Abstract

The higher-order Kerr effect (HOKE) has recently been advocated to explain measurements of the saturation of the nonlinear refractive index in gases. Here we show that cascaded third-harmonic generation results in an effective fifth-order nonlinearity that is negative and significant. Higher-order harmonic cascading will also occur from the HOKE, and the cascading contributions may significantly modify the observed nonlinear index change. At lower wavelengths, cascading increases the HOKE saturation intensity, while for longer wavelengths cascading will decrease the HOKE saturation intensity.

© 2012 Optical Society of America

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2012

2011

C. Brée, A. Demircan, and G. Steinmeyer, Phys. Rev. Lett. 106, 183902 (2011).
[CrossRef]

J. K. Wahlstrand, Y.-H. Cheng, Y.-H. Chen, and H. M. Milchberg, Phys. Rev. Lett. 107, 103901 (2011).
[CrossRef]

P. Polynkin, M. Kolesik, E. M. Wright, and J. V. Moloney, Phys. Rev. Lett. 106, 153902 (2011).
[CrossRef]

P. Béjot, E. Hertz, J. Kasparian, B. Lavorel, J. P. Wolf, and O. Faucher, Phys. Rev. Lett. 106, 243902 (2011).
[CrossRef]

2010

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, erratum: Opt. Express 18, 3011 (2010).
[CrossRef]

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef]

W. Ettoumi, Y. Petit, J. Kasparian, and J.-P. Wolf, Opt. Express 18, 6613 (2010).
[CrossRef]

2009

2008

2007

2006

M. Kolesik, E. Wright, A. Becker, and J. Moloney, Appl. Phys. B 85, 531 (2006).
[CrossRef]

1997

1996

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

1967

L. A. Ostrovskii, Pisma Zh. Eksp. Teor. Fiz. 5, 331 (1967).

Ališauskas, S.

Ariunbold, G. O.

Bache, M.

B. B. Zhou, A. Chong, F. W. Wise, and M. Bache, Phys. Rev. Lett. 109, 043902 (2012).
[CrossRef]

M. Bache, O. Bang, J. Moses, and F. W. Wise, Opt. Lett. 32, 2490 (2007).
[CrossRef]

Baltuška, A.

Bang, O.

Becker, A.

M. Kolesik, E. Wright, A. Becker, and J. Moloney, Appl. Phys. B 85, 531 (2006).
[CrossRef]

Béjot, P.

D. Kartashov, S. Ališauskas, A. Pugžlys, A. Voronin, A. Zheltikov, M. Petrarca, P. Béjot, J. Kasparian, J.-P. Wolf, and A. Baltuška, Opt. Lett. 37, 3456 (2012).
[CrossRef]

M. Petrarca, Y. Petit, S. Henin, R. Delagrange, P. Béjot, and J. Kasparian, Opt. Lett. 37, 4347 (2012).

P. Béjot, E. Hertz, J. Kasparian, B. Lavorel, J. P. Wolf, and O. Faucher, Phys. Rev. Lett. 106, 243902 (2011).
[CrossRef]

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef]

Boardman, A. D.

Börzsönyi, A.

Brée, C.

C. Brée, A. Demircan, and G. Steinmeyer, Phys. Rev. Lett. 106, 183902 (2011).
[CrossRef]

Chen, Y.-H.

J. K. Wahlstrand, Y.-H. Cheng, Y.-H. Chen, and H. M. Milchberg, Phys. Rev. Lett. 107, 103901 (2011).
[CrossRef]

Cheng, Y.-H.

J. K. Wahlstrand, Y.-H. Cheng, Y.-H. Chen, and H. M. Milchberg, Phys. Rev. Lett. 107, 103901 (2011).
[CrossRef]

Chong, A.

B. B. Zhou, A. Chong, F. W. Wise, and M. Bache, Phys. Rev. Lett. 109, 043902 (2012).
[CrossRef]

Couairon, A.

A. Couairon and A. Mysyrowicz, Phys. Rep. 441, 47 (2007).
[CrossRef]

Delagrange, R.

Demircan, A.

C. Brée, A. Demircan, and G. Steinmeyer, Phys. Rev. Lett. 106, 183902 (2011).
[CrossRef]

Ettoumi, W.

Faucher, O.

P. Béjot, E. Hertz, J. Kasparian, B. Lavorel, J. P. Wolf, and O. Faucher, Phys. Rev. Lett. 106, 243902 (2011).
[CrossRef]

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef]

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, erratum: Opt. Express 18, 3011 (2010).
[CrossRef]

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, Opt. Express 17, 13429 (2009).
[CrossRef]

Hagan, D. J.

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

Heiner, Z.

Henin, S.

M. Petrarca, Y. Petit, S. Henin, R. Delagrange, P. Béjot, and J. Kasparian, Opt. Lett. 37, 4347 (2012).

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef]

Hertz, E.

P. Béjot, E. Hertz, J. Kasparian, B. Lavorel, J. P. Wolf, and O. Faucher, Phys. Rev. Lett. 106, 243902 (2011).
[CrossRef]

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, erratum: Opt. Express 18, 3011 (2010).
[CrossRef]

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef]

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, Opt. Express 17, 13429 (2009).
[CrossRef]

Kalashnikov, M. P.

Kartashov, D.

Kasparian, J.

M. Petrarca, Y. Petit, S. Henin, R. Delagrange, P. Béjot, and J. Kasparian, Opt. Lett. 37, 4347 (2012).

D. Kartashov, S. Ališauskas, A. Pugžlys, A. Voronin, A. Zheltikov, M. Petrarca, P. Béjot, J. Kasparian, J.-P. Wolf, and A. Baltuška, Opt. Lett. 37, 3456 (2012).
[CrossRef]

P. Béjot, E. Hertz, J. Kasparian, B. Lavorel, J. P. Wolf, and O. Faucher, Phys. Rev. Lett. 106, 243902 (2011).
[CrossRef]

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef]

W. Ettoumi, Y. Petit, J. Kasparian, and J.-P. Wolf, Opt. Express 18, 6613 (2010).
[CrossRef]

Kolesik, M.

P. Polynkin, M. Kolesik, E. M. Wright, and J. V. Moloney, Phys. Rev. Lett. 106, 153902 (2011).
[CrossRef]

M. Kolesik, E. Wright, A. Becker, and J. Moloney, Appl. Phys. B 85, 531 (2006).
[CrossRef]

Kovács, A. P.

Lavorel, B.

P. Béjot, E. Hertz, J. Kasparian, B. Lavorel, J. P. Wolf, and O. Faucher, Phys. Rev. Lett. 106, 243902 (2011).
[CrossRef]

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, erratum: Opt. Express 18, 3011 (2010).
[CrossRef]

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef]

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, Opt. Express 17, 13429 (2009).
[CrossRef]

B. Lavorel, CNRS-Université de Bourgogne (personal communication, 2012).

Loriot, V.

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, erratum: Opt. Express 18, 3011 (2010).
[CrossRef]

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef]

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, Opt. Express 17, 13429 (2009).
[CrossRef]

Lu, Z. H.

Milchberg, H. M.

J. K. Wahlstrand, Y.-H. Cheng, Y.-H. Chen, and H. M. Milchberg, Phys. Rev. Lett. 107, 103901 (2011).
[CrossRef]

Moloney, J.

M. Kolesik, E. Wright, A. Becker, and J. Moloney, Appl. Phys. B 85, 531 (2006).
[CrossRef]

Moloney, J. V.

G. O. Ariunbold, P. Polynkin, and J. V. Moloney, Opt. Express 20, 1662 (2012).
[CrossRef]

P. Polynkin, M. Kolesik, E. M. Wright, and J. V. Moloney, Phys. Rev. Lett. 106, 153902 (2011).
[CrossRef]

Moses, J.

Mysyrowicz, A.

A. Couairon and A. Mysyrowicz, Phys. Rep. 441, 47 (2007).
[CrossRef]

Ostrovskii, L. A.

L. A. Ostrovskii, Pisma Zh. Eksp. Teor. Fiz. 5, 331 (1967).

Osvay, K.

Petit, Y.

Petrarca, M.

Polynkin, P.

G. O. Ariunbold, P. Polynkin, and J. V. Moloney, Opt. Express 20, 1662 (2012).
[CrossRef]

P. Polynkin, M. Kolesik, E. M. Wright, and J. V. Moloney, Phys. Rev. Lett. 106, 153902 (2011).
[CrossRef]

Pugžlys, A.

Saltiel, S.

Stegeman, G. I.

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

Steinmeyer, G.

C. Brée, A. Demircan, and G. Steinmeyer, Phys. Rev. Lett. 106, 183902 (2011).
[CrossRef]

Tanev, S.

Torner, L.

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

Vieillard, T.

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef]

Voronin, A.

Wahlstrand, J. K.

J. K. Wahlstrand, Y.-H. Cheng, Y.-H. Chen, and H. M. Milchberg, Phys. Rev. Lett. 107, 103901 (2011).
[CrossRef]

Wang, L. J.

Wise, F. W.

B. B. Zhou, A. Chong, F. W. Wise, and M. Bache, Phys. Rev. Lett. 109, 043902 (2012).
[CrossRef]

M. Bache, O. Bang, J. Moses, and F. W. Wise, Opt. Lett. 32, 2490 (2007).
[CrossRef]

Wolf, J. P.

P. Béjot, E. Hertz, J. Kasparian, B. Lavorel, J. P. Wolf, and O. Faucher, Phys. Rev. Lett. 106, 243902 (2011).
[CrossRef]

Wolf, J.-P.

Wright, E.

M. Kolesik, E. Wright, A. Becker, and J. Moloney, Appl. Phys. B 85, 531 (2006).
[CrossRef]

Wright, E. M.

P. Polynkin, M. Kolesik, E. M. Wright, and J. V. Moloney, Phys. Rev. Lett. 106, 153902 (2011).
[CrossRef]

Zhang, J.

Zheltikov, A.

Zhou, B. B.

B. B. Zhou, A. Chong, F. W. Wise, and M. Bache, Phys. Rev. Lett. 109, 043902 (2012).
[CrossRef]

Appl. Opt.

Appl. Phys. B

M. Kolesik, E. Wright, A. Becker, and J. Moloney, Appl. Phys. B 85, 531 (2006).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Quantum Electron.

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

Phys. Rep.

A. Couairon and A. Mysyrowicz, Phys. Rep. 441, 47 (2007).
[CrossRef]

Phys. Rev. Lett.

P. Béjot, E. Hertz, J. Kasparian, B. Lavorel, J. P. Wolf, and O. Faucher, Phys. Rev. Lett. 106, 243902 (2011).
[CrossRef]

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef]

P. Polynkin, M. Kolesik, E. M. Wright, and J. V. Moloney, Phys. Rev. Lett. 106, 153902 (2011).
[CrossRef]

J. K. Wahlstrand, Y.-H. Cheng, Y.-H. Chen, and H. M. Milchberg, Phys. Rev. Lett. 107, 103901 (2011).
[CrossRef]

B. B. Zhou, A. Chong, F. W. Wise, and M. Bache, Phys. Rev. Lett. 109, 043902 (2012).
[CrossRef]

C. Brée, A. Demircan, and G. Steinmeyer, Phys. Rev. Lett. 106, 183902 (2011).
[CrossRef]

Pisma Zh. Eksp. Teor. Fiz.

L. A. Ostrovskii, Pisma Zh. Eksp. Teor. Fiz. 5, 331 (1967).

Other

B. Lavorel, CNRS-Université de Bourgogne (personal communication, 2012).

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Figures (1)

Fig. 1.
Fig. 1.

(a) Nonlinear index change Δ n versus pump intensity for λ 1 = 0.8 μm . (b) Inversion intensity I inv versus FW wavelength. In both plots the thin lines are the data from [1,2], while the bold lines include cascading corrections. In (b) the nonlinear coefficients include frequency dispersion using Miller’s formula [19].

Tables (1)

Tables Icon

Table 1. Material [1,2] and Cascading Nonlinearities at λ 1 = 0.8 μm , p = 1 atm , and T = 293 K

Equations (4)

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

( i z 1 2 k 2 ( ω 1 ) τ τ ) E 1 + Γ ω 1 ( 3 ) [ E 1 | E 1 | 2 + 2 E 1 | E 3 | 2 + ( E 1 * ) 2 E 3 e i Δ k 13 z ] = 0 ,
( i z i d 13 τ 1 2 k 2 ( ω 3 ) τ τ ) E 3 + Γ ω 3 ( 3 ) [ E 3 | E 3 | 2 + 2 E 3 | E 1 | 2 + 1 3 E 1 3 e i Δ k 13 z ] = 0 .
n 4 , casc n 2 2 Δ k 13 ω 1 c .
n 6 , casc ( 3 ) n 2 3 n ( ω 3 ) Δ k 13 2 ω 1 2 c 2 , n 6 , casc ( 5 ) 5 n 2 n 4 2 Δ k 13 ω 1 c .

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