Abstract

We have numerically studied a hollow-core photonic crystal fiber, with its core filled with highly nonlinear liquids such as carbon disulfide and nitrobenzene. Calculations show that the fiber has an extremely high nonlinear parameter γ on the order of 2.4/W/m at 1.55 μm. The group velocity dispersion of this fiber exhibits an anomalous region in the near-infrared, and its zero-dispersion wavelength is around 1.55 μm. This leads to potentially significant improvements and a large bandwidth in supercontinuum generation. The spectral properties of the supercontinuum generation in liquid-core photonic crystal fibers are simulated by solving the generalized nonlinear Schrödinger equation. The results demonstrate that the liquid-core PCF is capable to generate dramatically broadened supercontinua in a range from 700 nm to more than 2500 nm when pumping at 1.55 μm with subpicosecond pulses.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. St. J. Russell, "Photonic crystal fibres," Science 299, 358-362 (2003).
    [CrossRef] [PubMed]
  2. P. Rigby, "A photonic crystal fibre," Nature 396, 415-416 (1998).
    [CrossRef]
  3. W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T. P. M. Man, and P. St. J. Russell, "Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source," J. Opt. Soc. Am. B 19, 2148-2155 (2002).
    [CrossRef]
  4. K. J. Ranka, S. R. 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]
  5. J. Hansryd and P. A. Andrekson, "Broad-band continuous-wave-pumped fiber optical parameteric amplifier with 49-dB gain and wavelength-conversion efficiency," IEEE Photon. Technol. Lett. 13, 194-196 (2001).
    [CrossRef]
  6. H. Takara, T. Ohara, K. Mori, K. Sato, E. Yamada, M. Abe, Y. Inoue, T. Shibata, T. Morioka, and K. I. Sato, "More than 1000 chammel optical frequency chain generation from single supercontinuum source with 12.5 GHz channel spacing," IEE Electron. Lett. 36, 2089-2090 (2000).
    [CrossRef]
  7. A. V. Husakou and J. Herrmann, "Supercontinuum generation, four-wave mixing, and fission of higher-order solitons in photonic-crystal fibers," Opt. Lett. 19, 2171-2182 (2002).
  8. J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, "Experimental Evidence for Supercontinuum Generation by Fission of Higher-Order Solitons in Photonic Fibers," Phys. Rev. Lett. 88, 173901 (2002).
    [CrossRef] [PubMed]
  9. S. Coen, AHL. Chau, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, "Supercontinuum generation by stimulated Raman scattering and parametric four-wave mixing in photonic crystal fibers," J. Opt. Soc. Am. B,  19, 753-764, (2002).
    [CrossRef]
  10. G. Genty, M. Lehtonen, and H. Ludvigsen, "Effect of cross-phase modulation on supercontinuum generated in microstructured fibers with sub- 30 fs pulses," Opt. Express 12, 4614-4624 (2004).
    [CrossRef] [PubMed]
  11. T. Schreiber, T. V. Andersen, D. Schimpf, J. Limpert, A. Tünnermann, " Supercontinuum generation by femtosecond single and dual wavelength pumping in photonic crystal fibers with two zero dispersion wavelengths, " Opt. Express 13, 9556-9569 (2005).
    [CrossRef] [PubMed]
  12. T. M. Monro, K. M. Kiang, J. H. Lee, K. Frampton, Z. Yusoff, R. Moore, J. Tucknott, D. W. Hewak, H. N. Rutt, and D. J. Richardson, "High nonlinearity extruded single-mode holey optical fibers," Anaheim, CA, Postdeadline Paper FA1, 19-21 March 2002.
  13. V. V. R. Kumar, A. George, W. Reeves, J. Knight, P. Russell, F. Omenetto, and A. Taylor, "Extruded soft glass photonic crystal fiber for ultrabroad supercontinuum generation," Opt. Express 10, 1520-1525 (2002).
    [PubMed]
  14. F. G. Omenetto, N. A. Wolchover, M. R. Wehner, M. Ross, A. Efimov, A. J. Taylor, V. V. R. K. Kumar, A. K. George, J. C. Knight, N. Y. Joly, and P. S. J. Russell, "Spectrally smooth supercontinuum from 350 nm to 3 μm in sub-centimeter lengths of soft-glass photonic crystal fibers," Opt. Express 14, 4928-4934 (2006).
    [CrossRef] [PubMed]
  15. G. S. He and P. N. Prasad, "Stimulated Kerr scattering and reorientation work of molecules in liquid CS2," Phys. Rev. A 41, 2687-2697 (1990).
    [CrossRef] [PubMed]
  16. T. J. Bridges, A. R. Chraplyvy, J. G. Bergman, Jr., and R. M. Hart, "Broadband infrared generation in liquid-bromine-core optical fibers," Opt. Lett. 7, 566-568 (1982).
    [CrossRef] [PubMed]
  17. C. Martelli, J. Canning, K. Lyytikainen, and N. Groothoff, "Water-core Fresnel fiber," Opt. Express 13, 3890-3895, (2005).
    [CrossRef] [PubMed]
  18. M. Böhm, H. Hartwig, and F. Mitschke, "Präparation von mit Flüssigkeiten gefüllten mikrostrukturierten Glasfasern," Frühjahrstagung der DPG Berlin 2005, Q 29.2 (2005).
  19. A. Fuerbach, P. Steinvurzel, J. Bolger, and B. Eggleton, "Nonlinear pulse propagation at zero dispersion wavelength in anti-resonant photonic crystal fibers," Opt. Express 13, 2977-2987 (2005)
    [CrossRef] [PubMed]
  20. 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 fiber," Opt. Express 13, 4786-4791 (2005).
    [CrossRef] [PubMed]
  21. F. M. Cox, A. Argyros, and M. C. J. Large, "Liquid-filled hollow core microstructured polymer optical fiber," Opt. Express 14, 4135-4140 (2006).
    [CrossRef] [PubMed]
  22. R. L. Sutherland, "Handbook of nonlinear optics," (Marcel Dekker, Inc., New York, USA, 1996), pp. 457.
  23. A. Samoc, "Dispersion of refractive properties of solvents: Chloroform, toluene, benzene, and carbon disulfide in ultraviolet, visible, and near-infrared," J. Appl. Phys. 94, 6167-6174 (2003).
    [CrossRef]
  24. T. Birks, J. Knight, and P.St. J. Russell, "Endlessly single-mode photonic crystal fiber," Opt. Lett. 22, 961-963 (1997).
    [CrossRef] [PubMed]
  25. T. P. White, R. C. McPhedran, L. C. Botten, G. H. Smith, and C. M. de Sterke, "Calculations of air-guided modes in photonic crystal fibers using the multipole method," Opt. Express 11, 721-732 (2001).
    [CrossRef]
  26. B. J. Eggleton, P.S. Westbrook, R. S. Windeler, S. Spalter, and T. A Strasser, "Grating resonances in air/silica micro structured optical fibers," Opt. Lett. 24, 1460-1462 (1999).
    [CrossRef]
  27. M. Midrio, M. P. Singh, and C. G. Someda, "The space filling mode of holey fibers: an analytical vectorial solution," J. Lightwave Technol. 18, 1031-1037 (2000).
    [CrossRef]
  28. Y. Li, C. Wang, M. Hu, "A fully vectorial effective index method for photonic crystal fibers: application to dispersion calculation," Opt. Commun. 238, 29-33 (2004).
    [CrossRef]
  29. G. P. Agrawal, "Nonlinear Fiber Optics - Optics and Photonics," Third Edition, (Academic Press, San Diego, USA, 2001), pp. 36.
  30. A. W. Snyder, and J. D. Love, "Optical waveguide theory," (London, 1983). Chapter 12-15.
  31. B. Kibler, J. M. Dudley, and S. Coen, "Supercontinuum generation and nonlinear pulse propagation in photonic crystal fiber: influence of the frequency-dependent effective mode area," Appl. Phys. B 81, 337-342 (2005).
    [CrossRef]
  32. J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, "Tapered Single-mode Fibres and Devices Part 1: Adiabaticity Criteria," IEE Proceedings-J. 138, 343-354 (1991).
  33. R. Zhang, X. P. Zhang, and H. Giessen, "Mode and group velocity dispersion evolution in the tapered region of a single-mode tapered fiber," Opt. Express 12, 5840-5849 (2004).
    [CrossRef] [PubMed]
  34. J. M. Dudley, and S. Coen, "Numerical simulations and coherence properties of supercontinuum generation in photonic crystal and tapered optical fibers," IEEE J. Sel. Top. Quantum Electron. 8, 651-659 (2002).
    [CrossRef]
  35. D. McMorrwo, W. T. Lotshaw, and G. A. Kenney-Wallace, "Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids," IEEE J. Quantum Electron. 24, 443-454 (1988).
    [CrossRef]
  36. R. W. Hellwarth, "Third- order optical susceptibilities of liquids and solids," Prog. Quantum Electron. 5, 1 (1977).
    [CrossRef]
  37. B. F. Levine and C. G. Bethea, "Second and third order hyperpolarizabilities of organic molecules," J. Chem. Phys. 63, 2666-2682 (1975).
    [CrossRef]
  38. I. A. Heisler, R. R. B. Correia, T. Buckup, and S. L. S. Cunha, "Time-resolved optical Kerr-effect investigation on CS2/polystyrene mixtures," J. Chem. Phys. 123, 054509 (2005).
    [CrossRef] [PubMed]

2006

2005

2004

2003

A. Samoc, "Dispersion of refractive properties of solvents: Chloroform, toluene, benzene, and carbon disulfide in ultraviolet, visible, and near-infrared," J. Appl. Phys. 94, 6167-6174 (2003).
[CrossRef]

P. St. J. Russell, "Photonic crystal fibres," Science 299, 358-362 (2003).
[CrossRef] [PubMed]

2002

T. M. Monro, K. M. Kiang, J. H. Lee, K. Frampton, Z. Yusoff, R. Moore, J. Tucknott, D. W. Hewak, H. N. Rutt, and D. J. Richardson, "High nonlinearity extruded single-mode holey optical fibers," Anaheim, CA, Postdeadline Paper FA1, 19-21 March 2002.

A. V. Husakou and J. Herrmann, "Supercontinuum generation, four-wave mixing, and fission of higher-order solitons in photonic-crystal fibers," Opt. Lett. 19, 2171-2182 (2002).

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, "Experimental Evidence for Supercontinuum Generation by Fission of Higher-Order Solitons in Photonic Fibers," Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef] [PubMed]

J. M. Dudley, and S. Coen, "Numerical simulations and coherence properties of supercontinuum generation in photonic crystal and tapered optical fibers," IEEE J. Sel. Top. Quantum Electron. 8, 651-659 (2002).
[CrossRef]

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

W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T. P. M. Man, and P. St. J. Russell, "Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source," J. Opt. Soc. Am. B 19, 2148-2155 (2002).
[CrossRef]

V. V. R. Kumar, A. George, W. Reeves, J. Knight, P. Russell, F. Omenetto, and A. Taylor, "Extruded soft glass photonic crystal fiber for ultrabroad supercontinuum generation," Opt. Express 10, 1520-1525 (2002).
[PubMed]

2001

T. P. White, R. C. McPhedran, L. C. Botten, G. H. Smith, and C. M. de Sterke, "Calculations of air-guided modes in photonic crystal fibers using the multipole method," Opt. Express 11, 721-732 (2001).
[CrossRef]

J. Hansryd and P. A. Andrekson, "Broad-band continuous-wave-pumped fiber optical parameteric amplifier with 49-dB gain and wavelength-conversion efficiency," IEEE Photon. Technol. Lett. 13, 194-196 (2001).
[CrossRef]

2000

H. Takara, T. Ohara, K. Mori, K. Sato, E. Yamada, M. Abe, Y. Inoue, T. Shibata, T. Morioka, and K. I. Sato, "More than 1000 chammel optical frequency chain generation from single supercontinuum source with 12.5 GHz channel spacing," IEE Electron. Lett. 36, 2089-2090 (2000).
[CrossRef]

M. Midrio, M. P. Singh, and C. G. Someda, "The space filling mode of holey fibers: an analytical vectorial solution," J. Lightwave Technol. 18, 1031-1037 (2000).
[CrossRef]

K. J. Ranka, S. R. 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]

1999

1998

P. Rigby, "A photonic crystal fibre," Nature 396, 415-416 (1998).
[CrossRef]

1997

1991

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, "Tapered Single-mode Fibres and Devices Part 1: Adiabaticity Criteria," IEE Proceedings-J. 138, 343-354 (1991).

1990

G. S. He and P. N. Prasad, "Stimulated Kerr scattering and reorientation work of molecules in liquid CS2," Phys. Rev. A 41, 2687-2697 (1990).
[CrossRef] [PubMed]

1988

D. McMorrwo, W. T. Lotshaw, and G. A. Kenney-Wallace, "Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids," IEEE J. Quantum Electron. 24, 443-454 (1988).
[CrossRef]

1982

1977

R. W. Hellwarth, "Third- order optical susceptibilities of liquids and solids," Prog. Quantum Electron. 5, 1 (1977).
[CrossRef]

1975

B. F. Levine and C. G. Bethea, "Second and third order hyperpolarizabilities of organic molecules," J. Chem. Phys. 63, 2666-2682 (1975).
[CrossRef]

Abe, M.

H. Takara, T. Ohara, K. Mori, K. Sato, E. Yamada, M. Abe, Y. Inoue, T. Shibata, T. Morioka, and K. I. Sato, "More than 1000 chammel optical frequency chain generation from single supercontinuum source with 12.5 GHz channel spacing," IEE Electron. Lett. 36, 2089-2090 (2000).
[CrossRef]

Andersen, T. V.

Andrekson, P. A.

J. Hansryd and P. A. Andrekson, "Broad-band continuous-wave-pumped fiber optical parameteric amplifier with 49-dB gain and wavelength-conversion efficiency," IEEE Photon. Technol. Lett. 13, 194-196 (2001).
[CrossRef]

Argyros, A.

Auguste, J. -L.

Bergman, J. G.

Bethea, C. G.

B. F. Levine and C. G. Bethea, "Second and third order hyperpolarizabilities of organic molecules," J. Chem. Phys. 63, 2666-2682 (1975).
[CrossRef]

Birks, T.

Birks, T. A.

Black, R. J.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, "Tapered Single-mode Fibres and Devices Part 1: Adiabaticity Criteria," IEE Proceedings-J. 138, 343-354 (1991).

Blondy, J. -M.

Bolger, J.

Botten, L. C.

T. P. White, R. C. McPhedran, L. C. Botten, G. H. Smith, and C. M. de Sterke, "Calculations of air-guided modes in photonic crystal fibers using the multipole method," Opt. Express 11, 721-732 (2001).
[CrossRef]

Bridges, T. J.

Buckup, T.

I. A. Heisler, R. R. B. Correia, T. Buckup, and S. L. S. Cunha, "Time-resolved optical Kerr-effect investigation on CS2/polystyrene mixtures," J. Chem. Phys. 123, 054509 (2005).
[CrossRef] [PubMed]

Canning, J.

Chau, AHL.

Chinaud, J.

Chraplyvy, A. R.

Coen, S.

B. Kibler, J. M. Dudley, and S. Coen, "Supercontinuum generation and nonlinear pulse propagation in photonic crystal fiber: influence of the frequency-dependent effective mode area," Appl. Phys. B 81, 337-342 (2005).
[CrossRef]

J. M. Dudley, and S. Coen, "Numerical simulations and coherence properties of supercontinuum generation in photonic crystal and tapered optical fibers," IEEE J. Sel. Top. Quantum Electron. 8, 651-659 (2002).
[CrossRef]

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

Correia, R. R. B.

I. A. Heisler, R. R. B. Correia, T. Buckup, and S. L. S. Cunha, "Time-resolved optical Kerr-effect investigation on CS2/polystyrene mixtures," J. Chem. Phys. 123, 054509 (2005).
[CrossRef] [PubMed]

Cox, F. M.

Cunha, S. L. S.

I. A. Heisler, R. R. B. Correia, T. Buckup, and S. L. S. Cunha, "Time-resolved optical Kerr-effect investigation on CS2/polystyrene mixtures," J. Chem. Phys. 123, 054509 (2005).
[CrossRef] [PubMed]

de Sterke, C. M.

T. P. White, R. C. McPhedran, L. C. Botten, G. H. Smith, and C. M. de Sterke, "Calculations of air-guided modes in photonic crystal fibers using the multipole method," Opt. Express 11, 721-732 (2001).
[CrossRef]

Delaye, P.

Dudley, J. M.

B. Kibler, J. M. Dudley, and S. Coen, "Supercontinuum generation and nonlinear pulse propagation in photonic crystal fiber: influence of the frequency-dependent effective mode area," Appl. Phys. B 81, 337-342 (2005).
[CrossRef]

J. M. Dudley, and S. Coen, "Numerical simulations and coherence properties of supercontinuum generation in photonic crystal and tapered optical fibers," IEEE J. Sel. Top. Quantum Electron. 8, 651-659 (2002).
[CrossRef]

Efimov, A.

Eggleton, B.

Eggleton, B. J.

Février, S.

Frampton, K.

T. M. Monro, K. M. Kiang, J. H. Lee, K. Frampton, Z. Yusoff, R. Moore, J. Tucknott, D. W. Hewak, H. N. Rutt, and D. J. Richardson, "High nonlinearity extruded single-mode holey optical fibers," Anaheim, CA, Postdeadline Paper FA1, 19-21 March 2002.

Frey, R.

Fuerbach, A.

Genty, G.

George, A.

George, A. K.

Giessen, H.

Gonthier, F.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, "Tapered Single-mode Fibres and Devices Part 1: Adiabaticity Criteria," IEE Proceedings-J. 138, 343-354 (1991).

Griebner, U.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, "Experimental Evidence for Supercontinuum Generation by Fission of Higher-Order Solitons in Photonic Fibers," Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef] [PubMed]

Groothoff, N.

Hansryd, J.

J. Hansryd and P. A. Andrekson, "Broad-band continuous-wave-pumped fiber optical parameteric amplifier with 49-dB gain and wavelength-conversion efficiency," IEEE Photon. Technol. Lett. 13, 194-196 (2001).
[CrossRef]

Hart, R. M.

Harvey, J. D.

He, G. S.

G. S. He and P. N. Prasad, "Stimulated Kerr scattering and reorientation work of molecules in liquid CS2," Phys. Rev. A 41, 2687-2697 (1990).
[CrossRef] [PubMed]

Heisler, I. A.

I. A. Heisler, R. R. B. Correia, T. Buckup, and S. L. S. Cunha, "Time-resolved optical Kerr-effect investigation on CS2/polystyrene mixtures," J. Chem. Phys. 123, 054509 (2005).
[CrossRef] [PubMed]

Hellwarth, R. W.

R. W. Hellwarth, "Third- order optical susceptibilities of liquids and solids," Prog. Quantum Electron. 5, 1 (1977).
[CrossRef]

Henry, W. M.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, "Tapered Single-mode Fibres and Devices Part 1: Adiabaticity Criteria," IEE Proceedings-J. 138, 343-354 (1991).

Herrmann, J.

A. V. Husakou and J. Herrmann, "Supercontinuum generation, four-wave mixing, and fission of higher-order solitons in photonic-crystal fibers," Opt. Lett. 19, 2171-2182 (2002).

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, "Experimental Evidence for Supercontinuum Generation by Fission of Higher-Order Solitons in Photonic Fibers," Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef] [PubMed]

Hewak, D. W.

T. M. Monro, K. M. Kiang, J. H. Lee, K. Frampton, Z. Yusoff, R. Moore, J. Tucknott, D. W. Hewak, H. N. Rutt, and D. J. Richardson, "High nonlinearity extruded single-mode holey optical fibers," Anaheim, CA, Postdeadline Paper FA1, 19-21 March 2002.

Hu, M.

Y. Li, C. Wang, M. Hu, "A fully vectorial effective index method for photonic crystal fibers: application to dispersion calculation," Opt. Commun. 238, 29-33 (2004).
[CrossRef]

Husakou, A.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, "Experimental Evidence for Supercontinuum Generation by Fission of Higher-Order Solitons in Photonic Fibers," Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef] [PubMed]

Husakou, A. V.

A. V. Husakou and J. Herrmann, "Supercontinuum generation, four-wave mixing, and fission of higher-order solitons in photonic-crystal fibers," Opt. Lett. 19, 2171-2182 (2002).

Inoue, Y.

H. Takara, T. Ohara, K. Mori, K. Sato, E. Yamada, M. Abe, Y. Inoue, T. Shibata, T. Morioka, and K. I. Sato, "More than 1000 chammel optical frequency chain generation from single supercontinuum source with 12.5 GHz channel spacing," IEE Electron. Lett. 36, 2089-2090 (2000).
[CrossRef]

Joly, N. Y.

Kenney-Wallace, G. A.

D. McMorrwo, W. T. Lotshaw, and G. A. Kenney-Wallace, "Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids," IEEE J. Quantum Electron. 24, 443-454 (1988).
[CrossRef]

Kiang, K. M.

T. M. Monro, K. M. Kiang, J. H. Lee, K. Frampton, Z. Yusoff, R. Moore, J. Tucknott, D. W. Hewak, H. N. Rutt, and D. J. Richardson, "High nonlinearity extruded single-mode holey optical fibers," Anaheim, CA, Postdeadline Paper FA1, 19-21 March 2002.

Kibler, B.

B. Kibler, J. M. Dudley, and S. Coen, "Supercontinuum generation and nonlinear pulse propagation in photonic crystal fiber: influence of the frequency-dependent effective mode area," Appl. Phys. B 81, 337-342 (2005).
[CrossRef]

Knight, J.

Knight, J. C.

Korn, G.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, "Experimental Evidence for Supercontinuum Generation by Fission of Higher-Order Solitons in Photonic Fibers," Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef] [PubMed]

Kumar, V. V. R.

Kumar, V. V. R. K.

Lacroix, S.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, "Tapered Single-mode Fibres and Devices Part 1: Adiabaticity Criteria," IEE Proceedings-J. 138, 343-354 (1991).

Large, M. C. J.

Lee, J. H.

T. M. Monro, K. M. Kiang, J. H. Lee, K. Frampton, Z. Yusoff, R. Moore, J. Tucknott, D. W. Hewak, H. N. Rutt, and D. J. Richardson, "High nonlinearity extruded single-mode holey optical fibers," Anaheim, CA, Postdeadline Paper FA1, 19-21 March 2002.

Lehtonen, M.

Leonhardt, R.

Levine, B. F.

B. F. Levine and C. G. Bethea, "Second and third order hyperpolarizabilities of organic molecules," J. Chem. Phys. 63, 2666-2682 (1975).
[CrossRef]

Li, Y.

Y. Li, C. Wang, M. Hu, "A fully vectorial effective index method for photonic crystal fibers: application to dispersion calculation," Opt. Commun. 238, 29-33 (2004).
[CrossRef]

Limpert, J.

Lotshaw, W. T.

D. McMorrwo, W. T. Lotshaw, and G. A. Kenney-Wallace, "Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids," IEEE J. Quantum Electron. 24, 443-454 (1988).
[CrossRef]

Love, J. D.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, "Tapered Single-mode Fibres and Devices Part 1: Adiabaticity Criteria," IEE Proceedings-J. 138, 343-354 (1991).

Ludvigsen, H.

Lyytikainen, K.

Man, T. P. M.

Martelli, C.

McMorrwo, D.

D. McMorrwo, W. T. Lotshaw, and G. A. Kenney-Wallace, "Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids," IEEE J. Quantum Electron. 24, 443-454 (1988).
[CrossRef]

McPhedran, R. C.

T. P. White, R. C. McPhedran, L. C. Botten, G. H. Smith, and C. M. de Sterke, "Calculations of air-guided modes in photonic crystal fibers using the multipole method," Opt. Express 11, 721-732 (2001).
[CrossRef]

Midrio, M.

Monro, T. M.

T. M. Monro, K. M. Kiang, J. H. Lee, K. Frampton, Z. Yusoff, R. Moore, J. Tucknott, D. W. Hewak, H. N. Rutt, and D. J. Richardson, "High nonlinearity extruded single-mode holey optical fibers," Anaheim, CA, Postdeadline Paper FA1, 19-21 March 2002.

Moore, R.

T. M. Monro, K. M. Kiang, J. H. Lee, K. Frampton, Z. Yusoff, R. Moore, J. Tucknott, D. W. Hewak, H. N. Rutt, and D. J. Richardson, "High nonlinearity extruded single-mode holey optical fibers," Anaheim, CA, Postdeadline Paper FA1, 19-21 March 2002.

Mori, K.

H. Takara, T. Ohara, K. Mori, K. Sato, E. Yamada, M. Abe, Y. Inoue, T. Shibata, T. Morioka, and K. I. Sato, "More than 1000 chammel optical frequency chain generation from single supercontinuum source with 12.5 GHz channel spacing," IEE Electron. Lett. 36, 2089-2090 (2000).
[CrossRef]

Morioka, T.

H. Takara, T. Ohara, K. Mori, K. Sato, E. Yamada, M. Abe, Y. Inoue, T. Shibata, T. Morioka, and K. I. Sato, "More than 1000 chammel optical frequency chain generation from single supercontinuum source with 12.5 GHz channel spacing," IEE Electron. Lett. 36, 2089-2090 (2000).
[CrossRef]

Nickel, D.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, "Experimental Evidence for Supercontinuum Generation by Fission of Higher-Order Solitons in Photonic Fibers," Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef] [PubMed]

Ohara, T.

H. Takara, T. Ohara, K. Mori, K. Sato, E. Yamada, M. Abe, Y. Inoue, T. Shibata, T. Morioka, and K. I. Sato, "More than 1000 chammel optical frequency chain generation from single supercontinuum source with 12.5 GHz channel spacing," IEE Electron. Lett. 36, 2089-2090 (2000).
[CrossRef]

Omenetto, F.

Omenetto, F. G.

Ortigosa-Blanch, A.

Prasad, P. N.

G. S. He and P. N. Prasad, "Stimulated Kerr scattering and reorientation work of molecules in liquid CS2," Phys. Rev. A 41, 2687-2697 (1990).
[CrossRef] [PubMed]

Ranka, K. J.

Reeves, W.

Richardson, D. J.

T. M. Monro, K. M. Kiang, J. H. Lee, K. Frampton, Z. Yusoff, R. Moore, J. Tucknott, D. W. Hewak, H. N. Rutt, and D. J. Richardson, "High nonlinearity extruded single-mode holey optical fibers," Anaheim, CA, Postdeadline Paper FA1, 19-21 March 2002.

Rigby, P.

P. Rigby, "A photonic crystal fibre," Nature 396, 415-416 (1998).
[CrossRef]

Roosen, G.

Ross, M.

Rouvie, A.

Roy, P.

Russell, P.

Russell, P. S. J.

Russell, P. St. J.

P. St. J. Russell, "Photonic crystal fibres," Science 299, 358-362 (2003).
[CrossRef] [PubMed]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, "Experimental Evidence for Supercontinuum Generation by Fission of Higher-Order Solitons in Photonic Fibers," Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef] [PubMed]

W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T. P. M. Man, and P. St. J. Russell, "Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source," J. Opt. Soc. Am. B 19, 2148-2155 (2002).
[CrossRef]

Russell, P.St. J.

Rutt, H. N.

T. M. Monro, K. M. Kiang, J. H. Lee, K. Frampton, Z. Yusoff, R. Moore, J. Tucknott, D. W. Hewak, H. N. Rutt, and D. J. Richardson, "High nonlinearity extruded single-mode holey optical fibers," Anaheim, CA, Postdeadline Paper FA1, 19-21 March 2002.

Samoc, A.

A. Samoc, "Dispersion of refractive properties of solvents: Chloroform, toluene, benzene, and carbon disulfide in ultraviolet, visible, and near-infrared," J. Appl. Phys. 94, 6167-6174 (2003).
[CrossRef]

Sato, K.

H. Takara, T. Ohara, K. Mori, K. Sato, E. Yamada, M. Abe, Y. Inoue, T. Shibata, T. Morioka, and K. I. Sato, "More than 1000 chammel optical frequency chain generation from single supercontinuum source with 12.5 GHz channel spacing," IEE Electron. Lett. 36, 2089-2090 (2000).
[CrossRef]

Sato, K. I.

H. Takara, T. Ohara, K. Mori, K. Sato, E. Yamada, M. Abe, Y. Inoue, T. Shibata, T. Morioka, and K. I. Sato, "More than 1000 chammel optical frequency chain generation from single supercontinuum source with 12.5 GHz channel spacing," IEE Electron. Lett. 36, 2089-2090 (2000).
[CrossRef]

Schimpf, D.

Schreiber, T.

Shibata, T.

H. Takara, T. Ohara, K. Mori, K. Sato, E. Yamada, M. Abe, Y. Inoue, T. Shibata, T. Morioka, and K. I. Sato, "More than 1000 chammel optical frequency chain generation from single supercontinuum source with 12.5 GHz channel spacing," IEE Electron. Lett. 36, 2089-2090 (2000).
[CrossRef]

Singh, M. P.

Smith, G. H.

T. P. White, R. C. McPhedran, L. C. Botten, G. H. Smith, and C. M. de Sterke, "Calculations of air-guided modes in photonic crystal fibers using the multipole method," Opt. Express 11, 721-732 (2001).
[CrossRef]

Someda, C. G.

Spalter, S.

St, P.

Steinvurzel, P.

Stentz, A. J.

Stewart, W. J.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, "Tapered Single-mode Fibres and Devices Part 1: Adiabaticity Criteria," IEE Proceedings-J. 138, 343-354 (1991).

Strasser, T. A

Takara, H.

H. Takara, T. Ohara, K. Mori, K. Sato, E. Yamada, M. Abe, Y. Inoue, T. Shibata, T. Morioka, and K. I. Sato, "More than 1000 chammel optical frequency chain generation from single supercontinuum source with 12.5 GHz channel spacing," IEE Electron. Lett. 36, 2089-2090 (2000).
[CrossRef]

Taylor, A.

Taylor, A. J.

Tucknott, J.

T. M. Monro, K. M. Kiang, J. H. Lee, K. Frampton, Z. Yusoff, R. Moore, J. Tucknott, D. W. Hewak, H. N. Rutt, and D. J. Richardson, "High nonlinearity extruded single-mode holey optical fibers," Anaheim, CA, Postdeadline Paper FA1, 19-21 March 2002.

Tünnermann, A.

Viale, P.

Wadsworth, W. J.

Wang, C.

Y. Li, C. Wang, M. Hu, "A fully vectorial effective index method for photonic crystal fibers: application to dispersion calculation," Opt. Commun. 238, 29-33 (2004).
[CrossRef]

Wehner, M. R.

Westbrook, P.S.

White, T. P.

T. P. White, R. C. McPhedran, L. C. Botten, G. H. Smith, and C. M. de Sterke, "Calculations of air-guided modes in photonic crystal fibers using the multipole method," Opt. Express 11, 721-732 (2001).
[CrossRef]

Windeler, R. S.

Windeler, S. R.

Wolchover, N. A.

Yamada, E.

H. Takara, T. Ohara, K. Mori, K. Sato, E. Yamada, M. Abe, Y. Inoue, T. Shibata, T. Morioka, and K. I. Sato, "More than 1000 chammel optical frequency chain generation from single supercontinuum source with 12.5 GHz channel spacing," IEE Electron. Lett. 36, 2089-2090 (2000).
[CrossRef]

Yiou, S.

Yusoff, Z.

T. M. Monro, K. M. Kiang, J. H. Lee, K. Frampton, Z. Yusoff, R. Moore, J. Tucknott, D. W. Hewak, H. N. Rutt, and D. J. Richardson, "High nonlinearity extruded single-mode holey optical fibers," Anaheim, CA, Postdeadline Paper FA1, 19-21 March 2002.

Zhang, R.

Zhang, X. P.

Zhavoronkov, N.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, "Experimental Evidence for Supercontinuum Generation by Fission of Higher-Order Solitons in Photonic Fibers," Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef] [PubMed]

Appl. Phys. B

B. Kibler, J. M. Dudley, and S. Coen, "Supercontinuum generation and nonlinear pulse propagation in photonic crystal fiber: influence of the frequency-dependent effective mode area," Appl. Phys. B 81, 337-342 (2005).
[CrossRef]

CA, Postdeadline Paper

T. M. Monro, K. M. Kiang, J. H. Lee, K. Frampton, Z. Yusoff, R. Moore, J. Tucknott, D. W. Hewak, H. N. Rutt, and D. J. Richardson, "High nonlinearity extruded single-mode holey optical fibers," Anaheim, CA, Postdeadline Paper FA1, 19-21 March 2002.

IEE Electron. Lett.

H. Takara, T. Ohara, K. Mori, K. Sato, E. Yamada, M. Abe, Y. Inoue, T. Shibata, T. Morioka, and K. I. Sato, "More than 1000 chammel optical frequency chain generation from single supercontinuum source with 12.5 GHz channel spacing," IEE Electron. Lett. 36, 2089-2090 (2000).
[CrossRef]

IEE Proceedings-J.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, "Tapered Single-mode Fibres and Devices Part 1: Adiabaticity Criteria," IEE Proceedings-J. 138, 343-354 (1991).

IEEE J. Quantum Electron.

D. McMorrwo, W. T. Lotshaw, and G. A. Kenney-Wallace, "Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids," IEEE J. Quantum Electron. 24, 443-454 (1988).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

J. M. Dudley, and S. Coen, "Numerical simulations and coherence properties of supercontinuum generation in photonic crystal and tapered optical fibers," IEEE J. Sel. Top. Quantum Electron. 8, 651-659 (2002).
[CrossRef]

IEEE Photon. Technol. Lett.

J. Hansryd and P. A. Andrekson, "Broad-band continuous-wave-pumped fiber optical parameteric amplifier with 49-dB gain and wavelength-conversion efficiency," IEEE Photon. Technol. Lett. 13, 194-196 (2001).
[CrossRef]

J. Appl. Phys.

A. Samoc, "Dispersion of refractive properties of solvents: Chloroform, toluene, benzene, and carbon disulfide in ultraviolet, visible, and near-infrared," J. Appl. Phys. 94, 6167-6174 (2003).
[CrossRef]

J. Chem. Phys.

B. F. Levine and C. G. Bethea, "Second and third order hyperpolarizabilities of organic molecules," J. Chem. Phys. 63, 2666-2682 (1975).
[CrossRef]

I. A. Heisler, R. R. B. Correia, T. Buckup, and S. L. S. Cunha, "Time-resolved optical Kerr-effect investigation on CS2/polystyrene mixtures," J. Chem. Phys. 123, 054509 (2005).
[CrossRef] [PubMed]

J. Lightwave Technol.

J. Opt. Soc. Am. B

Nature

P. Rigby, "A photonic crystal fibre," Nature 396, 415-416 (1998).
[CrossRef]

Opt. Commun.

Y. Li, C. Wang, M. Hu, "A fully vectorial effective index method for photonic crystal fibers: application to dispersion calculation," Opt. Commun. 238, 29-33 (2004).
[CrossRef]

Opt. Express

V. V. R. Kumar, A. George, W. Reeves, J. Knight, P. Russell, F. Omenetto, and A. Taylor, "Extruded soft glass photonic crystal fiber for ultrabroad supercontinuum generation," Opt. Express 10, 1520-1525 (2002).
[PubMed]

G. Genty, M. Lehtonen, and H. Ludvigsen, "Effect of cross-phase modulation on supercontinuum generated in microstructured fibers with sub- 30 fs pulses," Opt. Express 12, 4614-4624 (2004).
[CrossRef] [PubMed]

R. Zhang, X. P. Zhang, and H. Giessen, "Mode and group velocity dispersion evolution in the tapered region of a single-mode tapered fiber," Opt. Express 12, 5840-5849 (2004).
[CrossRef] [PubMed]

A. Fuerbach, P. Steinvurzel, J. Bolger, and B. Eggleton, "Nonlinear pulse propagation at zero dispersion wavelength in anti-resonant photonic crystal fibers," Opt. Express 13, 2977-2987 (2005)
[CrossRef] [PubMed]

C. Martelli, J. Canning, K. Lyytikainen, and N. Groothoff, "Water-core Fresnel fiber," Opt. Express 13, 3890-3895, (2005).
[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 fiber," Opt. Express 13, 4786-4791 (2005).
[CrossRef] [PubMed]

T. Schreiber, T. V. Andersen, D. Schimpf, J. Limpert, A. Tünnermann, " Supercontinuum generation by femtosecond single and dual wavelength pumping in photonic crystal fibers with two zero dispersion wavelengths, " Opt. Express 13, 9556-9569 (2005).
[CrossRef] [PubMed]

F. M. Cox, A. Argyros, and M. C. J. Large, "Liquid-filled hollow core microstructured polymer optical fiber," Opt. Express 14, 4135-4140 (2006).
[CrossRef] [PubMed]

F. G. Omenetto, N. A. Wolchover, M. R. Wehner, M. Ross, A. Efimov, A. J. Taylor, V. V. R. K. Kumar, A. K. George, J. C. Knight, N. Y. Joly, and P. S. J. Russell, "Spectrally smooth supercontinuum from 350 nm to 3 μm in sub-centimeter lengths of soft-glass photonic crystal fibers," Opt. Express 14, 4928-4934 (2006).
[CrossRef] [PubMed]

T. P. White, R. C. McPhedran, L. C. Botten, G. H. Smith, and C. M. de Sterke, "Calculations of air-guided modes in photonic crystal fibers using the multipole method," Opt. Express 11, 721-732 (2001).
[CrossRef]

Opt. Lett.

Phys. Rev. A

G. S. He and P. N. Prasad, "Stimulated Kerr scattering and reorientation work of molecules in liquid CS2," Phys. Rev. A 41, 2687-2697 (1990).
[CrossRef] [PubMed]

Phys. Rev. Lett.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, "Experimental Evidence for Supercontinuum Generation by Fission of Higher-Order Solitons in Photonic Fibers," Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef] [PubMed]

Prog. Quantum Electron.

R. W. Hellwarth, "Third- order optical susceptibilities of liquids and solids," Prog. Quantum Electron. 5, 1 (1977).
[CrossRef]

Science

P. St. J. Russell, "Photonic crystal fibres," Science 299, 358-362 (2003).
[CrossRef] [PubMed]

Other

M. Böhm, H. Hartwig, and F. Mitschke, "Präparation von mit Flüssigkeiten gefüllten mikrostrukturierten Glasfasern," Frühjahrstagung der DPG Berlin 2005, Q 29.2 (2005).

R. L. Sutherland, "Handbook of nonlinear optics," (Marcel Dekker, Inc., New York, USA, 1996), pp. 457.

G. P. Agrawal, "Nonlinear Fiber Optics - Optics and Photonics," Third Edition, (Academic Press, San Diego, USA, 2001), pp. 36.

A. W. Snyder, and J. D. Love, "Optical waveguide theory," (London, 1983). Chapter 12-15.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1.
Fig. 1.

Structure of the liquid-core photonic crystal fiber, where the red center core is filled with liquid and the white holes are filled with air. d is the hole diameter and Λ is the hole pitch.

Fig. 2.
Fig. 2.

Refractive index dispersion of nitrobenzene in dependence on wavelength.

Fig. 3
Fig. 3

The transmission curves of a 9.8 mm thick cuvette of carbon disulfide (dashed red) and nitrobenzene (solid black). Carbon disulfide has no absorption in the visible and in the near infrared region.

Fig. 4.
Fig. 4.

Group velocity dispersion of the hollow-core PCF: (a) dashed curve: core filled with nitrobenzene, d is 4 μm and Λ is 6 μm; (b) solid curve: core filled with CS2, d is 3 μm, and Λ is 4.5 μm.

Fig. 5.
Fig. 5.

Nonlinear parameter γ of the hollow-core PCF in dependence on wavelength: (a) dashed curve: core filled with nitrobenzene, d is 4 μm and Λ is 6 μm, and (b) solid curve: core filled with CS2, d is 3 μm, and Λ is 4.5 μm.

Fig. 6
Fig. 6

The normalized molecular response function of carbon disulfide with a relaxation time of 1.68 ps.

Fig. 7.
Fig. 7.

Calculated output spectrum (logarithmic) generated by a 5 cm long liquid-core PCF with input peak power of 10 kW and pulse duration of 100 fs. The central hole was filled with CS2.

Fig. 8.
Fig. 8.

Calculated output spectrum (logarithmic) generated by a 5 cm long liquid-core PCF with input peak power of 10 kW and pulse duration of 500 fs. The central hole was filled with CS2.

Fig. 9.
Fig. 9.

The calculated output spectrum (logarithmic) generated by a 10 cm long liquid-core PCF with a pump wavelength of 1.55 μm, an input peak power of 4 kW, and a pulse duration of 50 fs. The central hole was filled with CS2.

Fig. 10.
Fig. 10.

The calculated output spectrum (logarithmic) generated by a 10 cm long liquid-core PCF with a pump wavelength of 1.55 μm, an input peak power of 1 kW, and a pulse duration of 200 fs. The central hole was filled with CS2.

Fig. 11
Fig. 11

The calculated output spectrum (logarithmic) generated by a liquid-core PCF with a pumping wavelength at 1.7 μm, an input peak power of 1 kW, and a pulse duration of 200 fs. The central hole was filled with CS2.

Equations (11)

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

[ J m ( κ r core ) κ J m ( κ r core ) + K m ( γ r core ) γ K m ( γ r core ) ] [ J m ( κ r core ) κ J m ( κ r core ) + n eff 2 K m ( γ r core ) n core 2 γ K m ( γ r core ) ] = [ m β k 0 ( n core 2 n eff 2 ) r core κ 2 γ 2 n core ] 2 ,
I l + 1 ( w ) I l ( w ) = l w w 2 ( 1 + n 2 2 n 1 2 ) P w 1 4 ( 1 n 2 2 n 1 2 ) 2 P 2 + l 2 ( 1 u 2 + 1 w 2 ) ( n 1 2 w 2 + n 2 2 u 2 ) n 1 2 ;
P = Y l ( u R a ) J l ( ξ ) | ξ = u J l ( uR a ) Y l ( ξ ) | ξ = u u ( J l ( u ) Y l ( uR a ) Y l ( u ) J l ( uR a ) ) ;
u = k 0 2 ( n 2 2 n eff 2 ) a 2 and w = k 0 2 ( n eff 2 n 1 2 ) a 2 ,
γ = n 2 ω F ( x , y ) 4 dxdy c ( F ( x , y ) 2 dxdy ) 2 ,
A z i k 2 i k β k k ! k A t k = i γ ( 1 + i τ shock t ) ( A t R ( t ) A ( z , t t ) 2 d t ) ,
τ shock = 1 ω 0 + d d ω [ ln ( 1 n eff ( ω ) A eff ( ω ) ) ] ω 0 ,
R ( t ) = f e δ ( t ) + ( 1 f e ) h m ( t ) ,
h m ( t ) = 0.5048 exp ( t τ diff ) ( 1 exp ( t τ rise ) ) + 0.8314 exp ( t τ int ) ( 1 exp ( t τ rise ) ) ,
+ 1.633 exp ( α 2 t 2 2 ) sin ( ω 0 t ) ,
P 0 W 2 T 0 ,

Metrics