Abstract

We demonstrate by numerical simulations of coupled generalized nonlinear Schrödinger equations that the input pulse duration as well as the retarded material response have a crucial impact on the properties of an ultrafast nonlinear optofluidic fiber coupler. This device is composed of two waveguides in close vicinity embedded in a photonic crystal fiber which are filled with a highly nonlinear liquid. We show that in particular the critical peak power above which the coupling between the waveguides is suppressed increases dramatically for short input pulses and long characteristic response times of the liquid. We establish a simple model which describes these effects with high accuracy.

© 2011 OSA

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  1. M. Vieweg, T. Gissibl, S. Pricking, B. J. Eggleton, D. C. Wu, B. T. Kuhlmey, and H. Giessen, “Ultrafast nonlinear optofluidics in selectively liquid-filled photonic crystal fibers,” Opt. Express 18, 25232–25240 (2010).
    [CrossRef] [PubMed]
  2. B. Kuhlmey, B. J. Eggleton, and D. K. Wu, “Fluid-filled solid-core photonic bandgap fibers,” J. Lightwave Technol. 27, 1617–1630 (2009).
    [CrossRef]
  3. St. M. Jensen, “The nonlinear coherent coupler,” IEEE Trans. Microwave Theory Tech.30, 1568–1571(1982).
    [CrossRef]
  4. P. St. J. Russell, “Photonic crystal fibers,” Science 17, 358–362 (2003).
    [CrossRef]
  5. Y. V. Kartashov and V. A. Vysloukh, “Switching management in couplers with biharmonic longitudinal modulation of refractive index,” Opt. Lett. 34, 3544–3546 (2009).
    [CrossRef] [PubMed]
  6. S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Soliton switching in fiber nonlinear directional couplers,” Opt. Lett. 13, 672–674 (1988).
    [CrossRef] [PubMed]
  7. P. L. Chu, G. D. Peng, and B. A. Malomed, “Analytical solution to soliton switching in nonlinear twin-core fibers,” Opt. Lett. 18, 328–330 (1993).
    [CrossRef] [PubMed]
  8. B. A. Malomed, I. M. Skinner, and R. S. Tasgal, “Solitons in a nonlinear optical coupler in the presence of the Raman effect,” Opt. Commun. 139, 247–251 (1997).
    [CrossRef]
  9. Y. Wang and W. Wang, “Study of ultrafast pulse coupling dynamics considering retarded nonlinear response and self-steepening effects,” J. Lightwave Technol. 24, 1041–1047 (2006).
    [CrossRef]
  10. S. Pricking and H. Giessen, “Generalized retarded response of nonlinear media and its influence on soliton dynamics,” Opt. Express 19, 2895–2903 (2011).
    [CrossRef] [PubMed]
  11. R. Zhang, J. Teipel, and H. Giessen, “Theoretical design of a liquid-core photonic crystal fiber for supercontinuum generation,” Opt. Express 14, 6800–6812 (2006).
    [CrossRef] [PubMed]
  12. P. Wiewior and C. Radzewicz, “Dynamics of molecular liquids studied by femtosecond optical Kerr effect,” Opt. Appl. 30, 103–120 (2000).
  13. K. Itoh, Y. Toda, R. Morita, and M. Yamashita, “Coherent optical control of molecular motion uUsing polarized sequential pPulses,” Jpn. J. Appl. Phys. 436448–6451 (2004).
    [CrossRef]
  14. T. F. Laurent, H. Hennig, N. P. Ernsting, and S. A. Kovalenko, “The ultrafast optical Kerr effect in liquid fluoroform: an estimate of the collision-induced contribution,” Phys. Chem. Chem. Phys. 2, 2691–2697 (2000).
    [CrossRef]
  15. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 1995).
  16. H. H. Marvin, “The selective transmission and the dispersion of the liquid chlorides,” Phys. Rev. 34, 161–186 (1912).
  17. P. P. Ho and R. R. Alfano, “Optical Kerr effect in liquids,” Phys. Rev. A 20, 2170–2187 (1979).
    [CrossRef]
  18. K. Okamoto, Fundamentals of Optical Waveguides (Academic Press, 2005).

2011

2010

2009

2006

2004

K. Itoh, Y. Toda, R. Morita, and M. Yamashita, “Coherent optical control of molecular motion uUsing polarized sequential pPulses,” Jpn. J. Appl. Phys. 436448–6451 (2004).
[CrossRef]

2003

P. St. J. Russell, “Photonic crystal fibers,” Science 17, 358–362 (2003).
[CrossRef]

2000

T. F. Laurent, H. Hennig, N. P. Ernsting, and S. A. Kovalenko, “The ultrafast optical Kerr effect in liquid fluoroform: an estimate of the collision-induced contribution,” Phys. Chem. Chem. Phys. 2, 2691–2697 (2000).
[CrossRef]

P. Wiewior and C. Radzewicz, “Dynamics of molecular liquids studied by femtosecond optical Kerr effect,” Opt. Appl. 30, 103–120 (2000).

1997

B. A. Malomed, I. M. Skinner, and R. S. Tasgal, “Solitons in a nonlinear optical coupler in the presence of the Raman effect,” Opt. Commun. 139, 247–251 (1997).
[CrossRef]

1993

1988

1979

P. P. Ho and R. R. Alfano, “Optical Kerr effect in liquids,” Phys. Rev. A 20, 2170–2187 (1979).
[CrossRef]

1912

H. H. Marvin, “The selective transmission and the dispersion of the liquid chlorides,” Phys. Rev. 34, 161–186 (1912).

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 1995).

Alfano, R. R.

P. P. Ho and R. R. Alfano, “Optical Kerr effect in liquids,” Phys. Rev. A 20, 2170–2187 (1979).
[CrossRef]

Chu, P. L.

Eggleton, B. J.

Ernsting, N. P.

T. F. Laurent, H. Hennig, N. P. Ernsting, and S. A. Kovalenko, “The ultrafast optical Kerr effect in liquid fluoroform: an estimate of the collision-induced contribution,” Phys. Chem. Chem. Phys. 2, 2691–2697 (2000).
[CrossRef]

Giessen, H.

Gissibl, T.

Hennig, H.

T. F. Laurent, H. Hennig, N. P. Ernsting, and S. A. Kovalenko, “The ultrafast optical Kerr effect in liquid fluoroform: an estimate of the collision-induced contribution,” Phys. Chem. Chem. Phys. 2, 2691–2697 (2000).
[CrossRef]

Ho, P. P.

P. P. Ho and R. R. Alfano, “Optical Kerr effect in liquids,” Phys. Rev. A 20, 2170–2187 (1979).
[CrossRef]

Itoh, K.

K. Itoh, Y. Toda, R. Morita, and M. Yamashita, “Coherent optical control of molecular motion uUsing polarized sequential pPulses,” Jpn. J. Appl. Phys. 436448–6451 (2004).
[CrossRef]

Jensen, St. M.

St. M. Jensen, “The nonlinear coherent coupler,” IEEE Trans. Microwave Theory Tech.30, 1568–1571(1982).
[CrossRef]

Kartashov, Y. V.

Kovalenko, S. A.

T. F. Laurent, H. Hennig, N. P. Ernsting, and S. A. Kovalenko, “The ultrafast optical Kerr effect in liquid fluoroform: an estimate of the collision-induced contribution,” Phys. Chem. Chem. Phys. 2, 2691–2697 (2000).
[CrossRef]

Kuhlmey, B.

Kuhlmey, B. T.

Laurent, T. F.

T. F. Laurent, H. Hennig, N. P. Ernsting, and S. A. Kovalenko, “The ultrafast optical Kerr effect in liquid fluoroform: an estimate of the collision-induced contribution,” Phys. Chem. Chem. Phys. 2, 2691–2697 (2000).
[CrossRef]

Malomed, B. A.

B. A. Malomed, I. M. Skinner, and R. S. Tasgal, “Solitons in a nonlinear optical coupler in the presence of the Raman effect,” Opt. Commun. 139, 247–251 (1997).
[CrossRef]

P. L. Chu, G. D. Peng, and B. A. Malomed, “Analytical solution to soliton switching in nonlinear twin-core fibers,” Opt. Lett. 18, 328–330 (1993).
[CrossRef] [PubMed]

Marvin, H. H.

H. H. Marvin, “The selective transmission and the dispersion of the liquid chlorides,” Phys. Rev. 34, 161–186 (1912).

Morita, R.

K. Itoh, Y. Toda, R. Morita, and M. Yamashita, “Coherent optical control of molecular motion uUsing polarized sequential pPulses,” Jpn. J. Appl. Phys. 436448–6451 (2004).
[CrossRef]

Okamoto, K.

K. Okamoto, Fundamentals of Optical Waveguides (Academic Press, 2005).

Peng, G. D.

Pricking, S.

Radzewicz, C.

P. Wiewior and C. Radzewicz, “Dynamics of molecular liquids studied by femtosecond optical Kerr effect,” Opt. Appl. 30, 103–120 (2000).

Russell, P. St. J.

P. St. J. Russell, “Photonic crystal fibers,” Science 17, 358–362 (2003).
[CrossRef]

Skinner, I. M.

B. A. Malomed, I. M. Skinner, and R. S. Tasgal, “Solitons in a nonlinear optical coupler in the presence of the Raman effect,” Opt. Commun. 139, 247–251 (1997).
[CrossRef]

Stegeman, G. I.

Tasgal, R. S.

B. A. Malomed, I. M. Skinner, and R. S. Tasgal, “Solitons in a nonlinear optical coupler in the presence of the Raman effect,” Opt. Commun. 139, 247–251 (1997).
[CrossRef]

Teipel, J.

Toda, Y.

K. Itoh, Y. Toda, R. Morita, and M. Yamashita, “Coherent optical control of molecular motion uUsing polarized sequential pPulses,” Jpn. J. Appl. Phys. 436448–6451 (2004).
[CrossRef]

Trillo, S.

Vieweg, M.

Vysloukh, V. A.

Wabnitz, S.

Wang, W.

Wang, Y.

Wiewior, P.

P. Wiewior and C. Radzewicz, “Dynamics of molecular liquids studied by femtosecond optical Kerr effect,” Opt. Appl. 30, 103–120 (2000).

Wright, E. M.

Wu, D. C.

Wu, D. K.

Yamashita, M.

K. Itoh, Y. Toda, R. Morita, and M. Yamashita, “Coherent optical control of molecular motion uUsing polarized sequential pPulses,” Jpn. J. Appl. Phys. 436448–6451 (2004).
[CrossRef]

Zhang, R.

J. Lightwave Technol.

Jpn. J. Appl. Phys.

K. Itoh, Y. Toda, R. Morita, and M. Yamashita, “Coherent optical control of molecular motion uUsing polarized sequential pPulses,” Jpn. J. Appl. Phys. 436448–6451 (2004).
[CrossRef]

Opt. Appl.

P. Wiewior and C. Radzewicz, “Dynamics of molecular liquids studied by femtosecond optical Kerr effect,” Opt. Appl. 30, 103–120 (2000).

Opt. Commun.

B. A. Malomed, I. M. Skinner, and R. S. Tasgal, “Solitons in a nonlinear optical coupler in the presence of the Raman effect,” Opt. Commun. 139, 247–251 (1997).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Chem. Chem. Phys.

T. F. Laurent, H. Hennig, N. P. Ernsting, and S. A. Kovalenko, “The ultrafast optical Kerr effect in liquid fluoroform: an estimate of the collision-induced contribution,” Phys. Chem. Chem. Phys. 2, 2691–2697 (2000).
[CrossRef]

Phys. Rev.

H. H. Marvin, “The selective transmission and the dispersion of the liquid chlorides,” Phys. Rev. 34, 161–186 (1912).

Phys. Rev. A

P. P. Ho and R. R. Alfano, “Optical Kerr effect in liquids,” Phys. Rev. A 20, 2170–2187 (1979).
[CrossRef]

Science

P. St. J. Russell, “Photonic crystal fibers,” Science 17, 358–362 (2003).
[CrossRef]

Other

St. M. Jensen, “The nonlinear coherent coupler,” IEEE Trans. Microwave Theory Tech.30, 1568–1571(1982).
[CrossRef]

K. Okamoto, Fundamentals of Optical Waveguides (Academic Press, 2005).

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 1995).

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Figures (4)

Fig. 1
Fig. 1

a) Photonic crystal fiber with the two waveguides filled with the hypothetic medium. In our simulations the hole diameter is d = 2.7 μm, the hole-to-hole distance Λ = 5.6 μm, and the length L = 36 mm. b) Measured retarded responses of commonly used media, normalized to their maximum value (CS2 [11], toluene [12], CCl4 [13], chloroform [14], and fused silica [15]). The gray lines show the retarded responses of our hypothetic medium for different values of tR, rising quadratically from 2 fs (narrowest) to 200 fs (broadest). The inset is a zoom for t < 0.2 ps.

Fig. 2
Fig. 2

Pulse energy contained in waveguide 1, normalized to the input pulse energy, in dependence on input peak power P0 and propagation distance z: a,b,c) T0 = 50 fs, d,e,f) T0 = 5 ps; a,d) fR = 0, b,c,d,e) fR = 0.8; b,e) tR = 2 fs, c,f) tR = 200 fs.

Fig. 3
Fig. 3

The critical power PC in dependence of the input pulse duration T0, the characteristic response time tR, and the fraction fR: a) PC extracted from the simulations, b) PC calculated with our model.

Fig. 4
Fig. 4

The correction divisor DC in dependence of the input pulse duration T0, the characteristic response time tR, and the fraction fR.

Equations (6)

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A j z = k = 2 7 i k + 1 k ! β k k T k A j + i κ A 3 j + i γ ( 1 + i ω 0 T ) A j + R ( t ) × ( | A j ( T t ) | 2 + f j ( 3 j ) | A 3 j ( T t ) | 2 ) d t
R ( t ) = ( 1 f R ) δ ( t ) + f R h R ( t / t R ) t R .
h R ( x ) = 1 N 0 ( exp ( x ) + 1 x + 1 ) ( 1 exp ( x ) ) exp ( x 100 ) Θ ( x )
A 1 ( 0 , T ) = P 0 sech ( T T 0 ) , A 2 ( 0 , T ) = 0 ,
P C ( T ) = 4 κ γ ( R ( t ) | A 1 ( 0 , T t ) | 2 P 0 d t ) 1 = P ˜ C D C ( T )
D C ( τ ) = ( 1 f R ) sech 2 ( τ ) + f R τ R 0 h R ( τ τ R ) sech 2 ( τ τ ) d τ

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