Abstract

The evolutions of polarization and nonlinearities in an isotropic medium induced by anisotropy of third-order nonlinear susceptibility were studied experimentally and theoretically. The anisotropy of imaginary part of third-order susceptibility was verified to exist by the change of ellipticity of polarization ellipse in the isotropic nonlinear medium CS2. The changes of nonlinear refraction and nonlinear absorption depending upon the ellipticity of polarization ellipse are also presented. The numerical simulations based on two coupled nonlinear Schrödinger equations (NLSE) provide an excellent quantitative agreement with experimental results.

© 2008 Optical Society of America

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  1. P. D. Maker, R. W. Terhune, and C. M. Savage, "Intensity-dependent changes in the refractive index of liquids," Phys. Rev. Lett. 12, 507-509 (1964).
    [CrossRef]
  2. P. D. Maker and R. W. Terhune, "Study of optical effects due to an induced polarization third order in the electric field strength," Phys. Rev. 137, A801-818 (1965).
    [CrossRef]
  3. P. X. Nguyen and G. Rivoire, "Evolution of the polarization state of an intense electromagnetic field in a nonlinear medium," Opt. Acta. 25, 233-246 (1978).
    [CrossRef]
  4. P. X. Nguyen, J. L. Ferrier, J. Gazengel, and G. Rivoire, "Polarization of picosecond light pulses in nonlinear isotropic media," Opt. Commun. 46, 329-333 (1983).
    [CrossRef]
  5. A. J. van Wonderen, "Influence of transverse effect on self-induced polarization changes in an isotropic Kerr medium," J. Opt. Soc. Am. B 14, 1118-1130 (1997).
    [CrossRef]
  6. M. Lefkir and G. Rivoire, "Influence of transverse effects on measurement of third-order nonlinear susceptibility by self-induced polarization state changes," J. Opt. Soc. Am. B 14, 2856-2864 (1997).
    [CrossRef]
  7. M. V. Tratnik and J. E. Sipe, "Nonlinear polarization dynamics. I. The single-pulse equations," Phys. Rev. A 35, 2965-2975 (1987).
    [CrossRef] [PubMed]
  8. D. David, D. D. Holm, and M. V. Tratnik, "Hamiltonian chaos in nonlinear optical polarization dynamics," Phys. Rep. 187, 281-367 (1990).
    [CrossRef]
  9. A. L. Gaeta and R. W. Boyd, "Transverse instabilities in the polarizations and intensities of counterpropagating light waves," Phys. Rev. A 48, 1610-1624 (1993).
    [CrossRef] [PubMed]
  10. M. Delqué, G. Fanjoux, and T. Sylvestre, "Polarization dynamics of the fundamental vector soliton of isotropic Kerr media," Phys. Rev. E 75, 016611 (2007).
    [CrossRef]
  11. M. Delqué, T. Sylvestre, H. Maillotte, C. Cambournac, P. Kockaert, and M. Haelterman, "Experimental observation of the elliptically polarized fundamental vector soliton of isotropic Kerr media," Opt. Lett. 30, 3383-3385 (2005).
    [CrossRef]
  12. C. Cambournac, T. Sylvestre, H. Maillotte, B. Vanderlinden, P. Kockaert, Ph. Emplit, and M. Haelterman, "Symmetry-Breaking Instability of Multimode Vector Solitons," Phys. Rev. Lett. 89, 083901 (2002).
    [CrossRef] [PubMed]
  13. R. DeSalvo, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, "Z-scan measurements of anisotropy of nonlinear refraction and absorption in crystals," Opt. Lett. 18, 194-196 (1993).
    [CrossRef] [PubMed]
  14. Sean J. Wagner, J. Meier, A. S. Helmy, J. Stewart Aitchison, M. Sorel, and D. C. Hutchings, "Polarization-dependent nonlinear refraction and two-photon absorption in GaAs/AlAs superlattice waveguides below the half-bandgap," J. Opt. Soc. Am. B 24, 1557-1563 (2007).
    [CrossRef]
  15. Z. B. Liu, Y. L. Liu, B. Zhang, W. Y. Zhou, J. G. Tian, W. P. Zang, and C. P. Zhang, "Nonlinear absorption and optical limiting properties of carbon disulfide in short-wavelength region," J. Opt. Soc. Am. B 24, 1101-1104 (2007).
    [CrossRef]
  16. R. W. Boyd, Nonlinear Optics, second edition (Academic Press, San Diego, 2003).
  17. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, "Sensitive measurement of optical nonlinearities using a single beam," IEEE J. Quantum Electron 26, 760-169 (1990).
    [CrossRef]
  18. Z. B. Liu, X. Q. Yan, J. G. Tian, W. Y. Zhou, and W. P. Zang, "Nonlinear ellipse rotation modified Z-scan measurements of third-order nonlinear susceptibility tensor," Opt. Express 15, 13351-13359 (2007).
    [CrossRef] [PubMed]

2007 (4)

2005 (1)

2002 (1)

C. Cambournac, T. Sylvestre, H. Maillotte, B. Vanderlinden, P. Kockaert, Ph. Emplit, and M. Haelterman, "Symmetry-Breaking Instability of Multimode Vector Solitons," Phys. Rev. Lett. 89, 083901 (2002).
[CrossRef] [PubMed]

1997 (2)

1993 (2)

A. L. Gaeta and R. W. Boyd, "Transverse instabilities in the polarizations and intensities of counterpropagating light waves," Phys. Rev. A 48, 1610-1624 (1993).
[CrossRef] [PubMed]

R. DeSalvo, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, "Z-scan measurements of anisotropy of nonlinear refraction and absorption in crystals," Opt. Lett. 18, 194-196 (1993).
[CrossRef] [PubMed]

1990 (2)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, "Sensitive measurement of optical nonlinearities using a single beam," IEEE J. Quantum Electron 26, 760-169 (1990).
[CrossRef]

D. David, D. D. Holm, and M. V. Tratnik, "Hamiltonian chaos in nonlinear optical polarization dynamics," Phys. Rep. 187, 281-367 (1990).
[CrossRef]

1987 (1)

M. V. Tratnik and J. E. Sipe, "Nonlinear polarization dynamics. I. The single-pulse equations," Phys. Rev. A 35, 2965-2975 (1987).
[CrossRef] [PubMed]

1983 (1)

P. X. Nguyen, J. L. Ferrier, J. Gazengel, and G. Rivoire, "Polarization of picosecond light pulses in nonlinear isotropic media," Opt. Commun. 46, 329-333 (1983).
[CrossRef]

1978 (1)

P. X. Nguyen and G. Rivoire, "Evolution of the polarization state of an intense electromagnetic field in a nonlinear medium," Opt. Acta. 25, 233-246 (1978).
[CrossRef]

1965 (1)

P. D. Maker and R. W. Terhune, "Study of optical effects due to an induced polarization third order in the electric field strength," Phys. Rev. 137, A801-818 (1965).
[CrossRef]

1964 (1)

P. D. Maker, R. W. Terhune, and C. M. Savage, "Intensity-dependent changes in the refractive index of liquids," Phys. Rev. Lett. 12, 507-509 (1964).
[CrossRef]

Boyd, R. W.

A. L. Gaeta and R. W. Boyd, "Transverse instabilities in the polarizations and intensities of counterpropagating light waves," Phys. Rev. A 48, 1610-1624 (1993).
[CrossRef] [PubMed]

Cambournac, C.

M. Delqué, T. Sylvestre, H. Maillotte, C. Cambournac, P. Kockaert, and M. Haelterman, "Experimental observation of the elliptically polarized fundamental vector soliton of isotropic Kerr media," Opt. Lett. 30, 3383-3385 (2005).
[CrossRef]

C. Cambournac, T. Sylvestre, H. Maillotte, B. Vanderlinden, P. Kockaert, Ph. Emplit, and M. Haelterman, "Symmetry-Breaking Instability of Multimode Vector Solitons," Phys. Rev. Lett. 89, 083901 (2002).
[CrossRef] [PubMed]

David, D.

D. David, D. D. Holm, and M. V. Tratnik, "Hamiltonian chaos in nonlinear optical polarization dynamics," Phys. Rep. 187, 281-367 (1990).
[CrossRef]

Delqué, M.

DeSalvo, R.

Emplit, Ph.

C. Cambournac, T. Sylvestre, H. Maillotte, B. Vanderlinden, P. Kockaert, Ph. Emplit, and M. Haelterman, "Symmetry-Breaking Instability of Multimode Vector Solitons," Phys. Rev. Lett. 89, 083901 (2002).
[CrossRef] [PubMed]

Fanjoux, G.

M. Delqué, G. Fanjoux, and T. Sylvestre, "Polarization dynamics of the fundamental vector soliton of isotropic Kerr media," Phys. Rev. E 75, 016611 (2007).
[CrossRef]

Ferrier, J. L.

P. X. Nguyen, J. L. Ferrier, J. Gazengel, and G. Rivoire, "Polarization of picosecond light pulses in nonlinear isotropic media," Opt. Commun. 46, 329-333 (1983).
[CrossRef]

Gaeta, A. L.

A. L. Gaeta and R. W. Boyd, "Transverse instabilities in the polarizations and intensities of counterpropagating light waves," Phys. Rev. A 48, 1610-1624 (1993).
[CrossRef] [PubMed]

Gazengel, J.

P. X. Nguyen, J. L. Ferrier, J. Gazengel, and G. Rivoire, "Polarization of picosecond light pulses in nonlinear isotropic media," Opt. Commun. 46, 329-333 (1983).
[CrossRef]

Haelterman, M.

M. Delqué, T. Sylvestre, H. Maillotte, C. Cambournac, P. Kockaert, and M. Haelterman, "Experimental observation of the elliptically polarized fundamental vector soliton of isotropic Kerr media," Opt. Lett. 30, 3383-3385 (2005).
[CrossRef]

C. Cambournac, T. Sylvestre, H. Maillotte, B. Vanderlinden, P. Kockaert, Ph. Emplit, and M. Haelterman, "Symmetry-Breaking Instability of Multimode Vector Solitons," Phys. Rev. Lett. 89, 083901 (2002).
[CrossRef] [PubMed]

Hagan, D. J.

R. DeSalvo, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, "Z-scan measurements of anisotropy of nonlinear refraction and absorption in crystals," Opt. Lett. 18, 194-196 (1993).
[CrossRef] [PubMed]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, "Sensitive measurement of optical nonlinearities using a single beam," IEEE J. Quantum Electron 26, 760-169 (1990).
[CrossRef]

Holm, D. D.

D. David, D. D. Holm, and M. V. Tratnik, "Hamiltonian chaos in nonlinear optical polarization dynamics," Phys. Rep. 187, 281-367 (1990).
[CrossRef]

Kockaert, P.

M. Delqué, T. Sylvestre, H. Maillotte, C. Cambournac, P. Kockaert, and M. Haelterman, "Experimental observation of the elliptically polarized fundamental vector soliton of isotropic Kerr media," Opt. Lett. 30, 3383-3385 (2005).
[CrossRef]

C. Cambournac, T. Sylvestre, H. Maillotte, B. Vanderlinden, P. Kockaert, Ph. Emplit, and M. Haelterman, "Symmetry-Breaking Instability of Multimode Vector Solitons," Phys. Rev. Lett. 89, 083901 (2002).
[CrossRef] [PubMed]

Lefkir, M.

Liu, Y. L.

Liu, Z. B.

Maillotte, H.

M. Delqué, T. Sylvestre, H. Maillotte, C. Cambournac, P. Kockaert, and M. Haelterman, "Experimental observation of the elliptically polarized fundamental vector soliton of isotropic Kerr media," Opt. Lett. 30, 3383-3385 (2005).
[CrossRef]

C. Cambournac, T. Sylvestre, H. Maillotte, B. Vanderlinden, P. Kockaert, Ph. Emplit, and M. Haelterman, "Symmetry-Breaking Instability of Multimode Vector Solitons," Phys. Rev. Lett. 89, 083901 (2002).
[CrossRef] [PubMed]

Maker, P. D.

P. D. Maker and R. W. Terhune, "Study of optical effects due to an induced polarization third order in the electric field strength," Phys. Rev. 137, A801-818 (1965).
[CrossRef]

P. D. Maker, R. W. Terhune, and C. M. Savage, "Intensity-dependent changes in the refractive index of liquids," Phys. Rev. Lett. 12, 507-509 (1964).
[CrossRef]

Nguyen, P. X.

P. X. Nguyen, J. L. Ferrier, J. Gazengel, and G. Rivoire, "Polarization of picosecond light pulses in nonlinear isotropic media," Opt. Commun. 46, 329-333 (1983).
[CrossRef]

P. X. Nguyen and G. Rivoire, "Evolution of the polarization state of an intense electromagnetic field in a nonlinear medium," Opt. Acta. 25, 233-246 (1978).
[CrossRef]

Rivoire, G.

M. Lefkir and G. Rivoire, "Influence of transverse effects on measurement of third-order nonlinear susceptibility by self-induced polarization state changes," J. Opt. Soc. Am. B 14, 2856-2864 (1997).
[CrossRef]

P. X. Nguyen, J. L. Ferrier, J. Gazengel, and G. Rivoire, "Polarization of picosecond light pulses in nonlinear isotropic media," Opt. Commun. 46, 329-333 (1983).
[CrossRef]

P. X. Nguyen and G. Rivoire, "Evolution of the polarization state of an intense electromagnetic field in a nonlinear medium," Opt. Acta. 25, 233-246 (1978).
[CrossRef]

Said, A. A.

R. DeSalvo, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, "Z-scan measurements of anisotropy of nonlinear refraction and absorption in crystals," Opt. Lett. 18, 194-196 (1993).
[CrossRef] [PubMed]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, "Sensitive measurement of optical nonlinearities using a single beam," IEEE J. Quantum Electron 26, 760-169 (1990).
[CrossRef]

Savage, C. M.

P. D. Maker, R. W. Terhune, and C. M. Savage, "Intensity-dependent changes in the refractive index of liquids," Phys. Rev. Lett. 12, 507-509 (1964).
[CrossRef]

Sean,

Sheik-Bahae, M.

R. DeSalvo, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, "Z-scan measurements of anisotropy of nonlinear refraction and absorption in crystals," Opt. Lett. 18, 194-196 (1993).
[CrossRef] [PubMed]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, "Sensitive measurement of optical nonlinearities using a single beam," IEEE J. Quantum Electron 26, 760-169 (1990).
[CrossRef]

Sipe, J. E.

M. V. Tratnik and J. E. Sipe, "Nonlinear polarization dynamics. I. The single-pulse equations," Phys. Rev. A 35, 2965-2975 (1987).
[CrossRef] [PubMed]

Sylvestre, T.

M. Delqué, G. Fanjoux, and T. Sylvestre, "Polarization dynamics of the fundamental vector soliton of isotropic Kerr media," Phys. Rev. E 75, 016611 (2007).
[CrossRef]

M. Delqué, T. Sylvestre, H. Maillotte, C. Cambournac, P. Kockaert, and M. Haelterman, "Experimental observation of the elliptically polarized fundamental vector soliton of isotropic Kerr media," Opt. Lett. 30, 3383-3385 (2005).
[CrossRef]

C. Cambournac, T. Sylvestre, H. Maillotte, B. Vanderlinden, P. Kockaert, Ph. Emplit, and M. Haelterman, "Symmetry-Breaking Instability of Multimode Vector Solitons," Phys. Rev. Lett. 89, 083901 (2002).
[CrossRef] [PubMed]

Terhune, R. W.

P. D. Maker and R. W. Terhune, "Study of optical effects due to an induced polarization third order in the electric field strength," Phys. Rev. 137, A801-818 (1965).
[CrossRef]

P. D. Maker, R. W. Terhune, and C. M. Savage, "Intensity-dependent changes in the refractive index of liquids," Phys. Rev. Lett. 12, 507-509 (1964).
[CrossRef]

Tian, J. G.

Tratnik, M. V.

D. David, D. D. Holm, and M. V. Tratnik, "Hamiltonian chaos in nonlinear optical polarization dynamics," Phys. Rep. 187, 281-367 (1990).
[CrossRef]

M. V. Tratnik and J. E. Sipe, "Nonlinear polarization dynamics. I. The single-pulse equations," Phys. Rev. A 35, 2965-2975 (1987).
[CrossRef] [PubMed]

Van Stryland, E. W.

R. DeSalvo, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, "Z-scan measurements of anisotropy of nonlinear refraction and absorption in crystals," Opt. Lett. 18, 194-196 (1993).
[CrossRef] [PubMed]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, "Sensitive measurement of optical nonlinearities using a single beam," IEEE J. Quantum Electron 26, 760-169 (1990).
[CrossRef]

van Wonderen, A. J.

Vanderlinden, B.

C. Cambournac, T. Sylvestre, H. Maillotte, B. Vanderlinden, P. Kockaert, Ph. Emplit, and M. Haelterman, "Symmetry-Breaking Instability of Multimode Vector Solitons," Phys. Rev. Lett. 89, 083901 (2002).
[CrossRef] [PubMed]

Wei, T. H.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, "Sensitive measurement of optical nonlinearities using a single beam," IEEE J. Quantum Electron 26, 760-169 (1990).
[CrossRef]

Yan, X. Q.

Zang, W. P.

Zhang, B.

Zhang, C. P.

Zhou, W. Y.

IEEE J. Quantum Electron (1)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, "Sensitive measurement of optical nonlinearities using a single beam," IEEE J. Quantum Electron 26, 760-169 (1990).
[CrossRef]

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

Opt. Acta. (1)

P. X. Nguyen and G. Rivoire, "Evolution of the polarization state of an intense electromagnetic field in a nonlinear medium," Opt. Acta. 25, 233-246 (1978).
[CrossRef]

Opt. Commun. (1)

P. X. Nguyen, J. L. Ferrier, J. Gazengel, and G. Rivoire, "Polarization of picosecond light pulses in nonlinear isotropic media," Opt. Commun. 46, 329-333 (1983).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rep. (1)

D. David, D. D. Holm, and M. V. Tratnik, "Hamiltonian chaos in nonlinear optical polarization dynamics," Phys. Rep. 187, 281-367 (1990).
[CrossRef]

Phys. Rev. (1)

P. D. Maker and R. W. Terhune, "Study of optical effects due to an induced polarization third order in the electric field strength," Phys. Rev. 137, A801-818 (1965).
[CrossRef]

Phys. Rev. A (2)

A. L. Gaeta and R. W. Boyd, "Transverse instabilities in the polarizations and intensities of counterpropagating light waves," Phys. Rev. A 48, 1610-1624 (1993).
[CrossRef] [PubMed]

M. V. Tratnik and J. E. Sipe, "Nonlinear polarization dynamics. I. The single-pulse equations," Phys. Rev. A 35, 2965-2975 (1987).
[CrossRef] [PubMed]

Phys. Rev. E (1)

M. Delqué, G. Fanjoux, and T. Sylvestre, "Polarization dynamics of the fundamental vector soliton of isotropic Kerr media," Phys. Rev. E 75, 016611 (2007).
[CrossRef]

Phys. Rev. Lett. (2)

P. D. Maker, R. W. Terhune, and C. M. Savage, "Intensity-dependent changes in the refractive index of liquids," Phys. Rev. Lett. 12, 507-509 (1964).
[CrossRef]

C. Cambournac, T. Sylvestre, H. Maillotte, B. Vanderlinden, P. Kockaert, Ph. Emplit, and M. Haelterman, "Symmetry-Breaking Instability of Multimode Vector Solitons," Phys. Rev. Lett. 89, 083901 (2002).
[CrossRef] [PubMed]

Other (1)

R. W. Boyd, Nonlinear Optics, second edition (Academic Press, San Diego, 2003).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic of experimental Setup. G1 and G2 are Glan prisms, D1 and D2 are detectors.

Fig. 2.
Fig. 2.

Experimental and theoretical results: (a), (b), (c): transmittance for nonlinear output (open diamonds) and linear output (open circles) at 440 nm, 470 nm, and 532 nm, respectively. (d), (e), (f): the ellipticity e (open circles) and the rotation angle θ (open squares) as a function of input intensity I 0 at 440 nm, 470 nm and 532 nm. The solid lines are theoretical simulations with Re(A)=13, 8, 3.5×10-20 m2/V2, Im(A)=7, 2.5, 0×10-20 m2/V2, Re(B)=27, 20, 14×10-20 m2/V2, and Im(B)=19, 6, 0×10-20 m2/V2 for 440nm, 470nm, and 532nm, respectively.

Fig. 3.
Fig. 3.

Z-scan curves of nonlinear refraction and nonlinear absorption in the cases of linearly, elliptical and circular polarized input laser at 440nm. The solid lines are the theoretical fits with n 2lin =13.5×10-14 cm2/W, n 2ell =8.4×10-14 cm2/W, n 2cir =6.1×10-14 cm2/W, and βlin =17.4×10-9 cm/W, β ell =9.5×10-9 cm/W, β cir =6.5×10-9 cm/W.

Fig. 4.
Fig. 4.

The n 2 (open squares) and β (open circles) as a function of e at 440nm, 470nm, and 532nm. The solid lines are the theoretical results.

Equations (7)

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

1 r r ( r E + r ) 2 i k E + z + 4 π k 2 n 0 2 [ A E + 2 + ( A + B ) E 2 ] E + = 0 ,
1 r r ( r E r ) 2 i k E z + 4 π k 2 n 0 2 [ A E 2 + ( A + B ) E + 2 ] E = 0 ,
χ ± ( NL ) = A E ± 2 + ( A + B ) E 2 ,
Δ n ± = 2 π n 0 Re [ A E ± 2 + ( A + B ) E 2 ] ,
Δ α ± = 4 π k n 0 Im [ A E ± 2 + ( A + B ) E 2 ] .
n 2 ell = ( 1 q 2 ) n 2 cir + 2 qn 2 lin 1 + q 2 ,
β ell = ( 1 q 2 ) β cir + 2 q β lin 1 + q 2 ,

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