Abstract

We experimentally and theoretically study self-phase modulation by Kerr effect in a liquid filled hollow core photonic crystal fiber. We perform a complete characterization of the linear optical properties of the hollow core photonic bandgap fiber filled with deuterated acetone to determine all the characteristics of the propagation mode. The nonlinear coefficient of the fiber is determined by fitting the output spectra broadened by self-phase modulation with a new analytical expression giving the spectra of a hyperbolic secant pulse transmitted through a Kerr medium. The experiment allows a precise determination of the nonlinear index change n2I of acetone-d6 equal to (1.15±0.17)×1019m2W1.

© 2010 Optical Society of America

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Corrections

Minh Chau Phan Huy, Alexandre Baron, Sylvie Lebrun, Robert Frey, and Philippe Delaye, "Characterization of self-phase modulation in liquid filled hollow core photonic band gap fibers: erratum," J. Opt. Soc. Am. B 30, 1651-1651 (2013)
https://www.osapublishing.org/josab/abstract.cfm?uri=josab-30-6-1651

References

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    [CrossRef] [PubMed]
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    [CrossRef]
  6. F. Benabid, J. C. Knight, G. Antonopoulos, and P. S. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fibre,” Science 298, 399–402 (2002).
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    [CrossRef]
  8. S. Yiou, P. Delaye, A. Rouvie, J. Chinaud, R. Frey, G. Roosen, P. Viale, S. Février, P. Roy, J. L. Auguste, and J. M. Blondy, “Stimulated Raman scattering in an ethanol core microstructured optical fibre,” Opt. Express 13, 4786–4791 (2005).
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    [CrossRef]
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    [CrossRef] [PubMed]
  20. F. Kroeger, A. Ryasnyanskiy, A. Baron, N. Dubreuil, Ph. Delaye, R. Frey, G. Roosen, and D. Peyrade, “Saturation of Raman amplification by self-phase modulation in silicon nanowaveguides,” Appl. Phys. Lett. 96, 241102 (2010).
    [CrossRef]
  21. G. A. Campbell and R. M. Foster, Fourier Integrals for Practical Applications, 6th printing (D. Van Nostran, 1967), Formula 607.0, p. 68.
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    [CrossRef]
  26. J. Rheims, J. Koser, and T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8, 601–605 (1997).
    [CrossRef]
  27. G. Antonopoulos, F. Benabid, T. A. Birks, D. M. Bird, J. C. Knight, and P. St. J. Russell, “Experimental demonstration of the frequency shift of bandgaps in photonic crystal fibers due to refractive index scaling,” Opt. Express 14, 3000–3006 (2006).
    [CrossRef] [PubMed]
  28. R. W. Boyd, Nonlinear Optics (Academic, 2003), Table 4.1.2.
  29. S. Er-rhaimini, J. P. Lecoq, N. P. Xuan, G. Rivoire, and N. Tcherniega, “Amplitude object reconstruction by stimulated backward Raman scattering in the picosecond range with high efficiency conversion,” Opt. Commun. 104, 132–138 (1993).
    [CrossRef]
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    [CrossRef]
  32. F. Gérôme, R. Jamier, J. L. Auguste, G. Humbert, and J. M. Blondy, “Simplified hollow-core photonic crystal fiber,” Opt. Lett. 35, 1157–1159 (2010).
    [CrossRef] [PubMed]

2010 (5)

A. A. Voronin, V. P. Mitrokhin, A. A. Ivanov, A. B. Fedotov, D. A. Sidorov-Biryukov, V. I. Beloglazov, M. V. Alfimov, H. Ludvigsen, and A. M. Zheltikov, “Understanding the nonlinear-optical response of a liquid-core photonic-crystal fiber,” Laser Phys. Lett. 7, 46–49 (2010).
[CrossRef]

S. Lebrun, C. Buy, Ph. Delaye, R. Frey, G. Pauliat, and G. Roosen, “Optical characterization of a Raman generator based on a hollow core photonic crystal fiber filled with a liquid,” J. Nonlinear Opt. Phys. Mater. 19, 101–109 (2010).
[CrossRef]

F. Kroeger, A. Ryasnyanskiy, A. Baron, N. Dubreuil, Ph. Delaye, R. Frey, G. Roosen, and D. Peyrade, “Saturation of Raman amplification by self-phase modulation in silicon nanowaveguides,” Appl. Phys. Lett. 96, 241102 (2010).
[CrossRef]

J. Bethge, A. Husakou, F. Mitschke, F. Noack, U. Griebner, G. Steinmeyer, and J. Herrmann, “Two-octave supercontinuum generation in a water-filled photonic crystal fiber,” Opt. Express 18, 6230–6240 (2010).
[CrossRef] [PubMed]

F. Gérôme, R. Jamier, J. L. Auguste, G. Humbert, and J. M. Blondy, “Simplified hollow-core photonic crystal fiber,” Opt. Lett. 35, 1157–1159 (2010).
[CrossRef] [PubMed]

2009 (5)

A. Baron, A. Ryasnyanskiy, N. Dubreuil, P. Delaye, Q. Vy Tran, S. Combrié, A. de Rossi, R. Frey, and G. Roosen, “Light localization induced enhancement of third order nonlinearities in a GaAs photonic crystal waveguide,” Opt. Express 17, 552–557 (2009).
[CrossRef] [PubMed]

M. Liao, C. Chaudhari, G. Qin, X. Yan, C. Kito, T. Suzuki, Y. Ohishi, M. Matsumoto, and T. Misumi, “Fabrication and characterization of a chalcogenide-tellurite composite microstructure fiber with high nonlinearity,” Opt. Express 17, 21608–21614 (2009).
[CrossRef] [PubMed]

A. M. Weiner, Ultrafast Optics (Wiley, 2009).
[CrossRef]

F. Benabid, P. J. Roberts, F. Couny, and P. S. Light, “Light and gas confinement in hollow-core photonic crystal fibre based photonic microcells,” J. Eur. Opt. Soc. Rapid Publ. 4, 09004 (2009), and references therein.
[CrossRef]

F. Couny and F. Benabid, “Optical frequency comb generation in gas-filled hollow core photonic crystal fibres,” J. Opt. A, Pure Appl. Opt. 11, 103002 (2009), and references therein.
[CrossRef]

2008 (1)

2007 (2)

S. Lebrun, Ph. Delaye, R. Frey, and G. Roosen, “High efficiency single mode Raman generation in a liquid filled photonic band gap fibre,” Opt. Lett. 32, 337–339 (2007).
[CrossRef] [PubMed]

S. Lebrun, P. Delaye, and G. Roosen, “Stimulated Raman scattering in hollow core photonic crystal fibres,” Ann. Phys. (Paris) 32, 45–51 (2007).
[CrossRef]

2006 (3)

2005 (3)

S. Yiou, P. Delaye, A. Rouvie, J. Chinaud, R. Frey, G. Roosen, P. Viale, S. Février, P. Roy, J. L. Auguste, and J. M. Blondy, “Stimulated Raman scattering in an ethanol core microstructured optical fibre,” Opt. Express 13, 4786–4791 (2005).
[CrossRef] [PubMed]

S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonant optical interactions with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005).
[CrossRef] [PubMed]

S. O. Konorov, A. B. Fedotov, E. E. Serebryannikov, V. P. Mitrokhin, D. A. Sidorov-Biryukov, and A. M. Zheltikov, “Phase-matched coherent anti-Stokes Raman scattering in isolated air-guided modes of hollow photonic-crystal fibres,” J. Raman Spectrosc. 36, 129–133 (2005).
[CrossRef]

2003 (3)

R. W. Boyd, Nonlinear Optics (Academic, 2003), Table 4.1.2.

V. Finazzi, T. M. Monro, and D. J. Richardson, “Small-core silica holey fibers: nonlinearity and confinement loss trade-offs,” J. Opt. Soc. Am. B 20, 1427–1436 (2003).
[CrossRef]

M. J. Weber, Handbook of Optical Materials (CRC, 2003), Part 5.5.2.

2002 (2)

1997 (1)

J. Rheims, J. Koser, and T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8, 601–605 (1997).
[CrossRef]

1996 (1)

S. A. Wieczorek, A. Urbanczyk, and W. A. Van Hook, “Application of interferometric continuous-dilution differential refractometry to some solutions, including isotopomer solutions: isotope effects on polarizability in liquids,” J. Chem. Thermodyn. 28, 1009–1018 (1996).
[CrossRef]

1993 (1)

S. Er-rhaimini, J. P. Lecoq, N. P. Xuan, G. Rivoire, and N. Tcherniega, “Amplitude object reconstruction by stimulated backward Raman scattering in the picosecond range with high efficiency conversion,” Opt. Commun. 104, 132–138 (1993).
[CrossRef]

1985 (1)

1979 (1)

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

1978 (1)

R. H. Stolen and C. Lin, “Self-phase modulation in silica optical fibers,” Phys. Rev. A 17, 1448–1453 (1978).
[CrossRef]

1967 (1)

G. A. Campbell and R. M. Foster, Fourier Integrals for Practical Applications, 6th printing (D. Van Nostran, 1967), Formula 607.0, p. 68.

1953 (1)

Bateman Manuscript Project, Higher Transcendental Functions (McGraw-Hill Book, 1953).

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2006).

Alfano, R. R.

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

Alfimov, M. V.

A. A. Voronin, V. P. Mitrokhin, A. A. Ivanov, A. B. Fedotov, D. A. Sidorov-Biryukov, V. I. Beloglazov, M. V. Alfimov, H. Ludvigsen, and A. M. Zheltikov, “Understanding the nonlinear-optical response of a liquid-core photonic-crystal fiber,” Laser Phys. Lett. 7, 46–49 (2010).
[CrossRef]

Antonopoulos, G.

Auguste, J. L.

Baron, A.

F. Kroeger, A. Ryasnyanskiy, A. Baron, N. Dubreuil, Ph. Delaye, R. Frey, G. Roosen, and D. Peyrade, “Saturation of Raman amplification by self-phase modulation in silicon nanowaveguides,” Appl. Phys. Lett. 96, 241102 (2010).
[CrossRef]

A. Baron, A. Ryasnyanskiy, N. Dubreuil, P. Delaye, Q. Vy Tran, S. Combrié, A. de Rossi, R. Frey, and G. Roosen, “Light localization induced enhancement of third order nonlinearities in a GaAs photonic crystal waveguide,” Opt. Express 17, 552–557 (2009).
[CrossRef] [PubMed]

Beloglazov, V. I.

A. A. Voronin, V. P. Mitrokhin, A. A. Ivanov, A. B. Fedotov, D. A. Sidorov-Biryukov, V. I. Beloglazov, M. V. Alfimov, H. Ludvigsen, and A. M. Zheltikov, “Understanding the nonlinear-optical response of a liquid-core photonic-crystal fiber,” Laser Phys. Lett. 7, 46–49 (2010).
[CrossRef]

Benabid, F.

F. Benabid, P. J. Roberts, F. Couny, and P. S. Light, “Light and gas confinement in hollow-core photonic crystal fibre based photonic microcells,” J. Eur. Opt. Soc. Rapid Publ. 4, 09004 (2009), and references therein.
[CrossRef]

F. Couny and F. Benabid, “Optical frequency comb generation in gas-filled hollow core photonic crystal fibres,” J. Opt. A, Pure Appl. Opt. 11, 103002 (2009), and references therein.
[CrossRef]

G. Antonopoulos, F. Benabid, T. A. Birks, D. M. Bird, J. C. Knight, and P. St. J. Russell, “Experimental demonstration of the frequency shift of bandgaps in photonic crystal fibers due to refractive index scaling,” Opt. Express 14, 3000–3006 (2006).
[CrossRef] [PubMed]

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

Bethge, J.

Bird, D. M.

Birks, T. A.

Blondy, J. M.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 2003), Table 4.1.2.

Bozolan, A.

Buy, C.

S. Lebrun, C. Buy, Ph. Delaye, R. Frey, G. Pauliat, and G. Roosen, “Optical characterization of a Raman generator based on a hollow core photonic crystal fiber filled with a liquid,” J. Nonlinear Opt. Phys. Mater. 19, 101–109 (2010).
[CrossRef]

Campbell, G. A.

G. A. Campbell and R. M. Foster, Fourier Integrals for Practical Applications, 6th printing (D. Van Nostran, 1967), Formula 607.0, p. 68.

Chaudhari, C.

Chinaud, J.

Coen, S.

Combrié, S.

Cordeiro, C. M. B.

Couny, F.

F. Couny and F. Benabid, “Optical frequency comb generation in gas-filled hollow core photonic crystal fibres,” J. Opt. A, Pure Appl. Opt. 11, 103002 (2009), and references therein.
[CrossRef]

F. Benabid, P. J. Roberts, F. Couny, and P. S. Light, “Light and gas confinement in hollow-core photonic crystal fibre based photonic microcells,” J. Eur. Opt. Soc. Rapid Publ. 4, 09004 (2009), and references therein.
[CrossRef]

de Matos, C. J. S.

de Rossi, A.

Delaye, P.

Delaye, Ph.

S. Lebrun, C. Buy, Ph. Delaye, R. Frey, G. Pauliat, and G. Roosen, “Optical characterization of a Raman generator based on a hollow core photonic crystal fiber filled with a liquid,” J. Nonlinear Opt. Phys. Mater. 19, 101–109 (2010).
[CrossRef]

F. Kroeger, A. Ryasnyanskiy, A. Baron, N. Dubreuil, Ph. Delaye, R. Frey, G. Roosen, and D. Peyrade, “Saturation of Raman amplification by self-phase modulation in silicon nanowaveguides,” Appl. Phys. Lett. 96, 241102 (2010).
[CrossRef]

S. Lebrun, Ph. Delaye, R. Frey, and G. Roosen, “High efficiency single mode Raman generation in a liquid filled photonic band gap fibre,” Opt. Lett. 32, 337–339 (2007).
[CrossRef] [PubMed]

dos Santos, E. M.

Dubreuil, N.

F. Kroeger, A. Ryasnyanskiy, A. Baron, N. Dubreuil, Ph. Delaye, R. Frey, G. Roosen, and D. Peyrade, “Saturation of Raman amplification by self-phase modulation in silicon nanowaveguides,” Appl. Phys. Lett. 96, 241102 (2010).
[CrossRef]

A. Baron, A. Ryasnyanskiy, N. Dubreuil, P. Delaye, Q. Vy Tran, S. Combrié, A. de Rossi, R. Frey, and G. Roosen, “Light localization induced enhancement of third order nonlinearities in a GaAs photonic crystal waveguide,” Opt. Express 17, 552–557 (2009).
[CrossRef] [PubMed]

Er-rhaimini, S.

S. Er-rhaimini, J. P. Lecoq, N. P. Xuan, G. Rivoire, and N. Tcherniega, “Amplitude object reconstruction by stimulated backward Raman scattering in the picosecond range with high efficiency conversion,” Opt. Commun. 104, 132–138 (1993).
[CrossRef]

Fedotov, A. B.

A. A. Voronin, V. P. Mitrokhin, A. A. Ivanov, A. B. Fedotov, D. A. Sidorov-Biryukov, V. I. Beloglazov, M. V. Alfimov, H. Ludvigsen, and A. M. Zheltikov, “Understanding the nonlinear-optical response of a liquid-core photonic-crystal fiber,” Laser Phys. Lett. 7, 46–49 (2010).
[CrossRef]

S. O. Konorov, A. B. Fedotov, E. E. Serebryannikov, V. P. Mitrokhin, D. A. Sidorov-Biryukov, and A. M. Zheltikov, “Phase-matched coherent anti-Stokes Raman scattering in isolated air-guided modes of hollow photonic-crystal fibres,” J. Raman Spectrosc. 36, 129–133 (2005).
[CrossRef]

Février, S.

Finazzi, V.

Foster, R. M.

G. A. Campbell and R. M. Foster, Fourier Integrals for Practical Applications, 6th printing (D. Van Nostran, 1967), Formula 607.0, p. 68.

Frey, R.

Gaeta, A. L.

S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonant optical interactions with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005).
[CrossRef] [PubMed]

Gérôme, F.

Ghosh, S.

S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonant optical interactions with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005).
[CrossRef] [PubMed]

Griebner, U.

Harvey, J. D.

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]

Humbert, G.

Husakou, A.

Ivanov, A. A.

A. A. Voronin, V. P. Mitrokhin, A. A. Ivanov, A. B. Fedotov, D. A. Sidorov-Biryukov, V. I. Beloglazov, M. V. Alfimov, H. Ludvigsen, and A. M. Zheltikov, “Understanding the nonlinear-optical response of a liquid-core photonic-crystal fiber,” Laser Phys. Lett. 7, 46–49 (2010).
[CrossRef]

Jamier, R.

Kito, C.

Knight, J. C.

Konorov, S. O.

S. O. Konorov, A. B. Fedotov, E. E. Serebryannikov, V. P. Mitrokhin, D. A. Sidorov-Biryukov, and A. M. Zheltikov, “Phase-matched coherent anti-Stokes Raman scattering in isolated air-guided modes of hollow photonic-crystal fibres,” J. Raman Spectrosc. 36, 129–133 (2005).
[CrossRef]

Koser, J.

J. Rheims, J. Koser, and T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8, 601–605 (1997).
[CrossRef]

Kroeger, F.

F. Kroeger, A. Ryasnyanskiy, A. Baron, N. Dubreuil, Ph. Delaye, R. Frey, G. Roosen, and D. Peyrade, “Saturation of Raman amplification by self-phase modulation in silicon nanowaveguides,” Appl. Phys. Lett. 96, 241102 (2010).
[CrossRef]

Lebrun, S.

S. Lebrun, C. Buy, Ph. Delaye, R. Frey, G. Pauliat, and G. Roosen, “Optical characterization of a Raman generator based on a hollow core photonic crystal fiber filled with a liquid,” J. Nonlinear Opt. Phys. Mater. 19, 101–109 (2010).
[CrossRef]

S. Lebrun, P. Delaye, and G. Roosen, “Stimulated Raman scattering in hollow core photonic crystal fibres,” Ann. Phys. (Paris) 32, 45–51 (2007).
[CrossRef]

S. Lebrun, Ph. Delaye, R. Frey, and G. Roosen, “High efficiency single mode Raman generation in a liquid filled photonic band gap fibre,” Opt. Lett. 32, 337–339 (2007).
[CrossRef] [PubMed]

Lecoq, J. P.

S. Er-rhaimini, J. P. Lecoq, N. P. Xuan, G. Rivoire, and N. Tcherniega, “Amplitude object reconstruction by stimulated backward Raman scattering in the picosecond range with high efficiency conversion,” Opt. Commun. 104, 132–138 (1993).
[CrossRef]

Leonhardt, R.

Liao, M.

Light, P. S.

F. Benabid, P. J. Roberts, F. Couny, and P. S. Light, “Light and gas confinement in hollow-core photonic crystal fibre based photonic microcells,” J. Eur. Opt. Soc. Rapid Publ. 4, 09004 (2009), and references therein.
[CrossRef]

Lin, C.

R. H. Stolen and C. Lin, “Self-phase modulation in silica optical fibers,” Phys. Rev. A 17, 1448–1453 (1978).
[CrossRef]

Ludvigsen, H.

A. A. Voronin, V. P. Mitrokhin, A. A. Ivanov, A. B. Fedotov, D. A. Sidorov-Biryukov, V. I. Beloglazov, M. V. Alfimov, H. Ludvigsen, and A. M. Zheltikov, “Understanding the nonlinear-optical response of a liquid-core photonic-crystal fiber,” Laser Phys. Lett. 7, 46–49 (2010).
[CrossRef]

Lun Chau, A. H.

Matsumoto, M.

Misumi, T.

Mitrokhin, V. P.

A. A. Voronin, V. P. Mitrokhin, A. A. Ivanov, A. B. Fedotov, D. A. Sidorov-Biryukov, V. I. Beloglazov, M. V. Alfimov, H. Ludvigsen, and A. M. Zheltikov, “Understanding the nonlinear-optical response of a liquid-core photonic-crystal fiber,” Laser Phys. Lett. 7, 46–49 (2010).
[CrossRef]

S. O. Konorov, A. B. Fedotov, E. E. Serebryannikov, V. P. Mitrokhin, D. A. Sidorov-Biryukov, and A. M. Zheltikov, “Phase-matched coherent anti-Stokes Raman scattering in isolated air-guided modes of hollow photonic-crystal fibres,” J. Raman Spectrosc. 36, 129–133 (2005).
[CrossRef]

Mitschke, F.

Monro, T. M.

Noack, F.

Ohishi, Y.

Ouzounov, D. G.

S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonant optical interactions with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005).
[CrossRef] [PubMed]

Pauliat, G.

S. Lebrun, C. Buy, Ph. Delaye, R. Frey, G. Pauliat, and G. Roosen, “Optical characterization of a Raman generator based on a hollow core photonic crystal fiber filled with a liquid,” J. Nonlinear Opt. Phys. Mater. 19, 101–109 (2010).
[CrossRef]

Peyrade, D.

F. Kroeger, A. Ryasnyanskiy, A. Baron, N. Dubreuil, Ph. Delaye, R. Frey, G. Roosen, and D. Peyrade, “Saturation of Raman amplification by self-phase modulation in silicon nanowaveguides,” Appl. Phys. Lett. 96, 241102 (2010).
[CrossRef]

Pinault, S. C.

Potasek, M. J.

Qin, G.

Rheims, J.

J. Rheims, J. Koser, and T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8, 601–605 (1997).
[CrossRef]

Richardson, D. J.

Rivoire, G.

S. Er-rhaimini, J. P. Lecoq, N. P. Xuan, G. Rivoire, and N. Tcherniega, “Amplitude object reconstruction by stimulated backward Raman scattering in the picosecond range with high efficiency conversion,” Opt. Commun. 104, 132–138 (1993).
[CrossRef]

Roberts, P. J.

F. Benabid, P. J. Roberts, F. Couny, and P. S. Light, “Light and gas confinement in hollow-core photonic crystal fibre based photonic microcells,” J. Eur. Opt. Soc. Rapid Publ. 4, 09004 (2009), and references therein.
[CrossRef]

Roosen, G.

S. Lebrun, C. Buy, Ph. Delaye, R. Frey, G. Pauliat, and G. Roosen, “Optical characterization of a Raman generator based on a hollow core photonic crystal fiber filled with a liquid,” J. Nonlinear Opt. Phys. Mater. 19, 101–109 (2010).
[CrossRef]

F. Kroeger, A. Ryasnyanskiy, A. Baron, N. Dubreuil, Ph. Delaye, R. Frey, G. Roosen, and D. Peyrade, “Saturation of Raman amplification by self-phase modulation in silicon nanowaveguides,” Appl. Phys. Lett. 96, 241102 (2010).
[CrossRef]

A. Baron, A. Ryasnyanskiy, N. Dubreuil, P. Delaye, Q. Vy Tran, S. Combrié, A. de Rossi, R. Frey, and G. Roosen, “Light localization induced enhancement of third order nonlinearities in a GaAs photonic crystal waveguide,” Opt. Express 17, 552–557 (2009).
[CrossRef] [PubMed]

S. Lebrun, Ph. Delaye, R. Frey, and G. Roosen, “High efficiency single mode Raman generation in a liquid filled photonic band gap fibre,” Opt. Lett. 32, 337–339 (2007).
[CrossRef] [PubMed]

S. Lebrun, P. Delaye, and G. Roosen, “Stimulated Raman scattering in hollow core photonic crystal fibres,” Ann. Phys. (Paris) 32, 45–51 (2007).
[CrossRef]

S. Yiou, P. Delaye, A. Rouvie, J. Chinaud, R. Frey, G. Roosen, P. Viale, S. Février, P. Roy, J. L. Auguste, and J. M. Blondy, “Stimulated Raman scattering in an ethanol core microstructured optical fibre,” Opt. Express 13, 4786–4791 (2005).
[CrossRef] [PubMed]

Rouvie, A.

Roy, P.

Russell, P. S. J.

P. S. J. Russell, “Photonic crystal fibers,” J. Lightwave Technol. 24, 4729–4749 (2006), and references therein.
[CrossRef]

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

Russell, P. St. J.

Ryasnyanskiy, A.

F. Kroeger, A. Ryasnyanskiy, A. Baron, N. Dubreuil, Ph. Delaye, R. Frey, G. Roosen, and D. Peyrade, “Saturation of Raman amplification by self-phase modulation in silicon nanowaveguides,” Appl. Phys. Lett. 96, 241102 (2010).
[CrossRef]

A. Baron, A. Ryasnyanskiy, N. Dubreuil, P. Delaye, Q. Vy Tran, S. Combrié, A. de Rossi, R. Frey, and G. Roosen, “Light localization induced enhancement of third order nonlinearities in a GaAs photonic crystal waveguide,” Opt. Express 17, 552–557 (2009).
[CrossRef] [PubMed]

Serebryannikov, E. E.

S. O. Konorov, A. B. Fedotov, E. E. Serebryannikov, V. P. Mitrokhin, D. A. Sidorov-Biryukov, and A. M. Zheltikov, “Phase-matched coherent anti-Stokes Raman scattering in isolated air-guided modes of hollow photonic-crystal fibres,” J. Raman Spectrosc. 36, 129–133 (2005).
[CrossRef]

Sharping, J. E.

S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonant optical interactions with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005).
[CrossRef] [PubMed]

Sidorov-Biryukov, D. A.

A. A. Voronin, V. P. Mitrokhin, A. A. Ivanov, A. B. Fedotov, D. A. Sidorov-Biryukov, V. I. Beloglazov, M. V. Alfimov, H. Ludvigsen, and A. M. Zheltikov, “Understanding the nonlinear-optical response of a liquid-core photonic-crystal fiber,” Laser Phys. Lett. 7, 46–49 (2010).
[CrossRef]

S. O. Konorov, A. B. Fedotov, E. E. Serebryannikov, V. P. Mitrokhin, D. A. Sidorov-Biryukov, and A. M. Zheltikov, “Phase-matched coherent anti-Stokes Raman scattering in isolated air-guided modes of hollow photonic-crystal fibres,” J. Raman Spectrosc. 36, 129–133 (2005).
[CrossRef]

Steinmeyer, G.

Stolen, R. H.

R. H. Stolen and C. Lin, “Self-phase modulation in silica optical fibers,” Phys. Rev. A 17, 1448–1453 (1978).
[CrossRef]

Suzuki, T.

Tcherniega, N.

S. Er-rhaimini, J. P. Lecoq, N. P. Xuan, G. Rivoire, and N. Tcherniega, “Amplitude object reconstruction by stimulated backward Raman scattering in the picosecond range with high efficiency conversion,” Opt. Commun. 104, 132–138 (1993).
[CrossRef]

Travers, J.

Urbanczyk, A.

S. A. Wieczorek, A. Urbanczyk, and W. A. Van Hook, “Application of interferometric continuous-dilution differential refractometry to some solutions, including isotopomer solutions: isotope effects on polarizability in liquids,” J. Chem. Thermodyn. 28, 1009–1018 (1996).
[CrossRef]

Van Hook, W. A.

S. A. Wieczorek, A. Urbanczyk, and W. A. Van Hook, “Application of interferometric continuous-dilution differential refractometry to some solutions, including isotopomer solutions: isotope effects on polarizability in liquids,” J. Chem. Thermodyn. 28, 1009–1018 (1996).
[CrossRef]

Viale, P.

Voronin, A. A.

A. A. Voronin, V. P. Mitrokhin, A. A. Ivanov, A. B. Fedotov, D. A. Sidorov-Biryukov, V. I. Beloglazov, M. V. Alfimov, H. Ludvigsen, and A. M. Zheltikov, “Understanding the nonlinear-optical response of a liquid-core photonic-crystal fiber,” Laser Phys. Lett. 7, 46–49 (2010).
[CrossRef]

Vy Tran, Q.

Wadsworth, W. J.

Weber, M. J.

M. J. Weber, Handbook of Optical Materials (CRC, 2003), Part 5.5.2.

Weiner, A. M.

A. M. Weiner, Ultrafast Optics (Wiley, 2009).
[CrossRef]

Wieczorek, S. A.

S. A. Wieczorek, A. Urbanczyk, and W. A. Van Hook, “Application of interferometric continuous-dilution differential refractometry to some solutions, including isotopomer solutions: isotope effects on polarizability in liquids,” J. Chem. Thermodyn. 28, 1009–1018 (1996).
[CrossRef]

Wriedt, T.

J. Rheims, J. Koser, and T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8, 601–605 (1997).
[CrossRef]

Xuan, N. P.

S. Er-rhaimini, J. P. Lecoq, N. P. Xuan, G. Rivoire, and N. Tcherniega, “Amplitude object reconstruction by stimulated backward Raman scattering in the picosecond range with high efficiency conversion,” Opt. Commun. 104, 132–138 (1993).
[CrossRef]

Yan, X.

Yiou, S.

Zheltikov, A. M.

A. A. Voronin, V. P. Mitrokhin, A. A. Ivanov, A. B. Fedotov, D. A. Sidorov-Biryukov, V. I. Beloglazov, M. V. Alfimov, H. Ludvigsen, and A. M. Zheltikov, “Understanding the nonlinear-optical response of a liquid-core photonic-crystal fiber,” Laser Phys. Lett. 7, 46–49 (2010).
[CrossRef]

S. O. Konorov, A. B. Fedotov, E. E. Serebryannikov, V. P. Mitrokhin, D. A. Sidorov-Biryukov, and A. M. Zheltikov, “Phase-matched coherent anti-Stokes Raman scattering in isolated air-guided modes of hollow photonic-crystal fibres,” J. Raman Spectrosc. 36, 129–133 (2005).
[CrossRef]

Ann. Phys. (Paris) (1)

S. Lebrun, P. Delaye, and G. Roosen, “Stimulated Raman scattering in hollow core photonic crystal fibres,” Ann. Phys. (Paris) 32, 45–51 (2007).
[CrossRef]

Appl. Phys. Lett. (1)

F. Kroeger, A. Ryasnyanskiy, A. Baron, N. Dubreuil, Ph. Delaye, R. Frey, G. Roosen, and D. Peyrade, “Saturation of Raman amplification by self-phase modulation in silicon nanowaveguides,” Appl. Phys. Lett. 96, 241102 (2010).
[CrossRef]

J. Chem. Thermodyn. (1)

S. A. Wieczorek, A. Urbanczyk, and W. A. Van Hook, “Application of interferometric continuous-dilution differential refractometry to some solutions, including isotopomer solutions: isotope effects on polarizability in liquids,” J. Chem. Thermodyn. 28, 1009–1018 (1996).
[CrossRef]

J. Eur. Opt. Soc. Rapid Publ. (1)

F. Benabid, P. J. Roberts, F. Couny, and P. S. Light, “Light and gas confinement in hollow-core photonic crystal fibre based photonic microcells,” J. Eur. Opt. Soc. Rapid Publ. 4, 09004 (2009), and references therein.
[CrossRef]

J. Lightwave Technol. (1)

J. Nonlinear Opt. Phys. Mater. (1)

S. Lebrun, C. Buy, Ph. Delaye, R. Frey, G. Pauliat, and G. Roosen, “Optical characterization of a Raman generator based on a hollow core photonic crystal fiber filled with a liquid,” J. Nonlinear Opt. Phys. Mater. 19, 101–109 (2010).
[CrossRef]

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

F. Couny and F. Benabid, “Optical frequency comb generation in gas-filled hollow core photonic crystal fibres,” J. Opt. A, Pure Appl. Opt. 11, 103002 (2009), and references therein.
[CrossRef]

J. Opt. Soc. Am. B (3)

J. Raman Spectrosc. (1)

S. O. Konorov, A. B. Fedotov, E. E. Serebryannikov, V. P. Mitrokhin, D. A. Sidorov-Biryukov, and A. M. Zheltikov, “Phase-matched coherent anti-Stokes Raman scattering in isolated air-guided modes of hollow photonic-crystal fibres,” J. Raman Spectrosc. 36, 129–133 (2005).
[CrossRef]

Laser Phys. Lett. (1)

A. A. Voronin, V. P. Mitrokhin, A. A. Ivanov, A. B. Fedotov, D. A. Sidorov-Biryukov, V. I. Beloglazov, M. V. Alfimov, H. Ludvigsen, and A. M. Zheltikov, “Understanding the nonlinear-optical response of a liquid-core photonic-crystal fiber,” Laser Phys. Lett. 7, 46–49 (2010).
[CrossRef]

Meas. Sci. Technol. (1)

J. Rheims, J. Koser, and T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8, 601–605 (1997).
[CrossRef]

Opt. Commun. (1)

S. Er-rhaimini, J. P. Lecoq, N. P. Xuan, G. Rivoire, and N. Tcherniega, “Amplitude object reconstruction by stimulated backward Raman scattering in the picosecond range with high efficiency conversion,” Opt. Commun. 104, 132–138 (1993).
[CrossRef]

Opt. Express (6)

G. Antonopoulos, F. Benabid, T. A. Birks, D. M. Bird, J. C. Knight, and P. St. J. Russell, “Experimental demonstration of the frequency shift of bandgaps in photonic crystal fibers due to refractive index scaling,” Opt. Express 14, 3000–3006 (2006).
[CrossRef] [PubMed]

J. Bethge, A. Husakou, F. Mitschke, F. Noack, U. Griebner, G. Steinmeyer, and J. Herrmann, “Two-octave supercontinuum generation in a water-filled photonic crystal fiber,” Opt. Express 18, 6230–6240 (2010).
[CrossRef] [PubMed]

A. Bozolan, C. J. S. de Matos, C. M. B. Cordeiro, E. M. dos Santos, and J. Travers, “Supercontinuum generation in a water-core photonic crystal fiber,” Opt. Express 16, 9671–9676 (2008).
[CrossRef] [PubMed]

A. Baron, A. Ryasnyanskiy, N. Dubreuil, P. Delaye, Q. Vy Tran, S. Combrié, A. de Rossi, R. Frey, and G. Roosen, “Light localization induced enhancement of third order nonlinearities in a GaAs photonic crystal waveguide,” Opt. Express 17, 552–557 (2009).
[CrossRef] [PubMed]

S. Yiou, P. Delaye, A. Rouvie, J. Chinaud, R. Frey, G. Roosen, P. Viale, S. Février, P. Roy, J. L. Auguste, and J. M. Blondy, “Stimulated Raman scattering in an ethanol core microstructured optical fibre,” Opt. Express 13, 4786–4791 (2005).
[CrossRef] [PubMed]

M. Liao, C. Chaudhari, G. Qin, X. Yan, C. Kito, T. Suzuki, Y. Ohishi, M. Matsumoto, and T. Misumi, “Fabrication and characterization of a chalcogenide-tellurite composite microstructure fiber with high nonlinearity,” Opt. Express 17, 21608–21614 (2009).
[CrossRef] [PubMed]

Opt. Lett. (2)

Phys. Rev. A (2)

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

R. H. Stolen and C. Lin, “Self-phase modulation in silica optical fibers,” Phys. Rev. A 17, 1448–1453 (1978).
[CrossRef]

Phys. Rev. Lett. (1)

S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonant optical interactions with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005).
[CrossRef] [PubMed]

Science (1)

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

Other (6)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2006).

M. J. Weber, Handbook of Optical Materials (CRC, 2003), Part 5.5.2.

R. W. Boyd, Nonlinear Optics (Academic, 2003), Table 4.1.2.

A. M. Weiner, Ultrafast Optics (Wiley, 2009).
[CrossRef]

G. A. Campbell and R. M. Foster, Fourier Integrals for Practical Applications, 6th printing (D. Van Nostran, 1967), Formula 607.0, p. 68.

Bateman Manuscript Project, Higher Transcendental Functions (McGraw-Hill Book, 1953).

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Figures (8)

Fig. 1
Fig. 1

Calculated intensity spectrum of a hyperbolic secant pulse through a 1 m nonlinear fiber, for different values of the nonlinear phase shift (absorption is neglected for simplicity). The solid lines correspond to the analytical model [Eq. (9)] and the markers correspond to the numerical simulation using the split step Fourier method.

Fig. 2
Fig. 2

Schematic of experimental setup: BS, beam splitter cube; λ / 2 , half-wave plate; Pol., polarizer; M. Obj., 6.3× microscope objective; D, detector; OSA, optical spectrum analyzer; PCF, liquid filled HC-PCF.

Fig. 3
Fig. 3

Comparison between a batch of experimental spectra obtained with identical operating conditions for the laser ( λ = 926.8   nm ) and the theoretical spectrum calculated using Eq. (11) and the value of τ = 0.794   ps deduced from the autocorrelation measurement.

Fig. 4
Fig. 4

Power of a supercontinuum source transmitted through the HC-1550-02 hollow core fiber filled with acetone (blue dotted curve) and acetone-d6 (red solid curve). The additional losses due to overtones of infrared absorption bands of acetone are eliminated by deuteration, giving a full transmission band for the acetone-d6 filled fiber. The shift of the lower edge of the transmission band of the fiber filled with acetone-d6 is due to the slightly lower index of acetone-d6 compared to non-deuterated acetone [25]. The black dots show the measured variation of the group index of the fiber, from which the dispersion is deduced.

Fig. 5
Fig. 5

Image on the CCD camera of the fundamental mode exiting the fiber (black and white) at λ = 951   nm (left) with a two-dimensional Gaussian curve fit (color) (right).

Fig. 6
Fig. 6

Measured transmitted spectrum at different wavelengths at maximum pump power (green solid curves): (A) 926.8 nm ( τ = 0.794   ps ) , (B) 950.8 nm ( τ = 0.934   ps ) , and (C) 957.7 nm ( τ = 0.934   ps ) . (D) corresponds to (C) presented in logarithmic scale. The spectra are compared with the spectra calculated using expression (9) (blue dotted curves) and spectra given by the numerical split step Fourier model taking into account the measured dispersion of the fiber (red dashed curves). The pulse durations are deduced from the autocorrelation measurement.

Fig. 7
Fig. 7

Spectra of the pulses (red curves) transmitted through the liquid filled hollow core fiber and the fit (blue curves) with Eq. (9) at different incident pulse energies in the fiber at a wavelength of 926.8 nm (the incident spectra are the ones shown in Fig. 3).

Fig. 8
Fig. 8

Plot of the nonlinear coefficient determined by fitting the transmitted spectrum as a function of the energy of the pulse with measurements at three different wavelengths.

Tables (1)

Tables Icon

Table 1 Nonlinear Coefficient and Nonlinear Index Change Calculated from our Measurements at Different Wavelengths in the Liquid Filled Hollow Core Fiber

Equations (14)

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

U ( t , L ) = U ( t , 0 ) e α L / 2 e i γ L eff | U ( t , 0 ) | 2 ,
U ̃ ( ω , L ) = FT ( U ( t , L ) ) = + U ( t , L ) e i ω t d t .
δ ω ( t ) = γ L eff t | U ( t , 0 ) | 2 .
U ( t , L ) = P 0 f ( t ) e α L / 2 n = 0 + ( i γ L eff P 0 ) n | f ( t ) | 2 n n ! ,
U ̃ ( ω , L ) = P 0 e α L / 2 n = 0 + ( i γ L eff P 0 ) n n ! FT [ f ( t ) | f ( t ) | 2 n ] .
FT [ f ( t ) 2 n + 1 ] ( ω ) = 4 n π τ ( 2 n ) ! ( 1 2 + i τ ω 2 ) n ( 1 2 i τ ω 2 ) n sech ( π τ ω 2 )
U ̃ ( ω , L ) = P 0 e α L / 2 π τ   sech ( π τ ω 2 ) n = 0 + ( 1 2 + i τ ω 2 ) n ( 1 2 i τ ω 2 ) n ( 1 2 ) n ( 1 ) n ( i γ L eff P 0 ) n n ! .
U ̃ ( ω , L ) = P 0 e α L / 2 π τ   sech ( π τ ω 2 ) F 2 2 ( { 1 2 + i τ ω 2 , 1 2 i τ ω 2 } , { 1 2 , 1 } , i γ L eff P 0 ) ,
I ω ( ω , L ) = | U ̃ ( ω , L ) | 2 = P 0 e α L π 2 τ 2 sech 2 ( π τ ω 2 ) F 2 2 ( { 1 2 + i τ ω 2 , 1 2 i τ ω 2 } , { 1 2 , 1 } , i γ L eff P 0 ) F 2 2 ( { 1 2 i τ ω 2 , 1 2 + i τ ω 2 } , { 1 2 , 1 } , i γ L eff P 0 ) .
P 0 = E p 2 τ = P ¯ 2 τ f R .
I ω ( ω , L ) = P 0 e α L π 2 τ 2 sech 2 ( π τ ω 2 )
β 2 ( in   s 2 m 1 ) = 1.304 576 733 × 10 20 + 5.701 286 32 × 10 17 λ 1 9.964 374 186 × 10 14 λ 2 + 8.706 113 31 × 10 11 λ 3 3.802 860 616 × 10 8 λ 4 + 6.643 791 7 × 10 6 λ 5 ,
φ NL = γ α ( e α L 1 α L ) L P out ,
γ α = γ 0 α L e α L 1 .

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