Abstract

Novel type of microstructured optical fiber couplers is introduced where energy transfer is enabled by transverse resonator arrays built into a fiber crossection. Such a design allows unlimited spatial separation between interacting fiber cores which, in turn, eliminates inter-core crosstalk via proximity coupling, thus enabling scalable integration of many fiber cores. Moreover, in the limit of weak inter-resonator coupling, resonator arrays exhibit moderate polarization dependence.

© 2006 Optical Society of America

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References

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  1. M. Skorobogatiy, K. Saitoh, and M. Koshiba, "Transverse lightwave circuits in microstructured optical fibers: waveguides," Opt. Express 13, 7506-7515 (2005)http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-19-7506
    [CrossRef] [PubMed]
  2. B.J. Mangan, J.C. Knight, T.A. Birks, P.St.J. Russell, and A.H. Greenaway, "Experimental study of dual-core photonic crystal fibre," Electron. Lett. 36, 1358-1359 (2000).
    [CrossRef]
  3. B.H. Lee, J.B. Eom, J. Kim, D.S. Moon, U.-C. Paek, and G.-H. Yang, "Photonic crystal fiber coupler," Opt. Lett. 27, 812-814 (2002).
    [CrossRef]
  4. J. Canning, M.A. van Eijkelenborg, T. Ryan, M. Kristensen, K. Lyytikainen, "Complex mode coupling within air-silica structured optical fibres and applications," Opt. Commun. 185, 321 (2000).
    [CrossRef]
  5. W.E.P. Padden, M.A. van Eijkelenborg, A. Argyros, N. A. Issa, "Coupling in a twin-core microstructured polymer optical fiber," Appl. Phys. Lett. 84, 1689-1691 (2004).
    [CrossRef]
  6. H. Kim, J. Kim, U.-C. Paek, B.H. Lee, and K. T. Kim, "Tunable photonic crystal fiber coupler based on a sidepolishing technique," Opt. Lett. 29, 1194-1196 (2004).
    [CrossRef] [PubMed]
  7. J. Laegsgaard, O. Bang, and A. Bjarklev, "Photonic crystal fiber design for broadband directional coupling," Opt. Lett. 29, 2473-2475 (2004).
    [CrossRef] [PubMed]
  8. K. Saitoh and M. Koshiba, "Leakage loss and group velocity dispersion in air-core photonic bandgap fibers," Opt. Express 11, 3100 (2003).
    [CrossRef] [PubMed]
  9. K. Saitoh, M. Koshiba, "Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: application to photonic vrystal fibers," J. Quantum Electron. 38, 927-933 (2002).
    [CrossRef]
  10. K. Saitoh, M. Koshiba, "Full-vectorial imaginary-distance beam propagation method with perfectly matched layers for anysotropic optical waveguides," J. Lightwave Technol. 19, 405-413 (2001).
    [CrossRef]
  11. H.A. Haus, W.P. Huang, S. Kawakami, N. A. Whitaker, "Coupled-mode theory of optical waveguides," J. Lightwave Technol. 5, 16 (1987).
    [CrossRef]
  12. M. Skorobogatiy, M. Ibanescu, S.G. Johnson, O. Weiseberg, T.D. Engeness, M. Soljacic, S.A. Jacobs, and Y. Fink, "Analysis of general geometric scaling perturbations in a transmitting waveguide. The fundamental connection between polarization mode dispersion and group-velocity dispersion," J. Opt. Soc. Am. B 19, 2867-2875 (2002).
    [CrossRef]

2005 (1)

2004 (3)

2003 (1)

2002 (3)

2001 (1)

2000 (2)

J. Canning, M.A. van Eijkelenborg, T. Ryan, M. Kristensen, K. Lyytikainen, "Complex mode coupling within air-silica structured optical fibres and applications," Opt. Commun. 185, 321 (2000).
[CrossRef]

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

1987 (1)

H.A. Haus, W.P. Huang, S. Kawakami, N. A. Whitaker, "Coupled-mode theory of optical waveguides," J. Lightwave Technol. 5, 16 (1987).
[CrossRef]

Argyros, A.

W.E.P. Padden, M.A. van Eijkelenborg, A. Argyros, N. A. Issa, "Coupling in a twin-core microstructured polymer optical fiber," Appl. Phys. Lett. 84, 1689-1691 (2004).
[CrossRef]

Bang, O.

Birks, T.A.

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

Bjarklev, A.

Canning, J.

J. Canning, M.A. van Eijkelenborg, T. Ryan, M. Kristensen, K. Lyytikainen, "Complex mode coupling within air-silica structured optical fibres and applications," Opt. Commun. 185, 321 (2000).
[CrossRef]

Engeness, T.D.

Eom, J.B.

Fink, Y.

Greenaway, A.H.

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

Haus, H.A.

H.A. Haus, W.P. Huang, S. Kawakami, N. A. Whitaker, "Coupled-mode theory of optical waveguides," J. Lightwave Technol. 5, 16 (1987).
[CrossRef]

Huang, W.P.

H.A. Haus, W.P. Huang, S. Kawakami, N. A. Whitaker, "Coupled-mode theory of optical waveguides," J. Lightwave Technol. 5, 16 (1987).
[CrossRef]

Ibanescu, M.

Issa, N. A.

W.E.P. Padden, M.A. van Eijkelenborg, A. Argyros, N. A. Issa, "Coupling in a twin-core microstructured polymer optical fiber," Appl. Phys. Lett. 84, 1689-1691 (2004).
[CrossRef]

Jacobs, S.A.

Johnson, S.G.

Kawakami, S.

H.A. Haus, W.P. Huang, S. Kawakami, N. A. Whitaker, "Coupled-mode theory of optical waveguides," J. Lightwave Technol. 5, 16 (1987).
[CrossRef]

Kim, H.

Kim, J.

Kim, K. T.

Knight, J.C.

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

Koshiba, M.

Kristensen, M.

J. Canning, M.A. van Eijkelenborg, T. Ryan, M. Kristensen, K. Lyytikainen, "Complex mode coupling within air-silica structured optical fibres and applications," Opt. Commun. 185, 321 (2000).
[CrossRef]

Laegsgaard, J.

Lee, B.H.

Lyytikainen, K.

J. Canning, M.A. van Eijkelenborg, T. Ryan, M. Kristensen, K. Lyytikainen, "Complex mode coupling within air-silica structured optical fibres and applications," Opt. Commun. 185, 321 (2000).
[CrossRef]

Mangan, B.J.

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

Moon, D.S.

Padden, W.E.P.

W.E.P. Padden, M.A. van Eijkelenborg, A. Argyros, N. A. Issa, "Coupling in a twin-core microstructured polymer optical fiber," Appl. Phys. Lett. 84, 1689-1691 (2004).
[CrossRef]

Paek, U.-C.

Russell, P.St.J.

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

Ryan, T.

J. Canning, M.A. van Eijkelenborg, T. Ryan, M. Kristensen, K. Lyytikainen, "Complex mode coupling within air-silica structured optical fibres and applications," Opt. Commun. 185, 321 (2000).
[CrossRef]

Saitoh, K.

Skorobogatiy, M.

Soljacic, M.

van Eijkelenborg, M.A.

W.E.P. Padden, M.A. van Eijkelenborg, A. Argyros, N. A. Issa, "Coupling in a twin-core microstructured polymer optical fiber," Appl. Phys. Lett. 84, 1689-1691 (2004).
[CrossRef]

J. Canning, M.A. van Eijkelenborg, T. Ryan, M. Kristensen, K. Lyytikainen, "Complex mode coupling within air-silica structured optical fibres and applications," Opt. Commun. 185, 321 (2000).
[CrossRef]

Weiseberg, O.

Whitaker, N. A.

H.A. Haus, W.P. Huang, S. Kawakami, N. A. Whitaker, "Coupled-mode theory of optical waveguides," J. Lightwave Technol. 5, 16 (1987).
[CrossRef]

Yang, G.-H.

Appl. Phys. Lett. (1)

W.E.P. Padden, M.A. van Eijkelenborg, A. Argyros, N. A. Issa, "Coupling in a twin-core microstructured polymer optical fiber," Appl. Phys. Lett. 84, 1689-1691 (2004).
[CrossRef]

Electron. Lett. (1)

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

J. Lightwave Technol. (2)

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

J. Quantum Electron. (1)

K. Saitoh, M. Koshiba, "Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: application to photonic vrystal fibers," J. Quantum Electron. 38, 927-933 (2002).
[CrossRef]

Opt. Commun. (1)

J. Canning, M.A. van Eijkelenborg, T. Ryan, M. Kristensen, K. Lyytikainen, "Complex mode coupling within air-silica structured optical fibres and applications," Opt. Commun. 185, 321 (2000).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of a two hollow core MOF coupler. Cores are separated by N lattice periods. Transverse waveguide is formed by a periodic array of holes of smaller diameter (resonators) separated by Nrr periods; Nwr holes closest to the cores are not modified.

Fig. 2.
Fig. 2.

Schematic of the supermode dispersion relations in weakly coupled a) 1, b) 2, c) 3 resonator arrays. Dispersion relations are plotted with respect to the one of a stand alone hollow core waveguide. Solid red curves - even supermodes, dotted blue curves - odd su-permodes. Black dotted curve - dispersion relation of a fundamental mode of a stand alone resonator. Inserts - schematics of the field distributions at a phase matching point λ 0.

Fig. 3.
Fig. 3.

Supermode analysis predictions. Coupling length, loss per one coupling length, and intensities of electric fields at resonances for the weakly coupled a) 1, b) 2, c) 3 resonator arrays. Dotted blue curves - x polarization, solid red curves - y polarization.

Fig. 4.
Fig. 4.

Schematic of supermode dispersion relations in a weakly coupled Nr = 11 resonator array. Dispersion relations are plotted with respect to the one of a stand alone hollow core waveguide. Solid red curves - even supermodes, dotted blue curves - odd supermodes, black dotted curve - resonator mode in the absence of coupling. At each of the Nr coupling resonances λi,i = [-5,5] energy transfer from one hollow core into the other is possible via excitation of one of the collective resonance of an 11 resonator array.

Fig. 5.
Fig. 5.

Comparison between modal analysis predictions and BPM simulations for the a) coupling length, b) loss per one coupling length. Solid curves - mode analysis, dotted curves with circles - BPM. Blue curves - x polarization, red curves - y polarization; c) BPM simulations of power transfer from the left core into the right core. Blue dotted curves (x polarization) and red solid curves (y polarization) - power in the left and right cores after one coupling length; black curves - total power in both cores after one coupling length. Cyan dotted curves with circles (x polarization) and magenta solid curves with circles (x polarization) - power in the cores after propagation over a fixed distance Lc = 10.5cm corresponding to a coupling length at the resonance λ ≃ 1.3118μm.

Equations (10)

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F t ( r t , λ ) = i = 1 N r + 2 P i ( λ ) F ti 0 ( r t , λ 0 ) ,
β ( λ ) N P ¯ ( λ ) = ND ( λ ) P ¯ ( λ ) + Δ H P ¯ ( λ ) .
N j , i = 1 4 z ̂ d r t ( E t i 0 × H t j 0 * + E t j 0 * × H t i 0 )
ΔH j , i = ω 4 d r t ( ε ε i ) ( E t j 0 * · E t i 0 * + ε j ε E zj 0 * E zi 0 ) .
D i , i ( λ ) = β i 0 ( λ )
N = 1 N wr L N wr L * 1 N rr N rr * 1 N rr . . . N rr * 1 N rr N rr * 1 N wr R * N wr R 1 ; Δ H = 0 C wr L C rw L 0 C rr LR C rr RL 0 C rr LR . . . C rr RL 0 C rr LR C rr RL 0 C rw R C wr R 0 ,
L c = λ ( 2 Δ n eff )
Δ n eff = min ( Re ( n eff 1 n eff 2 ) , Re ( n eff 2 n eff 3 ) ) .
L d = λ ( 4 π max ( Im ( n eff 1 ) , Im ( n eff 2 ) , Im ( n eff 3 ) ) .
P ( L c ) P ( 0 ) = exp ( L c L d )

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