Abstract

We discuss the influence of the higher-order Kerr effect (HOKE) in wide bandgap solids at extreme intensities below the onset of optically induced damage. Using different theoretical models, we employ multiphoton absorption rates to compute the nonlinear refractive index by a Kramers–Kronig transform. Within this theoretical framework we provide an estimate for the appearance of significant deviations from the standard optical Kerr effect predicting a linear index change with intensity. We discuss the role of the observed saturation behavior in practically relevant situations, including Kerr lens mode-locking and supercontinuum generation in photonic crystal fibers. Furthermore, we present experimental data from a multiwave mixing experiment in BaF2, which can be explained by the appearance of the HOKE.

© 2012 Optical Society of America

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2011 (3)

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

J. K. Wahlstrand and H. M. Milchberg, Opt. Lett. 36, 3822 (2011).
[CrossRef]

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

2010 (1)

2009 (2)

2008 (1)

L. Bergé, S. Skupin, and G. Steinmeyer, Phys. Rev. Lett. 101, 213901 (2008).
[CrossRef]

2005 (1)

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, Phys. Rev. B 71, 115109 (2005).
[CrossRef]

2002 (1)

K. D. Moll, D. Homoelle, A. L. Gaeta, and R. W. Boyd, Phys. Rev. Lett. 88, 153901 (2002).
[CrossRef]

1996 (1)

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, and M. Sheik-Bahae, IEEE J. Quantum Electron. 32, 1324 (1996).
[CrossRef]

1991 (1)

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 27, 1296 (1991).
[CrossRef]

1987 (1)

1984 (1)

1983 (1)

H. S. Brandi and C. B. de Araújo, J. Phys. C 16, 5929 (1983).
[CrossRef]

1965 (1)

L. V. Keldysh, Sov. Phys. JETP 20, 1307 (1965).

Béjot, P.

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

Bergé, L.

L. Bergé, S. Skupin, and G. Steinmeyer, Phys. Rev. Lett. 101, 213901 (2008).
[CrossRef]

Boyd, R. W.

K. D. Moll, D. Homoelle, A. L. Gaeta, and R. W. Boyd, Phys. Rev. Lett. 88, 153901 (2002).
[CrossRef]

Boyer, K.

Brandi, H. S.

H. S. Brandi and C. B. de Araújo, J. Phys. C 16, 5929 (1983).
[CrossRef]

Brée, C.

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

de Araújo, C. B.

H. S. Brandi and C. B. de Araújo, J. Phys. C 16, 5929 (1983).
[CrossRef]

Demircan, A.

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

DeSalvo, R.

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, and M. Sheik-Bahae, IEEE J. Quantum Electron. 32, 1324 (1996).
[CrossRef]

Diels, J.-C.

Faucher, O.

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, Opt. Express 17, 13429 (2009).
[CrossRef]

Gaeta, A. L.

K. D. Moll, D. Homoelle, A. L. Gaeta, and R. W. Boyd, Phys. Rev. Lett. 88, 153901 (2002).
[CrossRef]

Gibson, G.

Hagan, D. J.

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, and M. Sheik-Bahae, IEEE J. Quantum Electron. 32, 1324 (1996).
[CrossRef]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 27, 1296 (1991).
[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, Opt. Express 17, 13429 (2009).
[CrossRef]

Homoelle, D.

K. D. Moll, D. Homoelle, A. L. Gaeta, and R. W. Boyd, Phys. Rev. Lett. 88, 153901 (2002).
[CrossRef]

Hutchings, D. C.

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 27, 1296 (1991).
[CrossRef]

Ivanov, M.

F. Krausz and M. Ivanov, Rev. Mod. Phys. 81, 163 (2009).
[CrossRef]

Jara, H.

Johann, U.

Kasparian, J.

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

Keldysh, L. V.

L. V. Keldysh, Sov. Phys. JETP 20, 1307 (1965).

Kolesik, M.

Krausz, F.

F. Krausz and M. Ivanov, Rev. Mod. Phys. 81, 163 (2009).
[CrossRef]

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, Opt. Express 17, 13429 (2009).
[CrossRef]

Liu, J.

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, Phys. Rev. B 71, 115109 (2005).
[CrossRef]

Loriot, V.

Luk, T. S.

McIntyre, I. A.

McPherson, A.

Mero, M.

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, Phys. Rev. B 71, 115109 (2005).
[CrossRef]

Milchberg, H. M.

Mirell, D.

Moll, K. D.

K. D. Moll, D. Homoelle, A. L. Gaeta, and R. W. Boyd, Phys. Rev. Lett. 88, 153901 (2002).
[CrossRef]

Moloney, J. V.

Rhodes, C. K.

Ristau, D.

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, Phys. Rev. B 71, 115109 (2005).
[CrossRef]

Rudolph, W.

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, Phys. Rev. B 71, 115109 (2005).
[CrossRef]

Said, A. A.

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, and M. Sheik-Bahae, IEEE J. Quantum Electron. 32, 1324 (1996).
[CrossRef]

Sheik-Bahae, M.

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, and M. Sheik-Bahae, IEEE J. Quantum Electron. 32, 1324 (1996).
[CrossRef]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 27, 1296 (1991).
[CrossRef]

Skupin, S.

L. Bergé, S. Skupin, and G. Steinmeyer, Phys. Rev. Lett. 101, 213901 (2008).
[CrossRef]

Starke, K.

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, Phys. Rev. B 71, 115109 (2005).
[CrossRef]

Steinmeyer, G.

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

L. Bergé, S. Skupin, and G. Steinmeyer, Phys. Rev. Lett. 101, 213901 (2008).
[CrossRef]

Van Stryland, E. W.

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, and M. Sheik-Bahae, IEEE J. Quantum Electron. 32, 1324 (1996).
[CrossRef]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 27, 1296 (1991).
[CrossRef]

Wahlstrand, J. K.

Wherrett, B. S.

Wolf, J.-P.

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

IEEE J. Quantum Electron. (2)

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 27, 1296 (1991).
[CrossRef]

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, and M. Sheik-Bahae, IEEE J. Quantum Electron. 32, 1324 (1996).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Phys. C (1)

H. S. Brandi and C. B. de Araújo, J. Phys. C 16, 5929 (1983).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. B (1)

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, Phys. Rev. B 71, 115109 (2005).
[CrossRef]

Phys. Rev. Lett. (4)

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

K. D. Moll, D. Homoelle, A. L. Gaeta, and R. W. Boyd, Phys. Rev. Lett. 88, 153901 (2002).
[CrossRef]

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

L. Bergé, S. Skupin, and G. Steinmeyer, Phys. Rev. Lett. 101, 213901 (2008).
[CrossRef]

Rev. Mod. Phys. (1)

F. Krausz and M. Ivanov, Rev. Mod. Phys. 81, 163 (2009).
[CrossRef]

Sov. Phys. JETP (1)

L. V. Keldysh, Sov. Phys. JETP 20, 1307 (1965).

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Figures (3)

Fig. 1.
Fig. 1.

Beam pattern observed in the far field of a multiwave mixing experiment in a 500 μm thick BaF2 crystal at elevated intensities, i.e., 10TW/cm2 in a single input beam with 800 nm center wavelength, 10 fs pulse duration, and peak power of 40 MW at 3 kHz repetition rate. The experiment is carried out in a boxcar geometry with a focal length of 20 cm and a crossing angle of 2°. Three primary input waves have been tagged by “1,” secondary waves with numerals according to order.

Fig. 2.
Fig. 2.

(a) TPA coefficients for SiO2. (b) Theoretically calculated [811] and experimentally measured dispersion [12] of the nonlinear refractive index n2 for SiO2.

Fig. 3.
Fig. 3.

Contributions to the refractive index from the Kerr effect (solid red line), plasma formation (dashed blue line), and their sum (dotted–dashed green line) at the center of a 10 fs Gaussian pulse as a function of peak intensity for (a) SiO2, (b) Al2O3, (c) BaF2, and (d) LiF. The dotted and solid vertical lines indicate a plasma density of 1020cm3 and 1021cm3, respectively, marking the range in which damage is expected.

Equations (3)

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n2(ω)=cπ0β2(12(ω+Ω))Ω2ω2dΩ,
dρ(t)dt=kβkI(t)k+αρ(t)I(t)ρ(t)Trec,
Δn=n0+n02ρ/ρc,

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