Abstract

The induced grating autocorrelation technique, a technique based on temporally resolved two-beam coupling in a photorefractive crystal, was used to measure the nonlinear coefficient γ of three photonic crystal fibers (PCFs): a 30-cm long highly nonlinear PCF, and two large mode area PCFs of 4.5-m and 4.9-m lengths. The measurement used intense 2-ps, 800-nm (850-nm in one case) pulses from a Ti: sapphire laser that experienced self-phase modulation and group velocity dispersion as it travels inside the fibers. This technique was also expanded to measure γ and the dispersion coefficient β 2 simultaneously.

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    [CrossRef] [PubMed]
  3. J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” J. Opt. Soc. Am. A 15(3), 748–752 (1998).
    [CrossRef]
  4. K. Saitoh and M. Koshiba, “Numerical modeling of photonic crystal fibers,” J. Lightwave Technol. 23(11), 3580–3590 (2005).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  15. X. S. Yao, V. Dominic, and J. Feinberg, “Theory of beam coupling and pulse shaping of mode-locked laser pulses in a photorefractive crystal,” J. Opt. Soc. Am. B 7(12), 2347–2355 (1990).
    [CrossRef]
  16. F. P. Strohkendl, J. M. C. Jonathan, and R. W. Hellwarth, “Hole - electron competition in photorefractive gratings,” Opt. Lett. 11(5), 312–314 (1986).
    [CrossRef] [PubMed]
  17. H. Garcia, “Time domain measurement of the nonlinear refractive index in optical fibers and semiconductors films,” Ph.D. dissertation (New Jersey Institute of Technology, Newark, NJ, 2000).
  18. F. A. Oguama, A. M. Johnson, and W. A. Reed, “Measurement of the nonlinear coefficient of telecommunication fibers as a function of Er, Al, and Ge doping profiles by using the photorefractive beam-coupling technique,” J. Opt. Soc. Am. B 22(8), 1600–1604 (2005).
    [CrossRef]
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  20. The ssprop code is available from the Photonics Research Laboratory at University of Maryland, College Park at http://www.photonics.umd.edu/software/ssprop
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  22. K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, “Frequency-resolved optical gating with the use of second-harmonic generation,” J. Opt. Soc. Am. B 11(11), 2206–2215 (1994).
    [CrossRef]
  23. D. Milam, “Review and assessment of measured values of the nonlinear refractive-index coefficient of fused silica,” Appl. Opt. 37(3), 546–550 (1998).
    [CrossRef]
  24. G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59(8), 880–883 (1987).
    [CrossRef] [PubMed]
  25. Obtained from www.nktphotonics.com .

2007 (1)

C. J. Hensley, D. G. Ouzounov, A. L. Gaeta, N. Venkataraman, M. T. Gallagher, and K. W. Koch, “Silica-glass contribution to the effective nonlinearity of hollow-core photonic band-gap fibers,” Opt. Express 15(6), 3507–3512 (2007).
[CrossRef] [PubMed]

2005 (3)

K. Saitoh and M. Koshiba, “Numerical modeling of photonic crystal fibers,” J. Lightwave Technol. 23(11), 3580–3590 (2005).
[CrossRef]

F. A. Oguama, H. Garcia, and A. M. Johnson, “Simultaneous measurement of the Raman gain coefficient and the nonlinear refractive index of optical fibers: theory and experiment,” J. Opt. Soc. Am. B 22(2), 426–436 (2005).
[CrossRef]

F. A. Oguama, A. M. Johnson, and W. A. Reed, “Measurement of the nonlinear coefficient of telecommunication fibers as a function of Er, Al, and Ge doping profiles by using the photorefractive beam-coupling technique,” J. Opt. Soc. Am. B 22(8), 1600–1604 (2005).
[CrossRef]

2003 (1)

H. Garcia, A. M. Johnson, F. A. Oguama, and S. Trivedi, “New approach to the measurement of the nonlinear refractive index of short (<25 m) lengths of silica and erbium-doped fibers,” Opt. Lett. 28(19), 1796–1798 (2003).
[CrossRef] [PubMed]

1999 (1)

N. G. R. Broderick, T. M. Monro, P. J. Bennett, and D. J. Richardson, “Nonlinearity in holey optical fibers: measurement and future opportunities,” Opt. Lett. 24(20), 1395–1397 (1999).
[CrossRef]

1998 (2)

J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” J. Opt. Soc. Am. A 15(3), 748–752 (1998).
[CrossRef]

D. Milam, “Review and assessment of measured values of the nonlinear refractive-index coefficient of fused silica,” Appl. Opt. 37(3), 546–550 (1998).
[CrossRef]

1997 (1)

T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22(13), 961–963 (1997).
[CrossRef] [PubMed]

1996 (2)

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21(19), 1547–1549 (1996).
[CrossRef] [PubMed]

A. Boskovic, S. V. Chernikov, J. R. Taylor, L. Gruner-Nielsen, and O. A. Levring, ““Direct continuous-wave measurement of n2 in various types of telecommunication fiber at 1.55 µm,” Opt. Lett. 21, 1966–1968 (1996). For an additional measurement approach in single-mode fiber see for example, C. Vinegone, M. Wegmuller, and N. Gisin, “Measurements of the Nonlinear Coefficient of Standard SMF, DSF, and DCF Fibers Using a Self-Aligned Interferometer and a Faraday Mirror,” IEEE Photon. Technol. Lett. 13, 1337–1339 (2001).
[CrossRef] [PubMed]

1994 (1)

K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, “Frequency-resolved optical gating with the use of second-harmonic generation,” J. Opt. Soc. Am. B 11(11), 2206–2215 (1994).
[CrossRef]

1990 (2)

V. Dominic, X. S. Yao, R. M. Pierce, and J. Feinberg, “Measuring the coherence length of mode-locked laser pulses in real time,” Appl. Phys. Lett. 56(6), 521–523 (1990).
[CrossRef]

X. S. Yao, V. Dominic, and J. Feinberg, “Theory of beam coupling and pulse shaping of mode-locked laser pulses in a photorefractive crystal,” J. Opt. Soc. Am. B 7(12), 2347–2355 (1990).
[CrossRef]

1987 (1)

G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59(8), 880–883 (1987).
[CrossRef] [PubMed]

1986 (1)

F. P. Strohkendl, J. M. C. Jonathan, and R. W. Hellwarth, “Hole - electron competition in photorefractive gratings,” Opt. Lett. 11(5), 312–314 (1986).
[CrossRef] [PubMed]

Agrawal, G. P.

G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59(8), 880–883 (1987).
[CrossRef] [PubMed]

Atkin, D. M.

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21(19), 1547–1549 (1996).
[CrossRef] [PubMed]

Bennett, P. J.

N. G. R. Broderick, T. M. Monro, P. J. Bennett, and D. J. Richardson, “Nonlinearity in holey optical fibers: measurement and future opportunities,” Opt. Lett. 24(20), 1395–1397 (1999).
[CrossRef]

Birks, T. A.

J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” J. Opt. Soc. Am. A 15(3), 748–752 (1998).
[CrossRef]

T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22(13), 961–963 (1997).
[CrossRef] [PubMed]

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21(19), 1547–1549 (1996).
[CrossRef] [PubMed]

Boskovic, A.

A. Boskovic, S. V. Chernikov, J. R. Taylor, L. Gruner-Nielsen, and O. A. Levring, ““Direct continuous-wave measurement of n2 in various types of telecommunication fiber at 1.55 µm,” Opt. Lett. 21, 1966–1968 (1996). For an additional measurement approach in single-mode fiber see for example, C. Vinegone, M. Wegmuller, and N. Gisin, “Measurements of the Nonlinear Coefficient of Standard SMF, DSF, and DCF Fibers Using a Self-Aligned Interferometer and a Faraday Mirror,” IEEE Photon. Technol. Lett. 13, 1337–1339 (2001).
[CrossRef] [PubMed]

Broderick, N. G. R.

N. G. R. Broderick, T. M. Monro, P. J. Bennett, and D. J. Richardson, “Nonlinearity in holey optical fibers: measurement and future opportunities,” Opt. Lett. 24(20), 1395–1397 (1999).
[CrossRef]

Chernikov, S. V.

A. Boskovic, S. V. Chernikov, J. R. Taylor, L. Gruner-Nielsen, and O. A. Levring, ““Direct continuous-wave measurement of n2 in various types of telecommunication fiber at 1.55 µm,” Opt. Lett. 21, 1966–1968 (1996). For an additional measurement approach in single-mode fiber see for example, C. Vinegone, M. Wegmuller, and N. Gisin, “Measurements of the Nonlinear Coefficient of Standard SMF, DSF, and DCF Fibers Using a Self-Aligned Interferometer and a Faraday Mirror,” IEEE Photon. Technol. Lett. 13, 1337–1339 (2001).
[CrossRef] [PubMed]

de Sandro, J. P.

J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” J. Opt. Soc. Am. A 15(3), 748–752 (1998).
[CrossRef]

DeLong, K. W.

K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, “Frequency-resolved optical gating with the use of second-harmonic generation,” J. Opt. Soc. Am. B 11(11), 2206–2215 (1994).
[CrossRef]

Dominic, V.

V. Dominic, X. S. Yao, R. M. Pierce, and J. Feinberg, “Measuring the coherence length of mode-locked laser pulses in real time,” Appl. Phys. Lett. 56(6), 521–523 (1990).
[CrossRef]

X. S. Yao, V. Dominic, and J. Feinberg, “Theory of beam coupling and pulse shaping of mode-locked laser pulses in a photorefractive crystal,” J. Opt. Soc. Am. B 7(12), 2347–2355 (1990).
[CrossRef]

Feinberg, J.

X. S. Yao, V. Dominic, and J. Feinberg, “Theory of beam coupling and pulse shaping of mode-locked laser pulses in a photorefractive crystal,” J. Opt. Soc. Am. B 7(12), 2347–2355 (1990).
[CrossRef]

V. Dominic, X. S. Yao, R. M. Pierce, and J. Feinberg, “Measuring the coherence length of mode-locked laser pulses in real time,” Appl. Phys. Lett. 56(6), 521–523 (1990).
[CrossRef]

Gaeta, A. L.

C. J. Hensley, D. G. Ouzounov, A. L. Gaeta, N. Venkataraman, M. T. Gallagher, and K. W. Koch, “Silica-glass contribution to the effective nonlinearity of hollow-core photonic band-gap fibers,” Opt. Express 15(6), 3507–3512 (2007).
[CrossRef] [PubMed]

Gallagher, M. T.

C. J. Hensley, D. G. Ouzounov, A. L. Gaeta, N. Venkataraman, M. T. Gallagher, and K. W. Koch, “Silica-glass contribution to the effective nonlinearity of hollow-core photonic band-gap fibers,” Opt. Express 15(6), 3507–3512 (2007).
[CrossRef] [PubMed]

Garcia, H.

F. A. Oguama, H. Garcia, and A. M. Johnson, “Simultaneous measurement of the Raman gain coefficient and the nonlinear refractive index of optical fibers: theory and experiment,” J. Opt. Soc. Am. B 22(2), 426–436 (2005).
[CrossRef]

H. Garcia, A. M. Johnson, F. A. Oguama, and S. Trivedi, “New approach to the measurement of the nonlinear refractive index of short (<25 m) lengths of silica and erbium-doped fibers,” Opt. Lett. 28(19), 1796–1798 (2003).
[CrossRef] [PubMed]

Gruner-Nielsen, L.

A. Boskovic, S. V. Chernikov, J. R. Taylor, L. Gruner-Nielsen, and O. A. Levring, ““Direct continuous-wave measurement of n2 in various types of telecommunication fiber at 1.55 µm,” Opt. Lett. 21, 1966–1968 (1996). For an additional measurement approach in single-mode fiber see for example, C. Vinegone, M. Wegmuller, and N. Gisin, “Measurements of the Nonlinear Coefficient of Standard SMF, DSF, and DCF Fibers Using a Self-Aligned Interferometer and a Faraday Mirror,” IEEE Photon. Technol. Lett. 13, 1337–1339 (2001).
[CrossRef] [PubMed]

Hellwarth, R. W.

F. P. Strohkendl, J. M. C. Jonathan, and R. W. Hellwarth, “Hole - electron competition in photorefractive gratings,” Opt. Lett. 11(5), 312–314 (1986).
[CrossRef] [PubMed]

Hensley, C. J.

C. J. Hensley, D. G. Ouzounov, A. L. Gaeta, N. Venkataraman, M. T. Gallagher, and K. W. Koch, “Silica-glass contribution to the effective nonlinearity of hollow-core photonic band-gap fibers,” Opt. Express 15(6), 3507–3512 (2007).
[CrossRef] [PubMed]

Hunter, J.

K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, “Frequency-resolved optical gating with the use of second-harmonic generation,” J. Opt. Soc. Am. B 11(11), 2206–2215 (1994).
[CrossRef]

Johnson, A. M.

F. A. Oguama, A. M. Johnson, and W. A. Reed, “Measurement of the nonlinear coefficient of telecommunication fibers as a function of Er, Al, and Ge doping profiles by using the photorefractive beam-coupling technique,” J. Opt. Soc. Am. B 22(8), 1600–1604 (2005).
[CrossRef]

F. A. Oguama, H. Garcia, and A. M. Johnson, “Simultaneous measurement of the Raman gain coefficient and the nonlinear refractive index of optical fibers: theory and experiment,” J. Opt. Soc. Am. B 22(2), 426–436 (2005).
[CrossRef]

H. Garcia, A. M. Johnson, F. A. Oguama, and S. Trivedi, “New approach to the measurement of the nonlinear refractive index of short (<25 m) lengths of silica and erbium-doped fibers,” Opt. Lett. 28(19), 1796–1798 (2003).
[CrossRef] [PubMed]

Jonathan, J. M. C.

F. P. Strohkendl, J. M. C. Jonathan, and R. W. Hellwarth, “Hole - electron competition in photorefractive gratings,” Opt. Lett. 11(5), 312–314 (1986).
[CrossRef] [PubMed]

Knight, J. C.

J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” J. Opt. Soc. Am. A 15(3), 748–752 (1998).
[CrossRef]

T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22(13), 961–963 (1997).
[CrossRef] [PubMed]

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21(19), 1547–1549 (1996).
[CrossRef] [PubMed]

Koch, K. W.

C. J. Hensley, D. G. Ouzounov, A. L. Gaeta, N. Venkataraman, M. T. Gallagher, and K. W. Koch, “Silica-glass contribution to the effective nonlinearity of hollow-core photonic band-gap fibers,” Opt. Express 15(6), 3507–3512 (2007).
[CrossRef] [PubMed]

Koshiba, M.

K. Saitoh and M. Koshiba, “Numerical modeling of photonic crystal fibers,” J. Lightwave Technol. 23(11), 3580–3590 (2005).
[CrossRef]

Levring, O. A.

A. Boskovic, S. V. Chernikov, J. R. Taylor, L. Gruner-Nielsen, and O. A. Levring, ““Direct continuous-wave measurement of n2 in various types of telecommunication fiber at 1.55 µm,” Opt. Lett. 21, 1966–1968 (1996). For an additional measurement approach in single-mode fiber see for example, C. Vinegone, M. Wegmuller, and N. Gisin, “Measurements of the Nonlinear Coefficient of Standard SMF, DSF, and DCF Fibers Using a Self-Aligned Interferometer and a Faraday Mirror,” IEEE Photon. Technol. Lett. 13, 1337–1339 (2001).
[CrossRef] [PubMed]

Milam, D.

D. Milam, “Review and assessment of measured values of the nonlinear refractive-index coefficient of fused silica,” Appl. Opt. 37(3), 546–550 (1998).
[CrossRef]

Monro, T. M.

N. G. R. Broderick, T. M. Monro, P. J. Bennett, and D. J. Richardson, “Nonlinearity in holey optical fibers: measurement and future opportunities,” Opt. Lett. 24(20), 1395–1397 (1999).
[CrossRef]

Oguama, F. A.

F. A. Oguama, A. M. Johnson, and W. A. Reed, “Measurement of the nonlinear coefficient of telecommunication fibers as a function of Er, Al, and Ge doping profiles by using the photorefractive beam-coupling technique,” J. Opt. Soc. Am. B 22(8), 1600–1604 (2005).
[CrossRef]

F. A. Oguama, H. Garcia, and A. M. Johnson, “Simultaneous measurement of the Raman gain coefficient and the nonlinear refractive index of optical fibers: theory and experiment,” J. Opt. Soc. Am. B 22(2), 426–436 (2005).
[CrossRef]

H. Garcia, A. M. Johnson, F. A. Oguama, and S. Trivedi, “New approach to the measurement of the nonlinear refractive index of short (<25 m) lengths of silica and erbium-doped fibers,” Opt. Lett. 28(19), 1796–1798 (2003).
[CrossRef] [PubMed]

Ouzounov, D. G.

C. J. Hensley, D. G. Ouzounov, A. L. Gaeta, N. Venkataraman, M. T. Gallagher, and K. W. Koch, “Silica-glass contribution to the effective nonlinearity of hollow-core photonic band-gap fibers,” Opt. Express 15(6), 3507–3512 (2007).
[CrossRef] [PubMed]

Pierce, R. M.

V. Dominic, X. S. Yao, R. M. Pierce, and J. Feinberg, “Measuring the coherence length of mode-locked laser pulses in real time,” Appl. Phys. Lett. 56(6), 521–523 (1990).
[CrossRef]

Reed, W. A.

F. A. Oguama, A. M. Johnson, and W. A. Reed, “Measurement of the nonlinear coefficient of telecommunication fibers as a function of Er, Al, and Ge doping profiles by using the photorefractive beam-coupling technique,” J. Opt. Soc. Am. B 22(8), 1600–1604 (2005).
[CrossRef]

Richardson, D. J.

N. G. R. Broderick, T. M. Monro, P. J. Bennett, and D. J. Richardson, “Nonlinearity in holey optical fibers: measurement and future opportunities,” Opt. Lett. 24(20), 1395–1397 (1999).
[CrossRef]

Russell, P. St. J.

J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” J. Opt. Soc. Am. A 15(3), 748–752 (1998).
[CrossRef]

T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22(13), 961–963 (1997).
[CrossRef] [PubMed]

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21(19), 1547–1549 (1996).
[CrossRef] [PubMed]

Saitoh, K.

K. Saitoh and M. Koshiba, “Numerical modeling of photonic crystal fibers,” J. Lightwave Technol. 23(11), 3580–3590 (2005).
[CrossRef]

Strohkendl, F. P.

F. P. Strohkendl, J. M. C. Jonathan, and R. W. Hellwarth, “Hole - electron competition in photorefractive gratings,” Opt. Lett. 11(5), 312–314 (1986).
[CrossRef] [PubMed]

Taylor, J. R.

A. Boskovic, S. V. Chernikov, J. R. Taylor, L. Gruner-Nielsen, and O. A. Levring, ““Direct continuous-wave measurement of n2 in various types of telecommunication fiber at 1.55 µm,” Opt. Lett. 21, 1966–1968 (1996). For an additional measurement approach in single-mode fiber see for example, C. Vinegone, M. Wegmuller, and N. Gisin, “Measurements of the Nonlinear Coefficient of Standard SMF, DSF, and DCF Fibers Using a Self-Aligned Interferometer and a Faraday Mirror,” IEEE Photon. Technol. Lett. 13, 1337–1339 (2001).
[CrossRef] [PubMed]

Trebino, R.

K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, “Frequency-resolved optical gating with the use of second-harmonic generation,” J. Opt. Soc. Am. B 11(11), 2206–2215 (1994).
[CrossRef]

Trivedi, S.

H. Garcia, A. M. Johnson, F. A. Oguama, and S. Trivedi, “New approach to the measurement of the nonlinear refractive index of short (<25 m) lengths of silica and erbium-doped fibers,” Opt. Lett. 28(19), 1796–1798 (2003).
[CrossRef] [PubMed]

Venkataraman, N.

C. J. Hensley, D. G. Ouzounov, A. L. Gaeta, N. Venkataraman, M. T. Gallagher, and K. W. Koch, “Silica-glass contribution to the effective nonlinearity of hollow-core photonic band-gap fibers,” Opt. Express 15(6), 3507–3512 (2007).
[CrossRef] [PubMed]

White, W. E.

K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, “Frequency-resolved optical gating with the use of second-harmonic generation,” J. Opt. Soc. Am. B 11(11), 2206–2215 (1994).
[CrossRef]

Yao, X. S.

X. S. Yao, V. Dominic, and J. Feinberg, “Theory of beam coupling and pulse shaping of mode-locked laser pulses in a photorefractive crystal,” J. Opt. Soc. Am. B 7(12), 2347–2355 (1990).
[CrossRef]

V. Dominic, X. S. Yao, R. M. Pierce, and J. Feinberg, “Measuring the coherence length of mode-locked laser pulses in real time,” Appl. Phys. Lett. 56(6), 521–523 (1990).
[CrossRef]

Appl. Opt. (1)

D. Milam, “Review and assessment of measured values of the nonlinear refractive-index coefficient of fused silica,” Appl. Opt. 37(3), 546–550 (1998).
[CrossRef]

Appl. Phys. Lett. (1)

V. Dominic, X. S. Yao, R. M. Pierce, and J. Feinberg, “Measuring the coherence length of mode-locked laser pulses in real time,” Appl. Phys. Lett. 56(6), 521–523 (1990).
[CrossRef]

J. Lightwave Technol. (1)

K. Saitoh and M. Koshiba, “Numerical modeling of photonic crystal fibers,” J. Lightwave Technol. 23(11), 3580–3590 (2005).
[CrossRef]

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

J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” J. Opt. Soc. Am. A 15(3), 748–752 (1998).
[CrossRef]

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

K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, “Frequency-resolved optical gating with the use of second-harmonic generation,” J. Opt. Soc. Am. B 11(11), 2206–2215 (1994).
[CrossRef]

F. A. Oguama, A. M. Johnson, and W. A. Reed, “Measurement of the nonlinear coefficient of telecommunication fibers as a function of Er, Al, and Ge doping profiles by using the photorefractive beam-coupling technique,” J. Opt. Soc. Am. B 22(8), 1600–1604 (2005).
[CrossRef]

X. S. Yao, V. Dominic, and J. Feinberg, “Theory of beam coupling and pulse shaping of mode-locked laser pulses in a photorefractive crystal,” J. Opt. Soc. Am. B 7(12), 2347–2355 (1990).
[CrossRef]

F. A. Oguama, H. Garcia, and A. M. Johnson, “Simultaneous measurement of the Raman gain coefficient and the nonlinear refractive index of optical fibers: theory and experiment,” J. Opt. Soc. Am. B 22(2), 426–436 (2005).
[CrossRef]

Opt. Express (1)

C. J. Hensley, D. G. Ouzounov, A. L. Gaeta, N. Venkataraman, M. T. Gallagher, and K. W. Koch, “Silica-glass contribution to the effective nonlinearity of hollow-core photonic band-gap fibers,” Opt. Express 15(6), 3507–3512 (2007).
[CrossRef] [PubMed]

Opt. Lett. (6)

H. Garcia, A. M. Johnson, F. A. Oguama, and S. Trivedi, “New approach to the measurement of the nonlinear refractive index of short (<25 m) lengths of silica and erbium-doped fibers,” Opt. Lett. 28(19), 1796–1798 (2003).
[CrossRef] [PubMed]

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21(19), 1547–1549 (1996).
[CrossRef] [PubMed]

T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22(13), 961–963 (1997).
[CrossRef] [PubMed]

N. G. R. Broderick, T. M. Monro, P. J. Bennett, and D. J. Richardson, “Nonlinearity in holey optical fibers: measurement and future opportunities,” Opt. Lett. 24(20), 1395–1397 (1999).
[CrossRef]

A. Boskovic, S. V. Chernikov, J. R. Taylor, L. Gruner-Nielsen, and O. A. Levring, ““Direct continuous-wave measurement of n2 in various types of telecommunication fiber at 1.55 µm,” Opt. Lett. 21, 1966–1968 (1996). For an additional measurement approach in single-mode fiber see for example, C. Vinegone, M. Wegmuller, and N. Gisin, “Measurements of the Nonlinear Coefficient of Standard SMF, DSF, and DCF Fibers Using a Self-Aligned Interferometer and a Faraday Mirror,” IEEE Photon. Technol. Lett. 13, 1337–1339 (2001).
[CrossRef] [PubMed]

F. P. Strohkendl, J. M. C. Jonathan, and R. W. Hellwarth, “Hole - electron competition in photorefractive gratings,” Opt. Lett. 11(5), 312–314 (1986).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59(8), 880–883 (1987).
[CrossRef] [PubMed]

Other (9)

Obtained from www.nktphotonics.com .

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001).

The ssprop code is available from the Photonics Research Laboratory at University of Maryland, College Park at http://www.photonics.umd.edu/software/ssprop

R. Kuis, “Theoretical and Experimental Study of the Nonlinear Optical and Dispersive Properties of Conventional and Photonic Crystal Fibers,” Ph.D. dissertation (University of Maryland, Baltimore County, Baltimore, MD 2009).

H. Garcia, “Time domain measurement of the nonlinear refractive index in optical fibers and semiconductors films,” Ph.D. dissertation (New Jersey Institute of Technology, Newark, NJ, 2000).

A. M. Johnson, A. M. Glass, W. M. Simpson, R. B. Bylsma, and D. H. Olson, “Microwatt picosecond pulse autocorrelator using photorefractive GaAs:Cr,” in OSA Annual Meeting, Vol. 11 of 1988 Optical Society of America Technical Digest Series (Optical Society of America, Washington, D.C., 1988), p. 128.

A. M. Johnson, A. M. Glass, W. M. Simpson, and D. H. Olson, “Infrared picosecond pulse diagnostics using photorefractive beam coupling,” in Conference on Lasers and Electro-Optics, Vol. II of 1989 Optical Society of America Technical Digest Series (Optical Society of America, Washington, D.C., 1989), p. 226.

A. M. Johnson, W. M. Simpson, A. M. Glass, M. B. Klein, D. Rytz, and R. Trebino, “Infrared picosecond pulse correlation measurements using photorefractive beam coupling and harmonic generation in KNbO3 and BaTiO3,” in OSA Annual Meeting, Vol. 18 of 1989 Optical Society of America Technical Digest Series (Optical Society of America, Washington, D.C., 1989), p. 53.

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “Pure silica single-mode fiber with hexagonal photonic crystal cladding,” Conf. Optical Fiber Commun. (OFC) San Jose, CA, (1996).

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Figures (12)

Fig. 1
Fig. 1

Description of the photorefractive two-beam coupling in CdMnTe: V.

Fig. 2
Fig. 2

IGA experimental setup.

Fig. 3
Fig. 3

(a) experimental SHG-FROG trace for the 2 ps Ti: sapphire laser system and (b) the intensity and phase derived from FROG trace.

Fig. 4
Fig. 4

Intensity profile and hyperbolic secant squared fit.

Fig. 5
Fig. 5

Simulation of IGA traces (SPM only model) at ΔϕNL = 2, 4 and 6.

Fig. 6
Fig. 6

IGA trace of 15 m long silica fiber fitted using (a) SPM only model and (b) SPM and GVD model.

Fig. 7
Fig. 7

Theoretical IGA traces with and without dispersion.

Fig. 8
Fig. 8

(a) Experimental IGA trace for 0.95 m long F-SF fiber using 309 W peak power and (b) plot of the measured N 2 ξmax = ΔϕNL vs. peak power.

Fig. 9
Fig. 9

SEM Images of a) SC-PCF NL-2.4-800 and b) LMA-25 from data sheets.

Fig. 10
Fig. 10

(a) Experimental IGA trace with fit for a 30-cm long NL-2.4-800 fiber with 17 Watts of peak power and (b) plot of Δ φ N L vs. Po for each IGA trace with linear regression fit, where the slope of the line is ∝ γ.

Fig. 11
Fig. 11

(a) Experimental IGA trace with fit for a 4.5-m long LMA-20 fiber with 259Watts of peak power, (b) plot of Δ φ N L vs. Po for each IGA trace with linear regression fit, (c) experimental IGA trace with fit for a 4.9-m long LMA-25 fiber with 600 Watts of peak power, and (d) plot of Δ φ N L vs. Po for each IGA trace with linear regression fit.

Fig. 12
Fig. 12

(a) Experimental IGA trace with fit for a 15-m long F-SF fiber with 27 Watts of peak power and (b) plot of Δ φ N L vs. Po for each IGA trace with linear regression fit, where the slope of the line is ∝ γ .

Tables (2)

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Table 1 Fiber parameters

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Table 2 Summary of results

Equations (16)

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E S C = i b a E 1 ( r , t ) E 2 * ( r , t - τ d ) I o ,
Δ ε r = ε r ( R k ^ g ) ε r E S C ,
| E 1 ( z , t ) | 2 | E 1 ( 0 , t ) | 2 = 4 η 12 η 12 η 21 | E 1 ( z , t ) E 2 * ( z , t τ d ) | 2 [ exp ( 1 2 { η 12 η 21 } z ) 1 ] .
I G A ( τ d ) = | U ( t ) U ( t + τ d ) d t | 2 .
U z + i α 2 U β 2 2 T 0 2 2 U T 2 + γ P 0 | U | 2 A = 0 ,
γ = n 2 ω 0 c A e f f ,
U ( L e f f , T ) = U ( 0 , T ) exp [ i ϕ N L ( L e f f , T ) ] ,
ϕ N L ( L e f f , T ) = Δ ϕ N L | U ( 0 , T ) | 2 ,
Δ ϕ N L = L e f f L N L = L e f f P 0 γ ,
I n ( t τ p ) = sec h ( 1.763 t τ p ) 2 ,
γ = Δ ϕ N L P o L e f f .
i U ξ + sgn ( β 2 ) 1 2 2 A τ 2 + N 2 | U | 2 U = 0 ,
N 2 = L D L N L = γ P o τ p 2 1.763 2 β 2 .
ξ max = L e f f L D .
γ = N 2 ξ max P o L e f f .
β 2 = τ p 2 1.763 2 ξ max L e f f .

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