Abstract

We demonstrate by means of numerical simulations of the generalized Nonlinear Schrödinger Equation that the retarded response of a nonlinear medium embedded in a single hole of a photonic crystal fiber crucially affects the spectrum generated by ultrashort laser pulses. By introducing a hypothetic medium with fixed dispersion and nonlinearity and with a variable retarded response, we are able to separate the influence of the retarded response from other effects. We show that the fission length of a launched higher-order soliton dramatically increases if the characteristic time of the retarded response is close to the input pulse duration. Furthermore, we investigate the effect of the retarded response on the soliton self-frequency shift and find that the optimum input pulse duration for maximizing the spectral width has to be shortened for a larger characteristic retarded response time. Our work has important implications on future studies of spatiotemporal solitons in selectively liquid-filled photonic crystal fibers.

© 2011 Optical Society of America

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    [CrossRef] [PubMed]
  9. F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
    [CrossRef] [PubMed]
  10. C. R. Rosberg, F. H. Bennet, D. N. Neshev, P. D. Rasmussen, O. Bang, W. Krolikowski, A. Bjarklev, and Y. Kivshar, “Tunable diffraction and self-defocusing in liquid-filled photonic crystal fibers,” Opt. Express 15, 12145–12150 (2007).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2010 (4)

2009 (2)

2008 (2)

2007 (1)

2006 (2)

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]

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[CrossRef]

2005 (2)

P. J. Roberts, B. J. Mangan, H. Sabert, F. Couny, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Control of dispersion in photonic crystal fibers,” J. Opt. Fiber. Commun. Rep. 2, 435–461 (2005).
[CrossRef]

S. M. Kobtsev, S. V. Kukarin, N. V. Fateev, and S. V. Smirnov, “Coherent, polarization and temporal properties of self-frequency shifted solitons generated in polarization-maintaining microstructured fibre,” Appl. Phys. B 81, 265–269 (2005).
[CrossRef]

2004 (2)

K. Itoh, Y. Toda, R. Morita, and M. Yamashita, “Coherent optical control of molecular motion using polarized sequential pulses,” Jpn. J. Appl. Phys. 43, 6448–6451 (2004).
[CrossRef]

A. V. Yulin, D. V. Skryabin, and P. St. J. Russell, “Four-wave mixing of linear waves and solitons in fibers with higher-order dispersion,” Opt. Lett. 29, 2411–2413 (2004).
[CrossRef] [PubMed]

2003 (4)

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657–659 (2003).
[CrossRef] [PubMed]

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

J. C. Knight, “Photonic crystal fibers,” Nature 424, 847–851 (2003).
[CrossRef] [PubMed]

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, 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]

2002 (3)

2001 (1)

A. Husakou, and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001).
[CrossRef] [PubMed]

2000 (3)

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. 2, 2691–2697 (2000).
[CrossRef]

J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25, 25–27 (2000).
[CrossRef]

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

1995 (1)

N. Akhmediev, and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607 (1995).
[CrossRef] [PubMed]

1986 (2)

1979 (1)

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

1912 (1)

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

Akhmediev, N.

N. Akhmediev, and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607 (1995).
[CrossRef] [PubMed]

Alfano, R. R.

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

Allan, D. C.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657–659 (2003).
[CrossRef] [PubMed]

Antonopoulos, G.

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[CrossRef] [PubMed]

Bang, O.

Benabid, F.

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[CrossRef] [PubMed]

Bennet, F. H.

Bethge, J.

Biancalana, F.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, 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.

P. J. Roberts, B. J. Mangan, H. Sabert, F. Couny, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Control of dispersion in photonic crystal fibers,” J. Opt. Fiber. Commun. Rep. 2, 435–461 (2005).
[CrossRef]

Bjarklev, A.

Borrelli, N. F.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657–659 (2003).
[CrossRef] [PubMed]

Bozolan, A.

Chang, S.

H. Zhang, S. Chang, J. Yuan, and D. Huang, “Supercontinuum generation in chloroform-filled photonic crystal fibers,” Optik (Stuttg.) 121, 783–789 (2010).
[CrossRef]

Chau, A. H. L.

Chen, C.-M.

Coen, S.

Cordeiro, C. M. B.

Couny, F.

P. J. Roberts, B. J. Mangan, H. Sabert, F. Couny, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Control of dispersion in photonic crystal fibers,” J. Opt. Fiber. Commun. Rep. 2, 435–461 (2005).
[CrossRef]

de Matos, C. J. S.

dos Santos, E. M.

Dudley, J. M.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[CrossRef]

Efimov, A.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, 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]

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. 2, 2691–2697 (2000).
[CrossRef]

Fateev, N. V.

S. M. Kobtsev, S. V. Kukarin, N. V. Fateev, and S. V. Smirnov, “Coherent, polarization and temporal properties of self-frequency shifted solitons generated in polarization-maintaining microstructured fibre,” Appl. Phys. B 81, 265–269 (2005).
[CrossRef]

Gallagher, M. T.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657–659 (2003).
[CrossRef] [PubMed]

Genty, G.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[CrossRef]

Giessen, H.

Gissibl, T.

Gordon, J. P.

Griebner, U.

Harvey, J. D.

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. 2, 2691–2697 (2000).
[CrossRef]

Hermann, J.

Herrmann, J.

Ho, P. P.

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

Huang, D.

H. Zhang, S. Chang, J. Yuan, and D. Huang, “Supercontinuum generation in chloroform-filled photonic crystal fibers,” Optik (Stuttg.) 121, 783–789 (2010).
[CrossRef]

Husakou, A.

Itoh, K.

K. Itoh, Y. Toda, R. Morita, and M. Yamashita, “Coherent optical control of molecular motion using polarized sequential pulses,” Jpn. J. Appl. Phys. 43, 6448–6451 (2004).
[CrossRef]

Judge, A. C.

Karlsson, M.

N. Akhmediev, and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607 (1995).
[CrossRef] [PubMed]

Kelley, P. L.

Kivshar, Y.

Knight, J. C.

P. J. Roberts, B. J. Mangan, H. Sabert, F. Couny, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Control of dispersion in photonic crystal fibers,” J. Opt. Fiber. Commun. Rep. 2, 435–461 (2005).
[CrossRef]

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, 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 fibers,” Nature 424, 847–851 (2003).
[CrossRef] [PubMed]

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[CrossRef] [PubMed]

S. Coen, A. H. L. Chau, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Supercontinuum generation via stimulated Raman scattering and parametric four-wave-mixing in photonic crystal fibers,” J. Opt. Soc. Am. B 19, 753–764 (2002).
[CrossRef]

Kobtsev, S. M.

S. M. Kobtsev, S. V. Kukarin, N. V. Fateev, and S. V. Smirnov, “Coherent, polarization and temporal properties of self-frequency shifted solitons generated in polarization-maintaining microstructured fibre,” Appl. Phys. B 81, 265–269 (2005).
[CrossRef]

Koch, K. W.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657–659 (2003).
[CrossRef] [PubMed]

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. 2, 2691–2697 (2000).
[CrossRef]

Krolikowski, W.

Kuhlmey, B. T.

Kukarin, S. V.

S. M. Kobtsev, S. V. Kukarin, N. V. Fateev, and S. V. Smirnov, “Coherent, polarization and temporal properties of self-frequency shifted solitons generated in polarization-maintaining microstructured fibre,” Appl. Phys. B 81, 265–269 (2005).
[CrossRef]

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. 2, 2691–2697 (2000).
[CrossRef]

Leonhardt, R.

Mägi, E. C.

Mangan, B. J.

P. J. Roberts, B. J. Mangan, H. Sabert, F. Couny, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Control of dispersion in photonic crystal fibers,” J. Opt. Fiber. Commun. Rep. 2, 435–461 (2005).
[CrossRef]

Martijn de Sterke, C.

Marvin, H. H.

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

Mitschke, F.

Mitschke, F. M.

Mollenauer, L. F.

Morita, R.

K. Itoh, Y. Toda, R. Morita, and M. Yamashita, “Coherent optical control of molecular motion using polarized sequential pulses,” Jpn. J. Appl. Phys. 43, 6448–6451 (2004).
[CrossRef]

Müller, D.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657–659 (2003).
[CrossRef] [PubMed]

Neshev, D. N.

Noack, F.

Omenetto, F. G.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, 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]

Pant, R.

Porsezian, K.

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).

Raja, R. V. J.

Ranka, J. K.

Rasmussen, P. D.

Reeves, W. H.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, 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]

Roberts, P. J.

P. J. Roberts, B. J. Mangan, H. Sabert, F. Couny, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Control of dispersion in photonic crystal fibers,” J. Opt. Fiber. Commun. Rep. 2, 435–461 (2005).
[CrossRef]

Rosberg, C. R.

Russell, P. St. J.

P. J. Roberts, B. J. Mangan, H. Sabert, F. Couny, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Control of dispersion in photonic crystal fibers,” J. Opt. Fiber. Commun. Rep. 2, 435–461 (2005).
[CrossRef]

A. V. Yulin, D. V. Skryabin, and P. St. J. Russell, “Four-wave mixing of linear waves and solitons in fibers with higher-order dispersion,” Opt. Lett. 29, 2411–2413 (2004).
[CrossRef] [PubMed]

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, 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]

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

S. Coen, A. H. L. Chau, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Supercontinuum generation via stimulated Raman scattering and parametric four-wave-mixing in photonic crystal fibers,” J. Opt. Soc. Am. B 19, 753–764 (2002).
[CrossRef]

Sabert, H.

P. J. Roberts, B. J. Mangan, H. Sabert, F. Couny, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Control of dispersion in photonic crystal fibers,” J. Opt. Fiber. Commun. Rep. 2, 435–461 (2005).
[CrossRef]

Skryabin, D. V.

A. V. Yulin, D. V. Skryabin, and P. St. J. Russell, “Four-wave mixing of linear waves and solitons in fibers with higher-order dispersion,” Opt. Lett. 29, 2411–2413 (2004).
[CrossRef] [PubMed]

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, 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]

Smirnov, S. V.

S. M. Kobtsev, S. V. Kukarin, N. V. Fateev, and S. V. Smirnov, “Coherent, polarization and temporal properties of self-frequency shifted solitons generated in polarization-maintaining microstructured fibre,” Appl. Phys. B 81, 265–269 (2005).
[CrossRef]

Smith, C. M.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657–659 (2003).
[CrossRef] [PubMed]

St. Russell, P.

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[CrossRef] [PubMed]

Steinmeyer, G.

Stentz, A. J.

Taylor, A. J.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, 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]

Teipel, J.

Toda, Y.

K. Itoh, Y. Toda, R. Morita, and M. Yamashita, “Coherent optical control of molecular motion using polarized sequential pulses,” Jpn. J. Appl. Phys. 43, 6448–6451 (2004).
[CrossRef]

Travers, J.

Venkataraman, N.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657–659 (2003).
[CrossRef] [PubMed]

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C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657–659 (2003).
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P. Wiewior, and C. Radzewicz, “Dynamics of molecular liquids studied by femtosecond optical Kerr effect,” Opt. Appl. 30, 103–120 (2000).

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Wu, D. C.

Wu, D. K. C.

Yamashita, M.

K. Itoh, Y. Toda, R. Morita, and M. Yamashita, “Coherent optical control of molecular motion using polarized sequential pulses,” Jpn. J. Appl. Phys. 43, 6448–6451 (2004).
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H. Zhang, S. Chang, J. Yuan, and D. Huang, “Supercontinuum generation in chloroform-filled photonic crystal fibers,” Optik (Stuttg.) 121, 783–789 (2010).
[CrossRef]

Yulin, A. V.

Zhang, H.

H. Zhang, S. Chang, J. Yuan, and D. Huang, “Supercontinuum generation in chloroform-filled photonic crystal fibers,” Optik (Stuttg.) 121, 783–789 (2010).
[CrossRef]

Zhang, R.

Zheltikov, A. M.

Appl. Phys. B (1)

S. M. Kobtsev, S. V. Kukarin, N. V. Fateev, and S. V. Smirnov, “Coherent, polarization and temporal properties of self-frequency shifted solitons generated in polarization-maintaining microstructured fibre,” Appl. Phys. B 81, 265–269 (2005).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Fiber. Commun. Rep. (1)

P. J. Roberts, B. J. Mangan, H. Sabert, F. Couny, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Control of dispersion in photonic crystal fibers,” J. Opt. Fiber. Commun. Rep. 2, 435–461 (2005).
[CrossRef]

J. Opt. Soc. Am. B (4)

Jpn. J. Appl. Phys. (1)

K. Itoh, Y. Toda, R. Morita, and M. Yamashita, “Coherent optical control of molecular motion using polarized sequential pulses,” Jpn. J. Appl. Phys. 43, 6448–6451 (2004).
[CrossRef]

Nature (3)

J. C. Knight, “Photonic crystal fibers,” Nature 424, 847–851 (2003).
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W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, 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).
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C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657–659 (2003).
[CrossRef] [PubMed]

Opt. Appl. (1)

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

Opt. Express (5)

Opt. Lett. (5)

Optik (Stuttg.) (1)

H. Zhang, S. Chang, J. Yuan, and D. Huang, “Supercontinuum generation in chloroform-filled photonic crystal fibers,” Optik (Stuttg.) 121, 783–789 (2010).
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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. 2, 2691–2697 (2000).
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A. Husakou, and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001).
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J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
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Science (2)

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

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
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Figures (5)

Fig. 1
Fig. 1

a) Photonic crystal fiber with the central single strand filled with the hypothetic medium. In our simulations the hole diameter is d = 2.5 μm, the hole-to-hole distance Λ = 2.6 μm. The length of the PCF is set to 19 cm. b) Measured retarded responses of commonly used media (CS2 [15], toluene [18], CCl4 [19], fused silica [20], and chloroform [21]). The gray lines show the retarded responses of our hypothetic medium for different values of tR. These values rise quadratically from 2 fs (narrowest) to 200 fs (broadest). Note that all response functions are normalized to their maximum value to provide a better comparability, whereas in the simulations they are normalized such that their integral gives unity.

Fig. 2
Fig. 2

Output spectra for an input pulse centered at 1030 nm after a propagation distance of z0 = 19 cm in the single strand filled with our hypothetic medium in dependence of the retarded response fraction fR, the characteristic time of the retarded response tR, and the input pulse duration T0. The input peak power is fixed to 500 W.

Fig. 3
Fig. 3

a) Correction factor fF for the fission length z ˜ F = T 0 / 2 γ P 0 | β 2 |, if the retarded response is taken into account. b) TC in dependence of the fraction fR and the characteristic time tR of the retarded response. The symbols stand for data points extracted from our simulations, the lines describe the result of our model.

Fig. 4
Fig. 4

a) Frequency shift rate in dependence of input pulse duration T0 and the characteristic time of the retarded response tR. P0 is fixed to 500 W. b) Calculated maximum wavelength of the dominant red-shifted fundamental soliton in dependence of input pulse duration T0, the fraction and the characteristic time of the retarded response fR and tR, respectively.

Fig. 5
Fig. 5

a) TC (blue) and maximum wavelength of the dominant red-shifted fundamental soliton (red) in dependence of the input peak power. T0 is fixed to 500 fs, tR = 50 fs, and fR = 1. The dots denote the data extracted from the simulations, the lines are the results of our model. b) Influence of oscillations imposed on the retarded response function. Here, fR = 1 and tR = 50 fs. The bottom row shows the output spectra in dependence of T0 with varying amplitudes of the oscillations: Left A = 0.05, middle A = 0.22, right A = 0.60.

Equations (14)

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A ( z , T ) z = k 2 i k + 1 k ! β k k T k A ( z , T ) + i γ ( 1 + i ω 0 T ) ( A ( z , T ) + R ( t ) | A ( z , 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 ( 0 , T ) = P 0 sech ( T T 0 ) ,
N = T 0 γ P 0 | β 2 | .
T S = T 0 2 N 1 = T 0 | β 2 | 2 T 0 γ P 0 | β 2 | .
z F ( τ ) = τ T 0 2 β 2 Φ NL ( z F , τ ) τ ,
Φ NL ( z , τ ) = γ z R ( t ) | A ( 0 , τ T 0 t ) | 2 d t .
z F ( τ ) = z ˜ F [ ( 1 f R ) sinh τ τ cosh 3 τ + f R 0 ( x e x + e x + 1 ) ( 1 e x ) e x 100 sinh ( τ τ R x ) N 0 ( 1 + x ) τ cosh 3 ( τ τ R x ) d x ] 1 2
T C ( f R , τ R ) = 2 γ P 0 | β 2 | z 0 f F ( f R , τ R ) .
ω z = | β 2 | T S π 2 0 Im R ˜ ( Ω ) Ω 3 sinh 2 ( π 2 T S Ω ) d Ω .
ω z = | β 2 | T S t R 4 π 2 f R 0 Im h R ˜ ( x ) x 3 sinh 2 ( π 2 T S t R x ) d x
Δ ω max = ω z | ω 0 z R Θ ( z R ) .
R Osci ( t ) = ( 1 f R ) δ ( t ) + f R N Osci ( h R ( t / t R ) + A e t τ Osci sin ( ω Osci t ) Θ ( t ) ) .

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