Abstract

A beam of 33 fs laser pulse with peak power of 15–40 GW was employed to explore a convenient method to determine the nonlinear refractive index coefficient of an optical glass. It is rare to investigate nonlinearities of optical glass with such an extreme ultrashort and powerful laser pulse. According to our method, only a single beam and a few experimental apparatuses are necessary to measure the nonlinear refractive index coefficient. The results from our method are in reasonable agreement with the others, which demonstrates that this new method works well, and the nonlinear refractive index coefficient is independent of measuring technology. Meanwhile, according to our results and those obtained by others in different laser power ranges, it seems that the nonlinear refractive index coefficient has a weak dependence on the laser peak power.

© 2012 Optical Society of America

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2011

A. Goy and D. Psaltis, “Digital reverse propagation in focusing Kerr media,” Phys. Rev. A 83, 031802(R) (2011).
[CrossRef]

P. Polynkin and J. V. Moloney, “Optical breakdown of air triggered by femtosecond laser filaments,” Appl. Phys. Lett. 99, 151103 (2011).
[CrossRef]

X. L. Liu and B.-S. Hu, “Micro-displacement system of pulse equivalent and return difference of a stepping motor,” Laser Technol. 35, 603–605 (2011).

H. Wang, C. Fan, P. Zhang, C. Qiao, J. Zhang, and H. Ma, “Dynamics of femtosecond filamentation with higher-order Kerr response,” J. Opt. Soc. Am. B 28, 2081–2086 (2011).
[CrossRef]

2010

P. Samineni, Z. Perret, W. S. Warren, and M. C. Fischer, “Measurements of nonlinear refractive index in scattering media,” Opt. Express 18, 12727–12735 (2010).
[CrossRef]

B. Shim, S. E. Schrauth, C. J. Hensley, L. T. Vuong, P. Hui, A. A. Ishaaya, and A. L. Gaeta, “Controlled interactions of femtosecond light filaments in air,” Phys. Rev. A 81, 061803(R) (2010).
[CrossRef]

2009

J.-G. Kazem and H. Masalehdan, “Modeling of nonlinear responses in BK7 glass under irradiation of femtosecond laser pulses,” Opt. Quantum Electron. 41, 47–53 (2009).
[CrossRef]

2007

2006

O. G. Kosareva, T. Nguyen, N. A. Panov, W. Liu, A. Saliminia, V. P. Kandidov, N. Akozabek, M. Scalora, R. Vallee, and S. L. Chin, “Array of femtosecond plasma channels in fused silica,” Opt. Commun. 267, 511–523 (2006).
[CrossRef]

2005

A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Filamentation and damage in fused silica induced by tightly focused femtosecond laser pulses,” Phys. Rev. B 71, 125435 (2005).
[CrossRef]

W. Liu and S. L. Chin, “Direct measurement of the critical power of femtosecond Ti:sapphire laser pulse in air,” Opt. Express 13, 5750–5755 (2005).
[CrossRef]

2004

G. Méchain, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Organizing multiple femtosecond filaments in air,” Phys. Rev. Lett. 93, 035003 (2004).
[CrossRef]

2003

W. Liu, O. Kosareva, I. S. Golubtsov, A. Iwasaki, A. Becker, V. P. Kandidov, and S. L. Chin, “Femtosecond laser pulse filamentation versus optical breakdown in H2O,” Appl. Phys. B 76, 215–229 (2003).
[CrossRef]

V. P. Kandidov, O. G. Kasareva, and A. A. Koitun, “Nonlinear-optical transformation of a high-power femtosecond laser pulse in air,” Quantum Electron. 33, 69–75 (2003).
[CrossRef]

K. D. Moll, A. L. Gaeta, and G. Fibich, “Self-similar optical wave collapse: observation of the Townes profile,” Phys. Rev. Lett. 90, 203902 (2003).
[CrossRef]

2002

M. Falconieri, E. Palange, and H. L. Fragnito, “Achievement of phase distortion sensitivity in the measurement of optical nonlinearities by using a modulated Z-scan technique,” J. Opt. A 4, 404–407 (2002).
[CrossRef]

2001

W. Gawlik, R. Shuker, and A. Gallagher, “Temporal character of pulsed-laser cone emission,” Phys. Rev. A 64, 021801(R) (2001).
[CrossRef]

M. R. Junnarker, “Short pulse propagation in tight focusing conditions,” Opt. Commun. 195, 273–292 (2001).
[CrossRef]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-Focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86, 3296–3299 (2001).
[CrossRef]

C.-H. Fan and J. P. Longtin, “Modeling optical breakdown in dielectrics during ultrafast laser processing,” Appl. Opt. 40, 3124–3130 (2001).
[CrossRef]

2000

1999

A. A. Zozulya, “Propagation dynamics of intense femtosecond pulses: multiple splittings, coalescence, and continuum generation,” Phys. Rev. Lett. 82, 1430–1433 (1999).
[CrossRef]

A. Brodeur and S. L. Chin, “Ultrafast white-light continuum generation and self-focusing in transparent condensed media,” J. Opt. Soc. Am. B 16, 637–641, (1999).
[CrossRef]

1998

1997

1996

J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, “Observation of pulse splitting in nonlinear dispersive media,” Phys. Rev. Lett. 77, 3783–3786 (1996).
[CrossRef]

1995

E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, C. Le Blanc, and A. Mysyrowicz, “Measurement of the nonlinear refractive index of transparent materials by spectral analysis after nonlinear propagation,” Opt. Commun. 119, 479–484 (1995).
[CrossRef]

1987

1984

1978

N. L. Boling and A. J. Glass, “Empirical relationships for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. 14, 601–608 (1978).
[CrossRef]

1976

D. Milam and M. J. Weber, “Measurement of nonlinear refractive-index coefficients using time-resolved interferometry: Application to optical materials for high-power neodymium lasers,” J. Appl. Phys. 47, 2497–2501 (1976).
[CrossRef]

1973

A. Owyoung, “Ellipse rotation studies in laser host materials,” IEEE J. Quantum Electron. 9, 1064–1069 (1973).
[CrossRef]

A. Feldman, D. Horowitz, and R. M. Waxler, “Mechanisms for self-focusing in optical glasses,” IEEE J. Quantum Electron. 9, 1054–1061 (1973).
[CrossRef]

Adair, R.

Aitchison, J. S.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-Focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86, 3296–3299 (2001).
[CrossRef]

Akozabek, N.

O. G. Kosareva, T. Nguyen, N. A. Panov, W. Liu, A. Saliminia, V. P. Kandidov, N. Akozabek, M. Scalora, R. Vallee, and S. L. Chin, “Array of femtosecond plasma channels in fused silica,” Opt. Commun. 267, 511–523 (2006).
[CrossRef]

Alexeev, I.

Bao, Z.

Becker, A.

W. Liu, O. Kosareva, I. S. Golubtsov, A. Iwasaki, A. Becker, V. P. Kandidov, and S. L. Chin, “Femtosecond laser pulse filamentation versus optical breakdown in H2O,” Appl. Phys. B 76, 215–229 (2003).
[CrossRef]

Betz, M.

Boling, N. L.

N. L. Boling and A. J. Glass, “Empirical relationships for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. 14, 601–608 (1978).
[CrossRef]

Brodeur, A.

Chase, L. L.

Chen, Y.-H.

Chien, C. Y.

Chin, S. L.

O. G. Kosareva, T. Nguyen, N. A. Panov, W. Liu, A. Saliminia, V. P. Kandidov, N. Akozabek, M. Scalora, R. Vallee, and S. L. Chin, “Array of femtosecond plasma channels in fused silica,” Opt. Commun. 267, 511–523 (2006).
[CrossRef]

W. Liu and S. L. Chin, “Direct measurement of the critical power of femtosecond Ti:sapphire laser pulse in air,” Opt. Express 13, 5750–5755 (2005).
[CrossRef]

W. Liu, O. Kosareva, I. S. Golubtsov, A. Iwasaki, A. Becker, V. P. Kandidov, and S. L. Chin, “Femtosecond laser pulse filamentation versus optical breakdown in H2O,” Appl. Phys. B 76, 215–229 (2003).
[CrossRef]

A. Brodeur and S. L. Chin, “Ultrafast white-light continuum generation and self-focusing in transparent condensed media,” J. Opt. Soc. Am. B 16, 637–641, (1999).
[CrossRef]

A. Brodeur and S. L. Chin, “Band-gap dependence of the ultrafast white-light continuum,” Phys. Rev. Lett. 80, 4406–4409 (1998).
[CrossRef]

O. G. Kosareva, V. P. Kandidov, A. Brodeur, C. Y. Chien, and S. L. Chin, “Conical emission from laser plasma interactions in the filamentation of powerful ultrashort laser pulses in air,” Opt. Lett. 22, 1332–1334 (1997).
[CrossRef]

A. Brodeur, C. Y. Chien, F. A. Ilkov, S. L. Chin, O. G. Kosareva, and V. P. Kandidov, “Moving focus in the propagation of ultrashort laser pulses in air,” Opt. Lett. 22, 304–306 (1997).

Couairon, A.

A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Filamentation and damage in fused silica induced by tightly focused femtosecond laser pulses,” Phys. Rev. B 71, 125435 (2005).
[CrossRef]

G. Méchain, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Organizing multiple femtosecond filaments in air,” Phys. Rev. Lett. 93, 035003 (2004).
[CrossRef]

Eisenberg, H. S.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-Focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86, 3296–3299 (2001).
[CrossRef]

Falconieri, M.

M. Falconieri, E. Palange, and H. L. Fragnito, “Achievement of phase distortion sensitivity in the measurement of optical nonlinearities by using a modulated Z-scan technique,” J. Opt. A 4, 404–407 (2002).
[CrossRef]

Fan, C.

Fan, C.-H.

Feldman, A.

A. Feldman, D. Horowitz, and R. M. Waxler, “Mechanisms for self-focusing in optical glasses,” IEEE J. Quantum Electron. 9, 1054–1061 (1973).
[CrossRef]

Fibich, G.

K. D. Moll, A. L. Gaeta, and G. Fibich, “Self-similar optical wave collapse: observation of the Townes profile,” Phys. Rev. Lett. 90, 203902 (2003).
[CrossRef]

G. Fibich and A. L. Gaeta, “Critical power for self-focusing in bulk media and in hollow waveguides,” Opt. Lett. 25, 335–337 (2000).
[CrossRef]

Fischer, M. C.

Fragnito, H. L.

M. Falconieri, E. Palange, and H. L. Fragnito, “Achievement of phase distortion sensitivity in the measurement of optical nonlinearities by using a modulated Z-scan technique,” J. Opt. A 4, 404–407 (2002).
[CrossRef]

Franco, M.

A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Filamentation and damage in fused silica induced by tightly focused femtosecond laser pulses,” Phys. Rev. B 71, 125435 (2005).
[CrossRef]

G. Méchain, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Organizing multiple femtosecond filaments in air,” Phys. Rev. Lett. 93, 035003 (2004).
[CrossRef]

Franco, M. A.

E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, C. Le Blanc, and A. Mysyrowicz, “Measurement of the nonlinear refractive index of transparent materials by spectral analysis after nonlinear propagation,” Opt. Commun. 119, 479–484 (1995).
[CrossRef]

Gaeta, A. L.

B. Shim, S. E. Schrauth, C. J. Hensley, L. T. Vuong, P. Hui, A. A. Ishaaya, and A. L. Gaeta, “Controlled interactions of femtosecond light filaments in air,” Phys. Rev. A 81, 061803(R) (2010).
[CrossRef]

K. D. Moll, A. L. Gaeta, and G. Fibich, “Self-similar optical wave collapse: observation of the Townes profile,” Phys. Rev. Lett. 90, 203902 (2003).
[CrossRef]

A. L. Gaeta, “Catastrophic collapse of ultrashort pulses,” Phys. Rev. Lett. 84, 3582–3585 (2000).
[CrossRef]

G. Fibich and A. L. Gaeta, “Critical power for self-focusing in bulk media and in hollow waveguides,” Opt. Lett. 25, 335–337 (2000).
[CrossRef]

J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, “Observation of pulse splitting in nonlinear dispersive media,” Phys. Rev. Lett. 77, 3783–3786 (1996).
[CrossRef]

Gallagher, A.

W. Gawlik, R. Shuker, and A. Gallagher, “Temporal character of pulsed-laser cone emission,” Phys. Rev. A 64, 021801(R) (2001).
[CrossRef]

Gawlik, W.

W. Gawlik, R. Shuker, and A. Gallagher, “Temporal character of pulsed-laser cone emission,” Phys. Rev. A 64, 021801(R) (2001).
[CrossRef]

Glass, A. J.

N. L. Boling and A. J. Glass, “Empirical relationships for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. 14, 601–608 (1978).
[CrossRef]

Golubtsov, I. S.

W. Liu, O. Kosareva, I. S. Golubtsov, A. Iwasaki, A. Becker, V. P. Kandidov, and S. L. Chin, “Femtosecond laser pulse filamentation versus optical breakdown in H2O,” Appl. Phys. B 76, 215–229 (2003).
[CrossRef]

Goy, A.

A. Goy and D. Psaltis, “Digital reverse propagation in focusing Kerr media,” Phys. Rev. A 83, 031802(R) (2011).
[CrossRef]

Grillon, G.

E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, C. Le Blanc, and A. Mysyrowicz, “Measurement of the nonlinear refractive index of transparent materials by spectral analysis after nonlinear propagation,” Opt. Commun. 119, 479–484 (1995).
[CrossRef]

Hensley, C. J.

B. Shim, S. E. Schrauth, C. J. Hensley, L. T. Vuong, P. Hui, A. A. Ishaaya, and A. L. Gaeta, “Controlled interactions of femtosecond light filaments in air,” Phys. Rev. A 81, 061803(R) (2010).
[CrossRef]

Horowitz, D.

A. Feldman, D. Horowitz, and R. M. Waxler, “Mechanisms for self-focusing in optical glasses,” IEEE J. Quantum Electron. 9, 1054–1061 (1973).
[CrossRef]

Hsieh, B.

Hu, B.-S.

X. L. Liu and B.-S. Hu, “Micro-displacement system of pulse equivalent and return difference of a stepping motor,” Laser Technol. 35, 603–605 (2011).

Hui, P.

B. Shim, S. E. Schrauth, C. J. Hensley, L. T. Vuong, P. Hui, A. A. Ishaaya, and A. L. Gaeta, “Controlled interactions of femtosecond light filaments in air,” Phys. Rev. A 81, 061803(R) (2010).
[CrossRef]

Ilkov, F. A.

Ishaaya, A. A.

B. Shim, S. E. Schrauth, C. J. Hensley, L. T. Vuong, P. Hui, A. A. Ishaaya, and A. L. Gaeta, “Controlled interactions of femtosecond light filaments in air,” Phys. Rev. A 81, 061803(R) (2010).
[CrossRef]

Iwasaki, A.

W. Liu, O. Kosareva, I. S. Golubtsov, A. Iwasaki, A. Becker, V. P. Kandidov, and S. L. Chin, “Femtosecond laser pulse filamentation versus optical breakdown in H2O,” Appl. Phys. B 76, 215–229 (2003).
[CrossRef]

Junnarker, M. R.

M. R. Junnarker, “Short pulse propagation in tight focusing conditions,” Opt. Commun. 195, 273–292 (2001).
[CrossRef]

Kandidov, V. P.

O. G. Kosareva, T. Nguyen, N. A. Panov, W. Liu, A. Saliminia, V. P. Kandidov, N. Akozabek, M. Scalora, R. Vallee, and S. L. Chin, “Array of femtosecond plasma channels in fused silica,” Opt. Commun. 267, 511–523 (2006).
[CrossRef]

W. Liu, O. Kosareva, I. S. Golubtsov, A. Iwasaki, A. Becker, V. P. Kandidov, and S. L. Chin, “Femtosecond laser pulse filamentation versus optical breakdown in H2O,” Appl. Phys. B 76, 215–229 (2003).
[CrossRef]

V. P. Kandidov, O. G. Kasareva, and A. A. Koitun, “Nonlinear-optical transformation of a high-power femtosecond laser pulse in air,” Quantum Electron. 33, 69–75 (2003).
[CrossRef]

A. Brodeur, C. Y. Chien, F. A. Ilkov, S. L. Chin, O. G. Kosareva, and V. P. Kandidov, “Moving focus in the propagation of ultrashort laser pulses in air,” Opt. Lett. 22, 304–306 (1997).

O. G. Kosareva, V. P. Kandidov, A. Brodeur, C. Y. Chien, and S. L. Chin, “Conical emission from laser plasma interactions in the filamentation of powerful ultrashort laser pulses in air,” Opt. Lett. 22, 1332–1334 (1997).
[CrossRef]

Kasareva, O. G.

V. P. Kandidov, O. G. Kasareva, and A. A. Koitun, “Nonlinear-optical transformation of a high-power femtosecond laser pulse in air,” Quantum Electron. 33, 69–75 (2003).
[CrossRef]

Kazem, J.-G.

J.-G. Kazem and H. Masalehdan, “Modeling of nonlinear responses in BK7 glass under irradiation of femtosecond laser pulses,” Opt. Quantum Electron. 41, 47–53 (2009).
[CrossRef]

Koitun, A. A.

V. P. Kandidov, O. G. Kasareva, and A. A. Koitun, “Nonlinear-optical transformation of a high-power femtosecond laser pulse in air,” Quantum Electron. 33, 69–75 (2003).
[CrossRef]

Kosareva, O.

W. Liu, O. Kosareva, I. S. Golubtsov, A. Iwasaki, A. Becker, V. P. Kandidov, and S. L. Chin, “Femtosecond laser pulse filamentation versus optical breakdown in H2O,” Appl. Phys. B 76, 215–229 (2003).
[CrossRef]

Kosareva, O. G.

Le Blanc, C.

E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, C. Le Blanc, and A. Mysyrowicz, “Measurement of the nonlinear refractive index of transparent materials by spectral analysis after nonlinear propagation,” Opt. Commun. 119, 479–484 (1995).
[CrossRef]

Liu, W.

O. G. Kosareva, T. Nguyen, N. A. Panov, W. Liu, A. Saliminia, V. P. Kandidov, N. Akozabek, M. Scalora, R. Vallee, and S. L. Chin, “Array of femtosecond plasma channels in fused silica,” Opt. Commun. 267, 511–523 (2006).
[CrossRef]

W. Liu and S. L. Chin, “Direct measurement of the critical power of femtosecond Ti:sapphire laser pulse in air,” Opt. Express 13, 5750–5755 (2005).
[CrossRef]

W. Liu, O. Kosareva, I. S. Golubtsov, A. Iwasaki, A. Becker, V. P. Kandidov, and S. L. Chin, “Femtosecond laser pulse filamentation versus optical breakdown in H2O,” Appl. Phys. B 76, 215–229 (2003).
[CrossRef]

Liu, X. L.

X. L. Liu and B.-S. Hu, “Micro-displacement system of pulse equivalent and return difference of a stepping motor,” Laser Technol. 35, 603–605 (2011).

Longtin, J. P.

Luther-Davies, B.

Ma, H.

Masalehdan, H.

J.-G. Kazem and H. Masalehdan, “Modeling of nonlinear responses in BK7 glass under irradiation of femtosecond laser pulses,” Opt. Quantum Electron. 41, 47–53 (2009).
[CrossRef]

Méchain, G.

G. Méchain, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Organizing multiple femtosecond filaments in air,” Phys. Rev. Lett. 93, 035003 (2004).
[CrossRef]

Ménard, J.-M.

Mendonça, C. R.

C. R. Mendonça, L. Misoguti, and S. C. Zilio, “Measurements with Fourier analysis in ion-doped solids,” Appl. Phys. Lett. 71, 2094–2096 (1997).
[CrossRef]

Milam, D.

D. Milam and M. J. Weber, “Measurement of nonlinear refractive-index coefficients using time-resolved interferometry: Application to optical materials for high-power neodymium lasers,” J. Appl. Phys. 47, 2497–2501 (1976).
[CrossRef]

Milchberg, H. M.

Misoguti, L.

C. R. Mendonça, L. Misoguti, and S. C. Zilio, “Measurements with Fourier analysis in ion-doped solids,” Appl. Phys. Lett. 71, 2094–2096 (1997).
[CrossRef]

Moll, K. D.

K. D. Moll, A. L. Gaeta, and G. Fibich, “Self-similar optical wave collapse: observation of the Townes profile,” Phys. Rev. Lett. 90, 203902 (2003).
[CrossRef]

Moloney, J. V.

P. Polynkin and J. V. Moloney, “Optical breakdown of air triggered by femtosecond laser filaments,” Appl. Phys. Lett. 99, 151103 (2011).
[CrossRef]

Morandotti, R.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-Focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86, 3296–3299 (2001).
[CrossRef]

Mysyrowicz, A.

A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Filamentation and damage in fused silica induced by tightly focused femtosecond laser pulses,” Phys. Rev. B 71, 125435 (2005).
[CrossRef]

G. Méchain, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Organizing multiple femtosecond filaments in air,” Phys. Rev. Lett. 93, 035003 (2004).
[CrossRef]

E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, C. Le Blanc, and A. Mysyrowicz, “Measurement of the nonlinear refractive index of transparent materials by spectral analysis after nonlinear propagation,” Opt. Commun. 119, 479–484 (1995).
[CrossRef]

Nguyen, T.

O. G. Kosareva, T. Nguyen, N. A. Panov, W. Liu, A. Saliminia, V. P. Kandidov, N. Akozabek, M. Scalora, R. Vallee, and S. L. Chin, “Array of femtosecond plasma channels in fused silica,” Opt. Commun. 267, 511–523 (2006).
[CrossRef]

Nibbering, E. T. J.

E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, C. Le Blanc, and A. Mysyrowicz, “Measurement of the nonlinear refractive index of transparent materials by spectral analysis after nonlinear propagation,” Opt. Commun. 119, 479–484 (1995).
[CrossRef]

Owyoung, A.

A. Owyoung, “Ellipse rotation studies in laser host materials,” IEEE J. Quantum Electron. 9, 1064–1069 (1973).
[CrossRef]

Palange, E.

M. Falconieri, E. Palange, and H. L. Fragnito, “Achievement of phase distortion sensitivity in the measurement of optical nonlinearities by using a modulated Z-scan technique,” J. Opt. A 4, 404–407 (2002).
[CrossRef]

Panov, N. A.

O. G. Kosareva, T. Nguyen, N. A. Panov, W. Liu, A. Saliminia, V. P. Kandidov, N. Akozabek, M. Scalora, R. Vallee, and S. L. Chin, “Array of femtosecond plasma channels in fused silica,” Opt. Commun. 267, 511–523 (2006).
[CrossRef]

Payne, S. A.

Perret, Z.

Polynkin, P.

P. Polynkin and J. V. Moloney, “Optical breakdown of air triggered by femtosecond laser filaments,” Appl. Phys. Lett. 99, 151103 (2011).
[CrossRef]

Prade, B.

A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Filamentation and damage in fused silica induced by tightly focused femtosecond laser pulses,” Phys. Rev. B 71, 125435 (2005).
[CrossRef]

G. Méchain, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Organizing multiple femtosecond filaments in air,” Phys. Rev. Lett. 93, 035003 (2004).
[CrossRef]

Prade, B. S.

E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, C. Le Blanc, and A. Mysyrowicz, “Measurement of the nonlinear refractive index of transparent materials by spectral analysis after nonlinear propagation,” Opt. Commun. 119, 479–484 (1995).
[CrossRef]

Psaltis, D.

A. Goy and D. Psaltis, “Digital reverse propagation in focusing Kerr media,” Phys. Rev. A 83, 031802(R) (2011).
[CrossRef]

Qiao, C.

Ranka, J. K.

J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, “Observation of pulse splitting in nonlinear dispersive media,” Phys. Rev. Lett. 77, 3783–3786 (1996).
[CrossRef]

Saliminia, A.

O. G. Kosareva, T. Nguyen, N. A. Panov, W. Liu, A. Saliminia, V. P. Kandidov, N. Akozabek, M. Scalora, R. Vallee, and S. L. Chin, “Array of femtosecond plasma channels in fused silica,” Opt. Commun. 267, 511–523 (2006).
[CrossRef]

Samineni, P.

Samoc, A.

Samoc, M.

Scalora, M.

O. G. Kosareva, T. Nguyen, N. A. Panov, W. Liu, A. Saliminia, V. P. Kandidov, N. Akozabek, M. Scalora, R. Vallee, and S. L. Chin, “Array of femtosecond plasma channels in fused silica,” Opt. Commun. 267, 511–523 (2006).
[CrossRef]

Scherf, U.

Schirmer, R. W.

J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, “Observation of pulse splitting in nonlinear dispersive media,” Phys. Rev. Lett. 77, 3783–3786 (1996).
[CrossRef]

Schrauth, S. E.

B. Shim, S. E. Schrauth, C. J. Hensley, L. T. Vuong, P. Hui, A. A. Ishaaya, and A. L. Gaeta, “Controlled interactions of femtosecond light filaments in air,” Phys. Rev. A 81, 061803(R) (2010).
[CrossRef]

Shen, Y. R.

Shim, B.

B. Shim, S. E. Schrauth, C. J. Hensley, L. T. Vuong, P. Hui, A. A. Ishaaya, and A. L. Gaeta, “Controlled interactions of femtosecond light filaments in air,” Phys. Rev. A 81, 061803(R) (2010).
[CrossRef]

Shuker, R.

W. Gawlik, R. Shuker, and A. Gallagher, “Temporal character of pulsed-laser cone emission,” Phys. Rev. A 64, 021801(R) (2001).
[CrossRef]

Sigal, I.

Silberberg, Y.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-Focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86, 3296–3299 (2001).
[CrossRef]

Sorel, M.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-Focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86, 3296–3299 (2001).
[CrossRef]

Sudrie, L.

A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Filamentation and damage in fused silica induced by tightly focused femtosecond laser pulses,” Phys. Rev. B 71, 125435 (2005).
[CrossRef]

Vallee, R.

O. G. Kosareva, T. Nguyen, N. A. Panov, W. Liu, A. Saliminia, V. P. Kandidov, N. Akozabek, M. Scalora, R. Vallee, and S. L. Chin, “Array of femtosecond plasma channels in fused silica,” Opt. Commun. 267, 511–523 (2006).
[CrossRef]

van Driel, H. M.

Varma, S.

Vuong, L. T.

B. Shim, S. E. Schrauth, C. J. Hensley, L. T. Vuong, P. Hui, A. A. Ishaaya, and A. L. Gaeta, “Controlled interactions of femtosecond light filaments in air,” Phys. Rev. A 81, 061803(R) (2010).
[CrossRef]

Wang, H.

Warren, W. S.

Waxler, R. M.

A. Feldman, D. Horowitz, and R. M. Waxler, “Mechanisms for self-focusing in optical glasses,” IEEE J. Quantum Electron. 9, 1054–1061 (1973).
[CrossRef]

Weber, M. J.

D. Milam and M. J. Weber, “Measurement of nonlinear refractive-index coefficients using time-resolved interferometry: Application to optical materials for high-power neodymium lasers,” J. Appl. Phys. 47, 2497–2501 (1976).
[CrossRef]

Yang, G. Y.

Yu, L.

Zhang, J.

Zhang, P.

Zilio, S. C.

C. R. Mendonça, L. Misoguti, and S. C. Zilio, “Measurements with Fourier analysis in ion-doped solids,” Appl. Phys. Lett. 71, 2094–2096 (1997).
[CrossRef]

Zozulya, A. A.

A. A. Zozulya, “Propagation dynamics of intense femtosecond pulses: multiple splittings, coalescence, and continuum generation,” Phys. Rev. Lett. 82, 1430–1433 (1999).
[CrossRef]

Appl. Opt.

Appl. Phys. B

W. Liu, O. Kosareva, I. S. Golubtsov, A. Iwasaki, A. Becker, V. P. Kandidov, and S. L. Chin, “Femtosecond laser pulse filamentation versus optical breakdown in H2O,” Appl. Phys. B 76, 215–229 (2003).
[CrossRef]

Appl. Phys. Lett.

P. Polynkin and J. V. Moloney, “Optical breakdown of air triggered by femtosecond laser filaments,” Appl. Phys. Lett. 99, 151103 (2011).
[CrossRef]

C. R. Mendonça, L. Misoguti, and S. C. Zilio, “Measurements with Fourier analysis in ion-doped solids,” Appl. Phys. Lett. 71, 2094–2096 (1997).
[CrossRef]

IEEE J. Quantum Electron.

N. L. Boling and A. J. Glass, “Empirical relationships for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. 14, 601–608 (1978).
[CrossRef]

A. Feldman, D. Horowitz, and R. M. Waxler, “Mechanisms for self-focusing in optical glasses,” IEEE J. Quantum Electron. 9, 1054–1061 (1973).
[CrossRef]

A. Owyoung, “Ellipse rotation studies in laser host materials,” IEEE J. Quantum Electron. 9, 1064–1069 (1973).
[CrossRef]

J. Appl. Phys.

D. Milam and M. J. Weber, “Measurement of nonlinear refractive-index coefficients using time-resolved interferometry: Application to optical materials for high-power neodymium lasers,” J. Appl. Phys. 47, 2497–2501 (1976).
[CrossRef]

J. Opt. A

M. Falconieri, E. Palange, and H. L. Fragnito, “Achievement of phase distortion sensitivity in the measurement of optical nonlinearities by using a modulated Z-scan technique,” J. Opt. A 4, 404–407 (2002).
[CrossRef]

J. Opt. Soc. Am. B

Laser Technol.

X. L. Liu and B.-S. Hu, “Micro-displacement system of pulse equivalent and return difference of a stepping motor,” Laser Technol. 35, 603–605 (2011).

Opt. Commun.

E. T. J. Nibbering, M. A. Franco, B. S. Prade, G. Grillon, C. Le Blanc, and A. Mysyrowicz, “Measurement of the nonlinear refractive index of transparent materials by spectral analysis after nonlinear propagation,” Opt. Commun. 119, 479–484 (1995).
[CrossRef]

O. G. Kosareva, T. Nguyen, N. A. Panov, W. Liu, A. Saliminia, V. P. Kandidov, N. Akozabek, M. Scalora, R. Vallee, and S. L. Chin, “Array of femtosecond plasma channels in fused silica,” Opt. Commun. 267, 511–523 (2006).
[CrossRef]

M. R. Junnarker, “Short pulse propagation in tight focusing conditions,” Opt. Commun. 195, 273–292 (2001).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Quantum Electron.

J.-G. Kazem and H. Masalehdan, “Modeling of nonlinear responses in BK7 glass under irradiation of femtosecond laser pulses,” Opt. Quantum Electron. 41, 47–53 (2009).
[CrossRef]

Phys. Rev. A

W. Gawlik, R. Shuker, and A. Gallagher, “Temporal character of pulsed-laser cone emission,” Phys. Rev. A 64, 021801(R) (2001).
[CrossRef]

B. Shim, S. E. Schrauth, C. J. Hensley, L. T. Vuong, P. Hui, A. A. Ishaaya, and A. L. Gaeta, “Controlled interactions of femtosecond light filaments in air,” Phys. Rev. A 81, 061803(R) (2010).
[CrossRef]

A. Goy and D. Psaltis, “Digital reverse propagation in focusing Kerr media,” Phys. Rev. A 83, 031802(R) (2011).
[CrossRef]

Phys. Rev. B

A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Filamentation and damage in fused silica induced by tightly focused femtosecond laser pulses,” Phys. Rev. B 71, 125435 (2005).
[CrossRef]

Phys. Rev. Lett.

A. A. Zozulya, “Propagation dynamics of intense femtosecond pulses: multiple splittings, coalescence, and continuum generation,” Phys. Rev. Lett. 82, 1430–1433 (1999).
[CrossRef]

A. Brodeur and S. L. Chin, “Band-gap dependence of the ultrafast white-light continuum,” Phys. Rev. Lett. 80, 4406–4409 (1998).
[CrossRef]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-Focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86, 3296–3299 (2001).
[CrossRef]

A. L. Gaeta, “Catastrophic collapse of ultrashort pulses,” Phys. Rev. Lett. 84, 3582–3585 (2000).
[CrossRef]

G. Méchain, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Organizing multiple femtosecond filaments in air,” Phys. Rev. Lett. 93, 035003 (2004).
[CrossRef]

J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, “Observation of pulse splitting in nonlinear dispersive media,” Phys. Rev. Lett. 77, 3783–3786 (1996).
[CrossRef]

K. D. Moll, A. L. Gaeta, and G. Fibich, “Self-similar optical wave collapse: observation of the Townes profile,” Phys. Rev. Lett. 90, 203902 (2003).
[CrossRef]

Quantum Electron.

V. P. Kandidov, O. G. Kasareva, and A. A. Koitun, “Nonlinear-optical transformation of a high-power femtosecond laser pulse in air,” Quantum Electron. 33, 69–75 (2003).
[CrossRef]

Other

Y. R. Shen, Principles of Nonlinear Optics (Wiley, 1984).

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Figures (6)

Fig. 1.
Fig. 1.

Simplified schematic of the experimental arrangement.

Fig. 2.
Fig. 2.

Shape and length of filament inside BK7 glass at different laser energies and D conditions. (a)–(d) for laser pulse peak energies equal to 0.525, 0.840, 1.070, and 1.370 mJ, respectively, and the D equal to 1795 mm. (e)–(f) for laser pulse peak energy fixed to 0.870 mJ and the D equal to 1820 and 1910 mm, respectively.

Fig. 3.
Fig. 3.

(a) Filament emission spectrum detected via the detecting system when FP=9.00±0.12mm and LPPPmax=23.90±0.16GW, D=1795±0.5mm. (b) All the filament emission spectra for different FPs and fixed LPP Pmax=23.90±0.16GW and D=1795±0.5mm.

Fig. 4.
Fig. 4.

Intensity of light emitted from filament as a function of FP with fixed laser peak power LPP Pmax=30.5±0.7GW. FP=3.01±0.04mm (corresponding to the maximum intensity shown in the present figure) is equal to self-focusing length of LPP.

Fig. 5.
Fig. 5.

Results of self-focusing critical power of BK7 sample under various single pulse energies and different BK7 D conditions, the mean value of critical power denoted by dashed line. Error bars denote total errors, and the error band shows the systematic error, respectively. Note that all systematic errors are added to an arbitrary positive number 0.5 for drawing the graph.

Fig. 6.
Fig. 6.

Comparison of NRIC measured values and the others obtained by employed various methods with different laser pulses. The dashed line denotes the calculation value with Abbe number formula. Total errors are shown by error bars. Systematic errors are denoted with error band. All systematic errors are added to an arbitrary positive number 2.1×1020.

Equations (8)

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

n=n0+n2Iorn=n0+n2|E|2,
n2=n240π/cn0,
Pcr=3.77λ028πn0n2,
zself=0.184kw2{[(PPcr)120.852]20.0219}1/2,
P(t)=Pmaxexp[(4ln2)(tτp)2],
Ep=Pmaxexp[(4ln2)(tτp)2]dt=1.064Pmaxτp.
w(z)=w01+(λ0zπw02)2,
n2×(1013esu)=68(nd1)(nd2+2)2vd[1.517+vd(nd+1)(nd2+2)6nd]1/2,

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