Abstract

Soliton switching in nonlinear directional couplers implemented in photonic crystal fibers (PCF) examined here. A vector finite element method (FEM) has been developed to precisely calculate the dispersion along with coupling length of the guided modes. The PCF coupler geometry was carefully designed so that it can support soliton pulses. Soliton switching is demonstrated numerically at 1.55 µm for 100 femto-second (fs) pulses. Our theoretical results explain some of the key spectral features previously observed in the experiment.

© 2008 Optical Society of America

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References

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    [CrossRef]
  4. B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, and A. H. Greenaway, "Experimental study of dualcore photonic crystal fibre," Electron. Lett. 36, 1358-1359 (2000).
    [CrossRef]
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    [CrossRef]
  6. K. R. Khan and T. X. Wu, "Short pulse propagation in wavelength selective index guided photonics crystal fiber coupler," accepted by IEEE J. Sel. Top. Quantum Electron. 14, (May/June 2008).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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2008 (1)

K. R. Khan and T. X. Wu, "Short pulse propagation in wavelength selective index guided photonics crystal fiber coupler," accepted by IEEE J. Sel. Top. Quantum Electron. 14, (May/June 2008).

2007 (1)

A. V. Gorbach and D. V. Skryabin, "Light trapping in gravity-like potentials and expansion of supercontinuum spectra in photonic-crystal fibres," Nature Photon. 1,653-657 (2007).
[CrossRef]

2006 (3)

2004 (1)

2003 (5)

2002 (2)

2000 (1)

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

1999 (2)

A. L. Sala, B. G. Bagley, and R. T. Deck, "Temporal soliton switching in rectangular nonlinear directional coupler," Appl. Opt. 38, 5133-5143 (1999).
[CrossRef]

M. J. Gander, R. McBride, J. D. C. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, and P. S. J. Russell, "Experimental measurement of group velocity dispersion in photonic crystal fibre," Electron. Lett. 35, 63-64 (1999).
[CrossRef]

1988 (2)

1987 (2)

1984 (1)

D. N. Christodoulides and R. I. Joseph, "Femtosecond solitary waves in optical fibers," Electron. Lett. 20,659-660 (1984).
[CrossRef]

Bagley, B. G.

Bassi, P.

Bellanca, G.

Betlej, A.

Biancalana, F.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, and F. G. Omenetto, A. Efimov, and A. J. Taylor, "Transformation and control of ultra short pulses in dispersion engineered photonic crystal fibres," Nature 424, 511-515 (2003).
[CrossRef] [PubMed]

Birks, T. A.

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

M. J. Gander, R. McBride, J. D. C. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, and P. S. J. Russell, "Experimental measurement of group velocity dispersion in photonic crystal fibre," Electron. Lett. 35, 63-64 (1999).
[CrossRef]

Bise, R. T.

Bourkoff, E.

Christodoulides, D. N.

Deck, R. T.

DiGiovanni, D. J.

Doran, N. J.

Druon, F.

Efimov, A.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, and F. G. Omenetto, A. Efimov, and A. J. Taylor, "Transformation and control of ultra short pulses in dispersion engineered photonic crystal fibres," Nature 424, 511-515 (2003).
[CrossRef] [PubMed]

Eom, J. B.

Fini, J.

Fogli, F.

Friberg, S. R.

Gander, M. J.

M. J. Gander, R. McBride, J. D. C. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, and P. S. J. Russell, "Experimental measurement of group velocity dispersion in photonic crystal fibre," Electron. Lett. 35, 63-64 (1999).
[CrossRef]

Georges, P.

Gorbach, A. V.

A. V. Gorbach and D. V. Skryabin, "Light trapping in gravity-like potentials and expansion of supercontinuum spectra in photonic-crystal fibres," Nature Photon. 1,653-657 (2007).
[CrossRef]

Greenaway, A. H.

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

Hansen, K. P.

Hasegawa, T.

Jankovic, L.

Jones, J. D. C.

M. J. Gander, R. McBride, J. D. C. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, and P. S. J. Russell, "Experimental measurement of group velocity dispersion in photonic crystal fibre," Electron. Lett. 35, 63-64 (1999).
[CrossRef]

Joseph, R. I.

Khan, K. R.

K. R. Khan and T. X. Wu, "Short pulse propagation in wavelength selective index guided photonics crystal fiber coupler," accepted by IEEE J. Sel. Top. Quantum Electron. 14, (May/June 2008).

Kim, J.

Knight, J. C.

F. Luan, A. V. Yulin, J. C. Knight, and D. V. Skryabin, "Polarization instability of solitons in photonic crystal fibers," Opt. Express 146550-6556 (2006).
[CrossRef] [PubMed]

F. Luan, D. V. Skryabin, A. V. Yulin, and J. C. Knight, "Energy exchange between colliding solitons in photonic crystal fibers," Opt. Express 14, 9844-9853 (2006).
[CrossRef] [PubMed]

J. C. Knight, "Photonic crystal fibres," Nature 424, 847-51 (2003).
[CrossRef] [PubMed]

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, and F. G. Omenetto, A. Efimov, and A. J. Taylor, "Transformation and control of ultra short pulses in dispersion engineered photonic crystal fibres," Nature 424, 511-515 (2003).
[CrossRef] [PubMed]

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

M. J. Gander, R. McBride, J. D. C. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, and P. S. J. Russell, "Experimental measurement of group velocity dispersion in photonic crystal fibre," Electron. Lett. 35, 63-64 (1999).
[CrossRef]

Koshiba, M.

Lee, B. H.

Luan, F.

Lucas-Leclin, G.

Makris, K. G.

Mangan, B. J.

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

McBride, R.

M. J. Gander, R. McBride, J. D. C. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, and P. S. J. Russell, "Experimental measurement of group velocity dispersion in photonic crystal fibre," Electron. Lett. 35, 63-64 (1999).
[CrossRef]

Mogilevtsev, D.

M. J. Gander, R. McBride, J. D. C. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, and P. S. J. Russell, "Experimental measurement of group velocity dispersion in photonic crystal fibre," Electron. Lett. 35, 63-64 (1999).
[CrossRef]

Moon, D. S.

Omenetto, F. G.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, and F. G. Omenetto, A. Efimov, and A. J. Taylor, "Transformation and control of ultra short pulses in dispersion engineered photonic crystal fibres," Nature 424, 511-515 (2003).
[CrossRef] [PubMed]

Paek, U.-C.

Petersson, A.

Reeves, W. H.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, and F. G. Omenetto, A. Efimov, and A. J. Taylor, "Transformation and control of ultra short pulses in dispersion engineered photonic crystal fibres," Nature 424, 511-515 (2003).
[CrossRef] [PubMed]

Russell, P. S. J.

M. J. Gander, R. McBride, J. D. C. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, and P. S. J. Russell, "Experimental measurement of group velocity dispersion in photonic crystal fibre," Electron. Lett. 35, 63-64 (1999).
[CrossRef]

Russell, P. St. J.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, and F. G. Omenetto, A. Efimov, and A. J. Taylor, "Transformation and control of ultra short pulses in dispersion engineered photonic crystal fibres," Nature 424, 511-515 (2003).
[CrossRef] [PubMed]

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

Saccomandi, L.

Saitoh, K.

Sala, A. L.

Sanner, N.

Sasaoka, E.

Sato, Y.

Sfez, B. G.

Silberberg, Y.

Skryabin, D. V.

A. V. Gorbach and D. V. Skryabin, "Light trapping in gravity-like potentials and expansion of supercontinuum spectra in photonic-crystal fibres," Nature Photon. 1,653-657 (2007).
[CrossRef]

F. Luan, D. V. Skryabin, A. V. Yulin, and J. C. Knight, "Energy exchange between colliding solitons in photonic crystal fibers," Opt. Express 14, 9844-9853 (2006).
[CrossRef] [PubMed]

F. Luan, A. V. Yulin, J. C. Knight, and D. V. Skryabin, "Polarization instability of solitons in photonic crystal fibers," Opt. Express 146550-6556 (2006).
[CrossRef] [PubMed]

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, and F. G. Omenetto, A. Efimov, and A. J. Taylor, "Transformation and control of ultra short pulses in dispersion engineered photonic crystal fibres," Nature 424, 511-515 (2003).
[CrossRef] [PubMed]

Smith, P. S.

Stegeman, G. I.

Suntsov, S.

Taylor, A. J.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, and F. G. Omenetto, A. Efimov, and A. J. Taylor, "Transformation and control of ultra short pulses in dispersion engineered photonic crystal fibres," Nature 424, 511-515 (2003).
[CrossRef] [PubMed]

Trillo, S.

Weiner, A. M.

Wibnitz, S.

Woods, D.

Wright, E.

Wu, T. X.

K. R. Khan and T. X. Wu, "Short pulse propagation in wavelength selective index guided photonics crystal fiber coupler," accepted by IEEE J. Sel. Top. Quantum Electron. 14, (May/June 2008).

Yang, G.-H.

Yulin, A. V.

Zhao, W.

Appl. Opt. (2)

Electron. Lett. (3)

D. N. Christodoulides and R. I. Joseph, "Femtosecond solitary waves in optical fibers," Electron. Lett. 20,659-660 (1984).
[CrossRef]

M. J. Gander, R. McBride, J. D. C. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, and P. S. J. Russell, "Experimental measurement of group velocity dispersion in photonic crystal fibre," Electron. Lett. 35, 63-64 (1999).
[CrossRef]

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

IEEE J. Sel. Top. Quantum Electron. (1)

K. R. Khan and T. X. Wu, "Short pulse propagation in wavelength selective index guided photonics crystal fiber coupler," accepted by IEEE J. Sel. Top. Quantum Electron. 14, (May/June 2008).

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

Nature (2)

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, and F. G. Omenetto, A. Efimov, and A. J. Taylor, "Transformation and control of ultra short pulses in dispersion engineered photonic crystal fibres," Nature 424, 511-515 (2003).
[CrossRef] [PubMed]

J. C. Knight, "Photonic crystal fibres," Nature 424, 847-51 (2003).
[CrossRef] [PubMed]

Nature Photon. (1)

A. V. Gorbach and D. V. Skryabin, "Light trapping in gravity-like potentials and expansion of supercontinuum spectra in photonic-crystal fibres," Nature Photon. 1,653-657 (2007).
[CrossRef]

Opt. Express (6)

Opt. Lett. (5)

Other (2)

G. P Agarwal, Nonlinear Fiber Optics, 3rd Edition (Academic press, 2001).

J. Jin, The Finite Element Method in Electromagnetics (J. Wiley & Sons, 2002).

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Figures (10)

Fig. 1.
Fig. 1.

Dual Core PCF geometry.

Fig. 2.
Fig. 2.

Soliton pulse propagation at 1.55 µm through the PCF coupler shown in Fig. 1(d=2.0 µm, C=2Λ and d/Λ=0.9) (a) bar channel and (b) cross channel.

Fig. 3.
Fig. 3.

2D view of 100 fs pulse propagation through the PCF bar channel: (a) Dispersed pulse at 20W peak power (b) Soliton pulse at 800W peak power.

Fig. 4.
Fig. 4.

Normalized power in bar channel P1 and cross channel P2 (a) at 4.16 GW/ cm2 (b) at 583 GW/ cm2

Fig. 5.
Fig. 5.

Transmission of the dual core PCF coupler (d=2.0 µm, C=2Λ and d/Λ=0.9) versus input intensity.

Fig. 6.
Fig. 6.

Coupling length of the dual core PCF sample (Five rings, d=1.0 µm, µ=2.5µm and C=10 µm): (a) PCF geometry (b) Lc.

Fig. 7.
Fig. 7.

Coupling coefficient of the dual core PCF sample: (a) κ0 (b) κ1 .

Fig. 8.
Fig. 8.

Frequency dependent dispersion characteristics of the PCF sample (a) β2 (b) β3 and (c) β4 .

Fig. 9.
Fig. 9.

Input pulse shape and the pulse shapes output from a 9mm PCF coupler (both bar and cross channel) are at a peak pulse power of: (a) 4 kW (b) 40 kW and (c) 114 kW.

Fig.10.
Fig.10.

Wavelength response of the cross channel output pulse of 9 mm PCF coupler shown in Fig. 6(a) at a peak pulse power of: (a) 4 kW (b) 40 kW and (c) 114 kW.

Equations (14)

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

× ( 1 μ r × E ) k 0 2 n 2 E = 0
t × ( 1 μ r t × E t ) + 1 μ r ( k z 2 t E z + k z 2 E t ) = k 0 2 n 2 E t
1 μ r [ t · ( t E z + E t ) ] = k 0 2 n 2 E z
n eff = Real ( k z ) k 0
L c = π k ze k zo
i q 1 z β 2 2 2 q 1 τ 2 i β 3 6 3 q 1 τ 3 + γ ( q 1 2 + η q 2 2 ) q 1 + i γ ω τ ( q 1 q 1 2 ) + π 2 L c q 2 = 0
i q 2 z β 2 2 2 q 2 τ 2 i β 3 6 3 q 2 τ 3 + γ ( q 2 2 + η q 1 2 ) q 2 + i γ ω τ ( q 2 q 2 2 ) + π 2 L c q 1 = 0
γ = ( n 2 ω c A eff )
A eff = ( E ( x , y ) 2 dxdy ) 2 E ( x , y ) 4 dxdy
i q 1 z β 2 2 2 q 1 τ 2 i β 3 6 3 q 1 τ 3 + β 4 24 4 q 1 τ 4 + γ ( q 1 2 + η q 2 2 ) q 1 +
i γ ω τ ( q 1 q 1 2 ) γ q 1 T R τ ( q 1 2 ) + κ 0 q 2 + κ 1 q 2 τ = 0
i q 2 z β 2 2 2 q 2 τ 2 i β 3 6 3 q 2 τ 3 + β 4 24 4 q 2 τ 4 + γ ( q 2 2 + η q 1 2 ) q 2 +
i γ ω τ ( q 2 q 2 2 ) γ q 2 T R τ ( q 2 2 ) + κ 0 q 1 + κ 1 q 1 τ = 0
κ = k ze k zo 2 = π 2 L c

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