have theoretically and experimentally investigated dual-core photonic bandgap fibers (PBGFs), which consist of a cladding with an array of high-index rods and two cores formed by omitting two nearby rods. We find novel features in their coupling characteristics such as maxima and minima in coupling length, complete decoupling of the cores, and an inversion of the usual ordering of supermodes so that the odd supermode has the higher propagation constant. This behavior is understood by considering the field distribution in the rods between the cores.

© 2007 Optical Society of America

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  1. F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D. M. Bird, J. C. Knight, and P. S. J. Russell, "All-solid photonic bandgap fiber," Opt. Lett. 29, 2369-2371 (2004).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  5. K. Saitoh, Y. Sato, and M. Koshiba, "Coupling characteristics of dual-core photonic crystal fiber couplers," Opt. Express 11, 3188-3195 (2003).
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  8. Z. Wang, G. Y. Kai, Y. G. Liu, J. F. Liu, C. S. Zhang, T. T. Sun, C. Wang, W. G. Zhang, S. Z. Yuan, and X. Y. Dong, "Coupling and decoupling of dual-core photonic bandgap fibers," Opt. Lett. 30, 2542-2544 (2005).
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    [CrossRef] [PubMed]
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    [CrossRef]
  11. T. Koponen, A. Huttunen, and P. Torma, "Conditions for waveguide decoupling in square-lattice photonic crystals," J. Appl. Phys. 96, 4039-4041 (2004).
    [CrossRef]
  12. F. S. S. Chien, S. C. Cheng, Y. J. Hsu, and W. F. Hsieh, "Dual-band multiplexer/demultiplexer with photonic-crystal-waveguide couplers for bidirectional communications," Opt. Commun. 266, 592-597 (2006).
    [CrossRef]
  13. Y. Tanaka, H. Nakamura, Y. Sugimoto, N. Ikeda, K. Asakawa, and K. Inoue, "Coupling properties in a 2-D photonic crystal slab directional coupler with a triangular lattice of air holes," IEEE J. Quantum Electron 41, 76-84 (2005).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  17. G. J. Pearce, T. D. Hedley, and D. M. Bird, "Adaptive curvilinear coordinates in a plain-wave solution of Maxwell's equations in photonic crystals," Phys. Rev. B 71, 195108 (2005)
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    [CrossRef] [PubMed]
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    [CrossRef]
  20. CUDOS MOF UTILITIES Software ©Commonwealth of Australia 2004. All rights reserved. http://www.physics.usyd.edu.au/cudos/mofsoftware/
  21. W. J. Wadsworth, N. Joly, J. C. Knight, T. A. Birks, F. Biancalana, and P. S. J. Russell, "Supercontinuum and four-wave mixing with Q-switched pulses in endlessly single-mode photonic crystal fibres," Opt. Express 12, 299-309 (2004).
    [CrossRef] [PubMed]

2006 (2)

F. S. S. Chien, S. C. Cheng, Y. J. Hsu, and W. F. Hsieh, "Dual-band multiplexer/demultiplexer with photonic-crystal-waveguide couplers for bidirectional communications," Opt. Commun. 266, 592-597 (2006).
[CrossRef]

M. Skorobogatiy, K. Saitoh, and M. Koshiba, "Transverse light guides in microstructured optical fibers," Opt. Lett. 31, 314-316 (2006).
[CrossRef] [PubMed]

2005 (6)

2004 (5)

2003 (1)

2002 (1)

S. Boscolo, M. Midrio, and C. G. Someda, "Coupling and decoupling of electromagnetic waves in parallel 2-D photonic crystal waveguides," IEEE J. Quantum Electron. 38, 47-53 (2002).
[CrossRef]

2001 (2)

2000 (1)

B. J. Mangan, J. C. Knight, T. A. Birks, P. S. Russell, and A. H. Greenaway, "Experimental study of dual-core photonic crystal fibre," Electron. Lett. 36, 1358-1359 (2000).
[CrossRef]

1991 (1)

Argyros, A.

Arriaga, J.

Asakawa, K.

Y. Tanaka, H. Nakamura, Y. Sugimoto, N. Ikeda, K. Asakawa, and K. Inoue, "Coupling properties in a 2-D photonic crystal slab directional coupler with a triangular lattice of air holes," IEEE J. Quantum Electron 41, 76-84 (2005).
[CrossRef]

Bang, O.

Biancalana, F.

Bigot, L.

Bird, D. M.

G. J. Pearce, T. D. Hedley, and D. M. Bird, "Adaptive curvilinear coordinates in a plain-wave solution of Maxwell's equations in photonic crystals," Phys. Rev. B 71, 195108 (2005)

F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D. M. Bird, J. C. Knight, and P. S. J. Russell, "All-solid photonic bandgap fiber," Opt. Lett. 29, 2369-2371 (2004).
[CrossRef] [PubMed]

Birks, T. A.

Bjarklev, A.

Boscolo, S.

S. Boscolo, M. Midrio, and C. G. Someda, "Coupling and decoupling of electromagnetic waves in parallel 2-D photonic crystal waveguides," IEEE J. Quantum Electron. 38, 47-53 (2002).
[CrossRef]

Bouwmans, G.

Cheng, S. C.

F. S. S. Chien, S. C. Cheng, Y. J. Hsu, and W. F. Hsieh, "Dual-band multiplexer/demultiplexer with photonic-crystal-waveguide couplers for bidirectional communications," Opt. Commun. 266, 592-597 (2006).
[CrossRef]

Chien, F. S. S.

F. S. S. Chien, S. C. Cheng, Y. J. Hsu, and W. F. Hsieh, "Dual-band multiplexer/demultiplexer with photonic-crystal-waveguide couplers for bidirectional communications," Opt. Commun. 266, 592-597 (2006).
[CrossRef]

Cordeiro, C. M. B.

Dong, X. Y.

Douay, M.

George, A. K.

Greenaway, A. H.

B. J. Mangan, J. C. Knight, T. A. Birks, P. S. Russell, and A. H. Greenaway, "Experimental study of dual-core photonic crystal fibre," Electron. Lett. 36, 1358-1359 (2000).
[CrossRef]

Hedley, T. D.

G. J. Pearce, T. D. Hedley, and D. M. Bird, "Adaptive curvilinear coordinates in a plain-wave solution of Maxwell's equations in photonic crystals," Phys. Rev. B 71, 195108 (2005)

F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D. M. Bird, J. C. Knight, and P. S. J. Russell, "All-solid photonic bandgap fiber," Opt. Lett. 29, 2369-2371 (2004).
[CrossRef] [PubMed]

Hsieh, W. F.

F. S. S. Chien, S. C. Cheng, Y. J. Hsu, and W. F. Hsieh, "Dual-band multiplexer/demultiplexer with photonic-crystal-waveguide couplers for bidirectional communications," Opt. Commun. 266, 592-597 (2006).
[CrossRef]

Hsu, Y. J.

F. S. S. Chien, S. C. Cheng, Y. J. Hsu, and W. F. Hsieh, "Dual-band multiplexer/demultiplexer with photonic-crystal-waveguide couplers for bidirectional communications," Opt. Commun. 266, 592-597 (2006).
[CrossRef]

Huttunen, A.

T. Koponen, A. Huttunen, and P. Torma, "Conditions for waveguide decoupling in square-lattice photonic crystals," J. Appl. Phys. 96, 4039-4041 (2004).
[CrossRef]

Ikeda, N.

Y. Tanaka, H. Nakamura, Y. Sugimoto, N. Ikeda, K. Asakawa, and K. Inoue, "Coupling properties in a 2-D photonic crystal slab directional coupler with a triangular lattice of air holes," IEEE J. Quantum Electron 41, 76-84 (2005).
[CrossRef]

Inoue, K.

Y. Tanaka, H. Nakamura, Y. Sugimoto, N. Ikeda, K. Asakawa, and K. Inoue, "Coupling properties in a 2-D photonic crystal slab directional coupler with a triangular lattice of air holes," IEEE J. Quantum Electron 41, 76-84 (2005).
[CrossRef]

Joannopoulos, J. D.

Johnson, S. G.

Joly, N.

Kai, G. Y.

Knight, J. C.

Koponen, T.

T. Koponen, A. Huttunen, and P. Torma, "Conditions for waveguide decoupling in square-lattice photonic crystals," J. Appl. Phys. 96, 4039-4041 (2004).
[CrossRef]

Koshiba, M.

Laegsgaard, J.

Lægsgaard, J.

J. Lægsgaard, "Gap formation and guided modes in photonic band gap fibres with high-inex rods," J. Opt. A: Pure Appl. Opt. 6, 798-804 (2004).
[CrossRef]

Laegsgaard, J.

Leon-Saval, S. G.

Liu, J. F.

Liu, Y. G.

Lopez, F.

Luan, F.

Mangan, B. J.

B. J. Mangan, J. Arriaga, T. A. Birks, J. C. Knight, and P. St. J. Russell, "Fundamental-mode cutoff in a photonic crystal fiber with a depressed-index core," Opt. Lett. 26, 1469-1471 (2001).
[CrossRef]

B. J. Mangan, J. C. Knight, T. A. Birks, P. S. Russell, and A. H. Greenaway, "Experimental study of dual-core photonic crystal fibre," Electron. Lett. 36, 1358-1359 (2000).
[CrossRef]

Midrio, M.

S. Boscolo, M. Midrio, and C. G. Someda, "Coupling and decoupling of electromagnetic waves in parallel 2-D photonic crystal waveguides," IEEE J. Quantum Electron. 38, 47-53 (2002).
[CrossRef]

Nakamura, H.

Y. Tanaka, H. Nakamura, Y. Sugimoto, N. Ikeda, K. Asakawa, and K. Inoue, "Coupling properties in a 2-D photonic crystal slab directional coupler with a triangular lattice of air holes," IEEE J. Quantum Electron 41, 76-84 (2005).
[CrossRef]

Pearce, G. J.

G. J. Pearce, T. D. Hedley, and D. M. Bird, "Adaptive curvilinear coordinates in a plain-wave solution of Maxwell's equations in photonic crystals," Phys. Rev. B 71, 195108 (2005)

F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D. M. Bird, J. C. Knight, and P. S. J. Russell, "All-solid photonic bandgap fiber," Opt. Lett. 29, 2369-2371 (2004).
[CrossRef] [PubMed]

Provino, L.

Quiquempois, Y.

Russell, P. S.

B. J. Mangan, J. C. Knight, T. A. Birks, P. S. Russell, and A. H. Greenaway, "Experimental study of dual-core photonic crystal fibre," Electron. Lett. 36, 1358-1359 (2000).
[CrossRef]

Russell, P. S. J.

Russell, P. St. J.

Saitoh, K.

Sato, Y.

Skorobogatiy, M.

Someda, C. G.

S. Boscolo, M. Midrio, and C. G. Someda, "Coupling and decoupling of electromagnetic waves in parallel 2-D photonic crystal waveguides," IEEE J. Quantum Electron. 38, 47-53 (2002).
[CrossRef]

C. G. Someda, "Antiresonant decoupling of parallel dielectric wave-guides," Opt. Lett. 16, 1240-1242 (1991).
[CrossRef] [PubMed]

Sugimoto, Y.

Y. Tanaka, H. Nakamura, Y. Sugimoto, N. Ikeda, K. Asakawa, and K. Inoue, "Coupling properties in a 2-D photonic crystal slab directional coupler with a triangular lattice of air holes," IEEE J. Quantum Electron 41, 76-84 (2005).
[CrossRef]

Sun, T. T.

Tanaka, Y.

Y. Tanaka, H. Nakamura, Y. Sugimoto, N. Ikeda, K. Asakawa, and K. Inoue, "Coupling properties in a 2-D photonic crystal slab directional coupler with a triangular lattice of air holes," IEEE J. Quantum Electron 41, 76-84 (2005).
[CrossRef]

Torma, P.

T. Koponen, A. Huttunen, and P. Torma, "Conditions for waveguide decoupling in square-lattice photonic crystals," J. Appl. Phys. 96, 4039-4041 (2004).
[CrossRef]

Wadsworth, W. J.

Wang, C.

Wang, Z.

Yuan, S. Z.

Zhang, C. S.

Zhang, W. G.

Electron. Lett. (1)

B. J. Mangan, J. C. Knight, T. A. Birks, P. S. Russell, and A. H. Greenaway, "Experimental study of dual-core photonic crystal fibre," Electron. Lett. 36, 1358-1359 (2000).
[CrossRef]

IEEE J. Quantum Electron (1)

Y. Tanaka, H. Nakamura, Y. Sugimoto, N. Ikeda, K. Asakawa, and K. Inoue, "Coupling properties in a 2-D photonic crystal slab directional coupler with a triangular lattice of air holes," IEEE J. Quantum Electron 41, 76-84 (2005).
[CrossRef]

IEEE J. Quantum Electron. (1)

S. Boscolo, M. Midrio, and C. G. Someda, "Coupling and decoupling of electromagnetic waves in parallel 2-D photonic crystal waveguides," IEEE J. Quantum Electron. 38, 47-53 (2002).
[CrossRef]

J. Appl. Phys. (1)

T. Koponen, A. Huttunen, and P. Torma, "Conditions for waveguide decoupling in square-lattice photonic crystals," J. Appl. Phys. 96, 4039-4041 (2004).
[CrossRef]

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

J. Lægsgaard, "Gap formation and guided modes in photonic band gap fibres with high-inex rods," J. Opt. A: Pure Appl. Opt. 6, 798-804 (2004).
[CrossRef]

Opt. Commun. (1)

F. S. S. Chien, S. C. Cheng, Y. J. Hsu, and W. F. Hsieh, "Dual-band multiplexer/demultiplexer with photonic-crystal-waveguide couplers for bidirectional communications," Opt. Commun. 266, 592-597 (2006).
[CrossRef]

Opt. Express (5)

Opt. Lett. (7)

Phys. Rev. B (1)

G. J. Pearce, T. D. Hedley, and D. M. Bird, "Adaptive curvilinear coordinates in a plain-wave solution of Maxwell's equations in photonic crystals," Phys. Rev. B 71, 195108 (2005)

Other (2)

CUDOS MOF UTILITIES Software ©Commonwealth of Australia 2004. All rights reserved. http://www.physics.usyd.edu.au/cudos/mofsoftware/

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

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Figures (9)

Fig. 1.
Fig. 1.

Dual-core PBGFs with core separations Dc of (a) 2Λ and (b) √3Λ.

Fig. 2.
Fig. 2.

Photonic DOS plotted against normalized frequency kΛ and effective index neff for the cladding of Fig. 1. The bandgaps (DOS = 0) are in red, with non-zero DOS in the bands represented on a grayscale (light for high DOS and dark for low DOS). Also marked are the modes of the rods from which the bands are formed [19].

Fig. 3.
Fig. 3.

Effective indices of the y-polarized even and odd supermodes in the (a) second and (b) third bandgaps, for both core separations Dc .

Fig. 4.
Fig. 4.

Coupling length Lc against frequency in both bandgaps, for both core separations and polarizations of light.

Fig. 5.
Fig. 5.

The dominant Ey field distribution for the y-polarized core-guided mode in a single-core PBGFs near the four band edges (a) kΛ=36, (b) kΛ=44, (c) kΛ=56, and (d) kΛ=64, over a quarter area (the rest is given by reflection symmetry). Field amplitude is represented by the scale on the right; to show the field distribution in the rods, the field in the guiding core is saturated. The labels 2Λ and √3Λ indicate a rod that could be removed to form the respective dual-core structures of Fig. 1, together with the corresponding lines of symmetry. The inset in each figure is the field of the LP lm rod mode forming the adjacent band edge, as would appear in the rod on which the symmetry axes have been marked in the main figure. The rod mode is therefore oriented to be symmetric about the line from the centre of the PBGF’s core.

Fig. 6.
Fig. 6.

Field distributions in the single-core PBGF along the line joining the center of the core and the centre of the rod that would be omitted to form a Dc = 2Λ structure, for frequencies in the middle of the two bandgaps. (The fields vary only in detail across each bandgap.) Also marked is where the second core would lie.

Fig. 7.
Fig. 7.

(a). The refractive index profile of the high index Ge-doped rod. Optical micrograph of the fibers for (b) Dc = 2Λ, (c) Dc = √3Λ. The outer diameter of the fibers was 210 μm.

Fig. 8.
Fig. 8.

(a). Transmission spectra of Dc = 2Λ fiber in the 2nd and 3rd bandgap. (b) Normalized intensity of (a) in the 2nd bandgap. Fiber length is 185 mm.

Fig. 9.
Fig. 9.

Coupling length as a function of normalized frequency in the fibers shown in Fig. 6. Solid curves represent the numerical results and dots represent the experimental results.

Equations (1)

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L c = π β even β odd = π k n even n odd

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