Third-order nonlinear susceptibility tensor elements of CS<sub>2</sub> at femtosecond time scale

doi:10.1364/OE.19.005559

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Third-order nonlinear susceptibility tensor elements of CS₂ at femtosecond time scale

Xiao-Qing Yan, Xiao-Liang Zhang, Shuo Shi, Zhi-Bo Liu, and Jian-Guo Tian »View Author Affiliations

Optics Express, Vol. 19, Issue 6, pp. 5559-5564 (2011)
http://dx.doi.org/10.1364/OE.19.005559

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– Abstract
1. Introduction
2. Experiments and results
3. Conclusions
– References and links

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Abstract

The real parts of third-order nonlinear susceptibility components of CS₂ are determined by polarized lights Z-Scan technique at 800 nm, and imaginary part is verified to be negligible. The contributions to susceptibility components from electron and nuclear are separated. These susceptibility values can be used as the reference values for third-order nonlinear susceptibility measurements by degenerate four-wave-mixing, optical Kerr gate/optical Kerr effect, optical heterodyne detection of optical Kerr effect, the ellipse rotation and so on.

1. Introduction

The third-order nonlinear optical materials have been receiving considerable interests because of their potential applications in optical communication, data storage, optical computing, optical switching and optical modulation. These materials should have large optical nonlinearities and fast response, especially in the femtosecond (fs) time domain [1

Z. B. Cai, J. R. Gao, X. N. Li, and B. Xiang, “Synthesis and characterization of symmetrical benzodifuranone compounds with femtosecond time-resolved degenerate four-wave mixing technique,” Opt. Commun. 272(2), 503–508 (2007). [CrossRef]

–14

Q. M. Liu, B. Lu, X. J. Zhao, F. X. Gan, J. Mi, and S. X. Qian, “Ultrafast non-linear optical properties of Ge₂₀As₂₅Se₅₅ chalcogenide films,” Opt. Commun. 258(1), 72–77 (2006). [CrossRef]

]. To find proper nonlinear optical materials for use in photonic devices, a wide variety of novel materials, including semiconductors, polymers, nanomaterials, organometallic compounds and special glasses, have been studied for their third-order optical nonlinearities by femtosecond pulsed laser [1

–15

R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker Inc, New York, 1996) Chapter 7.

]. And a number of approaches, including the Z-scan [16

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(4), 760–769 (1990). [CrossRef]

], degenerate four-wave-mixing (DFWM) [1

–5

H. B. Liao, R. F. Xiao, J. S. Fu, H. Wang, K. S. Wong, and G. K. L. Wong, “Origin of third-order optical nonlinearity in Au:SiO(2) composite films on femtosecond and picosecond time scales,” Opt. Lett. 23(5), 388–390 (1998). [CrossRef]

], optical Kerr gate (OKG) [6

H. L. Yang, X. Q. Wang, Q. Ren, G. H. Zhang, X. B. Sun, L. Feng, S. F. Wang, and Z. W. Wang, “Study on the third-order nonlinear optical properties of bis(tetrabutylammonium)bis(1,3-dithiole-2-thione- 4,5-dithiolato)cadium,” Opt. Commun. 256(4-6), 256–260 (2005). [CrossRef]

–10

Z. W. Wang, C. L. Liu, H. Xiang, Z. Li, Q. H. Gong, Y. J. Qin, Z. X. Guo, and D. B. Zhu, “Ultrafast third-order nonlinear optical response of two soluble multi-wall carbon nanotubes,” J. Phys. D Appl. Phys. 37(7), 1079–1082 (2004). [CrossRef]

]/optical Kerr effect (OKE) [11

Y. Liu, D. Li, R. Y. Zhu, G. J. You, S. X. Qian, Y. Yang, and J. L. Shi, “Third-order nonlinear optical response of Au-core CdS-shell composite nanoparticles embedded in BaTiO₃ thin films,” Appl. Phys. B 76(4), 435–439 (2003). [CrossRef]

,12

Q. Liu, C. Gao, H. Zhou, B. Lu, X. He, Q. Shixiong, and X. Zhao, “Ultrafast third-order optical non-linearity of 0.56GeS₂-0.24Ga₂S₃-0.2KX(X=Cl, Br, I) chalcohalide glasses by femtosecond optical Kerr effect,” Opt. Mater. 32(1), 26–29 (2009). [CrossRef]

] and optical heterodyne detection of optical Kerr effect (OHD-OKE) techniques [13

Q. M. Liu, X. J. Zhao, F. X. Gan, J. Mi, and S. X. Qian, “Femtosecond optical Kerr effect study of Ge₁₀As₄₀S₃₀Se₂₀ film,” Solid State Commun. 134(8), 513–517 (2005). [CrossRef]

–15

R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker Inc, New York, 1996) Chapter 7.

], are widely being used to characterize the third-order optical nonlinearities of these novel materials. In the latter three methods, for simplifying the measurements the CS₂ is usually chosen as a reference and assumed no imaginary part for susceptibility tensor elements. However, these methods relate to the modulus of

χ_{i j k l}^{(3)}

of the reference, (within the references [1

–14

| χ_{x x x x}^{(3)} |

for DFWM,

| χ_{x y y x}^{(3)} + χ_{x y x y}^{(3)} |

for OKG/OKE and OHD-OKE) [1

–15

R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker Inc, New York, 1996) Chapter 7.

]. Recently, several linearly polarized light open-aperture (OA) Z-scan experiments were carried out in CS₂ around 800 nm [17

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “nonlinear refraction in CS₂ ,” Appl. Phys. B 78(3-4), 433–438 (2004). [CrossRef]

–21

B. Gu, W. Ji, and X. Q. Huang, “Analytical expression for femtosecond-pulsed Z scans on instantaneous nonlinearity,” Appl. Opt. 47(9), 1187–1192 (2008). [CrossRef] [PubMed]

]. In these measurements there was obvious nonlinear absorption in CS₂, which means the no-imaginary assumption is challenged and the values from DFWM, OKG/OKE and OHD-OKE methods may be not reliable enough. Recently, the signal of the linearly polarized light OA Z-scan experiment was verified to arise mainly from nonlinear scattering, and the nonlinear absorption (or

Im (χ_{x x x x}^{(3)})

) of linear polarized light is negligible around 800 nm [22

X. Q. Yan, Z. B. Liu, S. Shi, W. Y. Zhou, and J. G. Tian, “Analysis on the origin of the ultrafast optical nonlinearity of carbon disulfide around 800 nm,” Opt. Express 18(25), 26169–26174 (2010). [CrossRef] [PubMed]

]. But we could not conclude that

Im (χ_{x y y x}^{(3)})

Im (χ_{x y x y}^{(3)})

is negligible. So, it is better to check whether the two imaginary parts are negligible.

As listed in Table 1 , the reference values of CS₂ are not identical for each method. One reason for the non-uniform reference values is the lack of report on the third-order susceptibility tensor elements at fs time scale. To make that the nonlinearities values measured by the three methods could be explicitly compared among novel materials, firstly, the reference value should be identical for every method. So, it is very necessary to know fully the real and imaginary parts of susceptibility tensor elements of CS₂ before determining the reference values for each method. Minoshima et al have given the value of

Re (χ_{z z z z}^{(3)})

at 100-fs pulses [23

K. Minoshima, M. Taiji, and T. Kobayashi, “Femtosecond time-resolved interferometry for the determination of complex nonlinear susceptibility,” Opt. Lett. 16(21), 1683–1685 (1991). [CrossRef] [PubMed]

]. However we cannot obtain the accurate values of real parts of other tensor components by using the relationship of

Re (χ_{x y y x}^{(3)}) / Re (χ_{x y x y}^{(3)}) = 1

as done by some researchers [11

,13

Q. M. Liu, X. J. Zhao, F. X. Gan, J. Mi, and S. X. Qian, “Femtosecond optical Kerr effect study of Ge₁₀As₄₀S₃₀Se₂₀ film,” Solid State Commun. 134(8), 513–517 (2005). [CrossRef]

,14

], because the Kleinman symmetry rule is no longer valid [24

R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic Press, San Diego, 2003) Chapter 1.

,25

I. J. Bigio and J. F. Ward, “Measurement of the hyperpolarizability ratio X_{y y y y}(-2ω;0,ω,ω)/X_{y y x x}(-2ω;0,ω,ω) for the inert gases,” Phys. Rev. A 9(1), 35–39 (1974). [CrossRef]

]. At this time scale of most commercial fs laser used for studying novel materials, there are fast non-instantaneous nuclear contribution (

Re (χ_{x y y x}^{(3), n u c l}) / Re (χ_{x y x y}^{(3), n u c l}) = 6

[26

J. Burgin, C. Guillon, and P. Langot, “Femtosecond investigation of the non-instantaneous third-order nonlinear suceptibility in liquids and glasses,” Appl. Phys. Lett. 87(21), 211916 (2005). [CrossRef]

,27

P. Langot, S. Montant, and E. Freysz, “Measurement of non-instantaneous contribution to the χ⁽³⁾ in different liquids using femtosecond chirped pulses,” Opt. Commun. 176(4-6), 459–472 (2000). [CrossRef]

]) as well as nonresonant electron contribution (

Re (χ_{x y y x}^{(3), e l e c}) / Re (χ_{x y x y}^{(3), e l e c}) = 1

[25

I. J. Bigio and J. F. Ward, “Measurement of the hyperpolarizability ratio X_{y y y y}(-2ω;0,ω,ω)/X_{y y x x}(-2ω;0,ω,ω) for the inert gases,” Phys. Rev. A 9(1), 35–39 (1974). [CrossRef]

,26

], ) to the nonlinear susceptibility of CS₂, which means that the ratio

Re (χ_{x y y x}^{(3)}) / Re (χ_{x y x y}^{(3)})

is between 1 and 6 [26

–29

C. Kalpouzos, W. T. Lotshaw, D. McMorrow, and G. A. Kenney-Wallace, “Femtosecond laser-induced Kerr responses in liquid carbon disulfide,” J. Phys. Chem. 91(8), 2028–2030 (1987). [CrossRef]

]. To our best knowledge, the research on the CS₂ third-order nonlinear susceptibility tensor elements at fs time scale is scarce although the nonlinear refractive index, nonlinear absorption coefficient or single tensor element has been widely studied [17

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “nonlinear refraction in CS₂ ,” Appl. Phys. B 78(3-4), 433–438 (2004). [CrossRef]

–23

]. Thus, to accomplish the measurement of susceptibility components of CS₂ and supply proper reference values for the three methods, it is better to study systematically the real and imaginary parts of third-order nonlinear susceptibility tensor elements of CS₂ at the fs time scale.

Table 1 Referenced Value of CS₂ Used in Literature

Methods	Related susceptibility components of CS₂	Referenced value of CS₂ used ( × 10⁻¹³ esu)	references
DFWM	$\| χ_{x x x x}^{(3)} \|$	0.67	[1 Z. B. Cai, J. R. Gao, X. N. Li, and B. Xiang, “Synthesis and characterization of symmetrical benzodifuranone compounds with femtosecond time-resolved degenerate four-wave mixing technique,” Opt. Commun. 272(2), 503–508 (2007). [CrossRef] ]
		1	[2 Z. Y. Li, Z. H. Chen, S. Xu, L. H. Niu, Z. Zhang, F. S. Zhang, and K. Kasatani, “Off-resonant third-order optical nonlinearities of novel diarylethene–phthalocyanine dyads,” Chem. Phys. Lett. 447(1-3), 110–114 (2007). [CrossRef] ,3 G. Heng-Qun and W. Qi-Ming, “Nonlinear Optical Response of nc-Si-SiO₂ Films Studied with Femtosecond Four-Wave Mixing Technique,” Chin. Phys. Lett. 23(11), 2989–2992 (2006). [CrossRef] ]
		5	[4 H. B. Liao, R. F. Xiao, H. Wang, K. S. Wong, and G. K. L. Wong, “Large third-order optical nonlinearity in Au:TiO2 composite films measured on a femtosecond time scale,” Appl. Phys. Lett. 72(15), 1817 (1998). [CrossRef] ,5 H. B. Liao, R. F. Xiao, J. S. Fu, H. Wang, K. S. Wong, and G. K. L. Wong, “Origin of third-order optical nonlinearity in Au:SiO(2) composite films on femtosecond and picosecond time scales,” Opt. Lett. 23(5), 388–390 (1998). [CrossRef] ]
OKG/OKE	$\| χ_{x y y x}^{(3)} + χ_{x y x y}^{(3)} \|$	0.67	[11 Y. Liu, D. Li, R. Y. Zhu, G. J. You, S. X. Qian, Y. Yang, and J. L. Shi, “Third-order nonlinear optical response of Au-core CdS-shell composite nanoparticles embedded in BaTiO₃ thin films,” Appl. Phys. B 76(4), 435–439 (2003). [CrossRef] ]
		1	[6 H. L. Yang, X. Q. Wang, Q. Ren, G. H. Zhang, X. B. Sun, L. Feng, S. F. Wang, and Z. W. Wang, “Study on the third-order nonlinear optical properties of bis(tetrabutylammonium)bis(1,3-dithiole-2-thione- 4,5-dithiolato)cadium,” Opt. Commun. 256(4-6), 256–260 (2005). [CrossRef] ,8 S. F. Wang, W. T. Huang, H. Yang, Q. H. Gong, Z. J. Shi, X. H. Zhou, D. Qiang, and Z. N. Gu, “Large and ultrafast third-order optical non-linearity of single-wall carbon nanotubes at 820 nm,” Chem. Phys. Lett. 320(5-6), 411–414 (2000). [CrossRef] ,10 Z. W. Wang, C. L. Liu, H. Xiang, Z. Li, Q. H. Gong, Y. J. Qin, Z. X. Guo, and D. B. Zhu, “Ultrafast third-order nonlinear optical response of two soluble multi-wall carbon nanotubes,” J. Phys. D Appl. Phys. 37(7), 1079–1082 (2004). [CrossRef] ,12 Q. Liu, C. Gao, H. Zhou, B. Lu, X. He, Q. Shixiong, and X. Zhao, “Ultrafast third-order optical non-linearity of 0.56GeS₂-0.24Ga₂S₃-0.2KX(X=Cl, Br, I) chalcohalide glasses by femtosecond optical Kerr effect,” Opt. Mater. 32(1), 26–29 (2009). [CrossRef] ]
		1.3	[9 S. S. Chu, F. M. Li, H. Z. Tao, H. Yang, S. F. Wang, C. G. Lin, X. J. Zhao, and Q. H. Gong, “SbS₃ enhanced ultrafast third-order optical nonlinearities of Ge-S chalcogenide glasses at 820 nm,” Opt. Mater. 31(2), 193–195 (2008). [CrossRef] ]
		10	[7 L. Tamayo-Rivera, R. Rangel-Rojo, Y. Mao, and W. H. Watson, “Ultra fast third-order non-linear response of amino-triazole donor-acceptor derivatives by optical Kerr effect,” Opt. Commun. 281(20), 5239–5243 (2008). [CrossRef] ]
OHD-OKE	$\| χ_{x y y x}^{(3)} + χ_{x y x y}^{(3)} \|$	0.67	[13 Q. M. Liu, X. J. Zhao, F. X. Gan, J. Mi, and S. X. Qian, “Femtosecond optical Kerr effect study of Ge₁₀As₄₀S₃₀Se₂₀ film,” Solid State Commun. 134(8), 513–517 (2005). [CrossRef] ,14 Q. M. Liu, B. Lu, X. J. Zhao, F. X. Gan, J. Mi, and S. X. Qian, “Ultrafast non-linear optical properties of Ge₂₀As₂₅Se₅₅ chalcogenide films,” Opt. Commun. 258(1), 72–77 (2006). [CrossRef] ]

The well-known Z-scan method has been widely used to measure the nonlinear refractive index and nonlinear absorption coefficient [16

]. Krauss et al showed that the independent components of χ⁽³⁾ can be specified in Z-scan method for isotropic medium by using both linearly and circularly polarized lights [30

T. D. Krauss, J. K. Ranka, F. W. Wise, and A. L. Gaeta, “Measurements of the tensor properties of third-order nonlinearities in wide-gap semiconductors,” Opt. Lett. 20(10), 1110–1112 (1995). [CrossRef] [PubMed]

In this work, we report on the values of real parts of susceptibility tensor elements of CS₂ determined by polarized lights Z-scan method with common fs laser pulses (λ = 800 nm, τ_FWHM = 125 fs) [1

–14

], and check whether the imaginary parts are negligible. The motivations of this work are both to supplement the values of CS₂ susceptibility tensor elements and to provide the reference values for DFWM, OKG/OKE, OHD-OKE and the ellipse rotation [15

R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker Inc, New York, 1996) Chapter 7.

] measurements.

2. Experiments and results

In our experiments, fs laser pulses at the wavelength of 800 nm with the duration of 120-fs (FWHM) were generated from a regenerated amplifier (mode-locked Ti: sapphire laser, Spitfire pro, Spectra Physics). The repetition rate was set to be 1 KHz. The details of the polarized fs pulses Z-scan experimental setup are described in Fig. 1 [31

X. Q. Yan, Z. B. Liu, X. L. Zhang, W. Y. Zhou, and J. G. Tian, “Polarization dependence of Z-scan measurement: theory and experiment,” Opt. Express 17(8), 6397–6406 (2009). [CrossRef] [PubMed]

]. A spatial filter was placed before the setup to produce a near Gaussian spatial distributed beam, which was confirmed by a CCD camera (L230, LBA-USB) [22

]. The beam was focused using a 250 mm focal-length lens preceded by a polarizer-waveplate (λ/4) combination to allow for a continuous change in its polarization state. After passing the polarizer-waveplate combination, the pulse width was about 125 fs. The beam waist radius w₀ of the focused laser beam was measured to be 33 ± 2 μm. The elliptically polarized light was produced by orienting the slow axis of the waveplate an angle (φ) 25 degrees to the polarizer [31

X. Q. Yan, Z. B. Liu, X. L. Zhang, W. Y. Zhou, and J. G. Tian, “Polarization dependence of Z-scan measurement: theory and experiment,” Opt. Express 17(8), 6397–6406 (2009). [CrossRef] [PubMed]

]. The CS₂ sample was filled in a 1-mm thick quartz cell. The measurement system was calibrated with ZnSe (OA Z-Scan [32

T. D. Krauss and F. W. Wise, “Femtosecond measurement of nonlinear absorption and refraction in CdS, ZnSe, and ZnS,” Appl. Phys. Lett. 65(14), 1739 (1994). [CrossRef]

]) and toluene (CA Z-scan [20

S. Couris, M. Renard, O. Faucher, B. Lavorel, R. Chaux, E. Koudoumas, and X. Michaut, “An experimental investigation of the nonlinear refractive index (n ₂) of carbon disulfide and toluene by spectral shearing interferometry and z-scan techniques,” Chem. Phys. Lett. 369(3-4), 318–324 (2003). [CrossRef]

]).

Fig. 1 Scheme of polarized lights Z-scan measurement. CA: with an aperture before detector 2; OA: with lens 2 before detector 2.

The real parts

The on-axis peak intensity I ₀ for closed-aperture (CA) Z-scan measurements was set to be 33-101 GW/cm². The normalized transmittance traces for different polarized lights at I ₀ = 55 GW/cm² are shown in Fig. 2(a) . Under this intensity, there was no observable nonlinear refraction signal from cell for these three type polarized lights in our measurements.

Fig. 2 (a) CA Z-scan traces of different polarized lights and theoretical fitting curves at 55 GW/cm². (b) The dependence of n₂ on I ₀ and polarization state.

From the figure we find the nonlinear refractive index decreases with ellipticity (0 for linearly polarized light, 0.4663 for elliptically polarized light and 1 for circularly polarized light). From the fittings of these experimental data the nonlinear refractive index n ₂ can be obtained for all polarized lights and listed in the inset of the figure [31

X. Q. Yan, Z. B. Liu, X. L. Zhang, W. Y. Zhou, and J. G. Tian, “Polarization dependence of Z-scan measurement: theory and experiment,” Opt. Express 17(8), 6397–6406 (2009). [CrossRef] [PubMed]

]. Furthermore, the values of

Re (χ_{x x x x}^{(3)})

and

Re (χ_{x y x y}^{(3)})

could be calculated from linearly and circularly polarized cases, respectively. Owing to

χ_{x x x x}^{(3)} = 2 χ_{x y x y}^{(3)} + χ_{x y y x}^{(3)}

for isotropic medium, the value of

Re (χ_{x y y x}^{(3)})

could be determined based on the values of

Re (χ_{x x x x}^{(3)})

and

Re (χ_{x y x y}^{(3)})

. The ratio of

Re (χ_{x y y x}^{(3)})

Re (χ_{x y x y}^{(3)})

is about 2.1, which is consistent with Burgin’s result [26

]. The n _2,lin value agrees well with others’ [17

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “nonlinear refraction in CS₂ ,” Appl. Phys. B 78(3-4), 433–438 (2004). [CrossRef]

–21

B. Gu, W. Ji, and X. Q. Huang, “Analytical expression for femtosecond-pulsed Z scans on instantaneous nonlinearity,” Appl. Opt. 47(9), 1187–1192 (2008). [CrossRef] [PubMed]

], and the value of

Re (χ_{x x x x}^{(3)})

is in good agreement with Gong and Minoshima’s results [10

,23

The nonlinear refractive indexes were also measured at other intensities. The dependence of nonlinear refractive index on intensity and polarization state is shown in Fig. 2(b). The lines are constant fittings, thus, there is no higher-order nonlinearity in the intensity region. By combining the constant fitting results of linearly and circularly polarized cases, the values of

Re (χ_{x y x y}^{(3)})

and

Re (χ_{x y y x}^{(3)})

were determined and listed in Table 2 . The ratio

Re (χ_{x y y x}^{(3)}) / Re (χ_{x y x y}^{(3)})

is about 1.8. So, there is fast non-instantaneous nuclear contribution at the time scale [26

–29

C. Kalpouzos, W. T. Lotshaw, D. McMorrow, and G. A. Kenney-Wallace, “Femtosecond laser-induced Kerr responses in liquid carbon disulfide,” J. Phys. Chem. 91(8), 2028–2030 (1987). [CrossRef]

], and it is unsuitable to calculate the real part value of other components from

Re (χ_{x x x x}^{(3)})

by using the Kleinman approximation. Furthermore, the values of the real parts of susceptibility components from different contributions can be separated through the values of

Re (χ_{x y x y}^{(3)})

and

Re (χ_{x y y x}^{(3)})

because the ratio

Re (χ_{x y y x}^{(3)}) / Re (χ_{x y x y}^{(3)})

is different for electronic and nuclear contributions. The results are listed in Table 3 . These values of the real parts are relatively independent of wavelength over the visible and near infrared region [17

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “nonlinear refraction in CS₂ ,” Appl. Phys. B 78(3-4), 433–438 (2004). [CrossRef]

,19

R. A. Ganeev, A. I. Ryasnyanskiĭ, and H. Kuroda, “Nonlinear optical characteristics of carbon disulfide,” Opt. Spectrosc. 100(1), 108–118 (2006). [CrossRef]

]. When the pulse width is less than 1 ps, these values increase little with pulse width (about 20% from 110 fs to 475 fs) due to the small increase of nuclear contribution [17

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “nonlinear refraction in CS₂ ,” Appl. Phys. B 78(3-4), 433–438 (2004). [CrossRef]

,26

Table 2 Values of Third-order Nonlinear Susceptibility Tensor Elements From Constant Fittings in Fig. 2(b)

Polarization	n ₂ ( × 10-15 cm2/W)	$Re (χ_{x y x y}^{(3)})$	$Re (χ_{x y y x}^{(3)})$	$Re (χ_{x x x x}^{(3)})$	$\frac{Re (χ_{x y y x}^{(3)})}{Re (χ_{x y x y}^{(3)})}$
Linearly	2.9 ± 0.2	(2.6 ± 0.2) × 10⁻¹⁴ esu	(4.6 ± 0.8) × 10⁻¹⁴ esu	(9.8 ± 0.7) × 10⁻¹⁴ esu	1.8 ± 0.3
Circularly	1.5 ± 0.1	(2.6 ± 0.2) × 10⁻¹⁴ esu	(4.6 ± 0.8) × 10⁻¹⁴ esu	(9.8 ± 0.7) × 10⁻¹⁴ esu	1.8 ± 0.3

Table 3 Contribution of Nonresonant Electron and Fast Non-instantaneous Nuclear to Real Part of Susceptibility Tensor Elements

Electron contribution (×10^-14 esu)			Nuclear contribution (×10^-14 esu)
$Re (χ_{x y x y}^{(3), e l e c}) = Re (χ_{x y y x}^{(3), e l e c})$	$Re (χ_{x x x x}^{(3), e l e c})$		$Re (χ_{x y x y}^{(3), n u c l})$	$Re (χ_{x y y x}^{(3), n u c l})$	$Re (χ_{x x x x}^{(3), n u c l})$
2.1±0.2	6.4±0.4		0.4±0.2	2.5±0.9	3.4±0.8

The imaginary parts

According to Krauss’ work, the values of

Im (χ_{x x x x}^{(3)})

and

Im (χ_{x y x y}^{(3)})

could be obtained by linearly and circularly polarized lights OA Z-scans since the two-photon absorption coefficient

β = 48 π^{2} ω [Im (χ_{x y x y}^{(3)}) + (1 - \sin^{2} 2 φ) Im (χ_{x y y x}^{(3)}) / 2] / n_{0}^{2} c^{2}

for the two polarized lights [30

,33

M. Lefkir, X. N. Phu, and G. Rivoire, “Existence of a bistable polarization state in a Kerr medium in the presence of two-photon absorption,” Quantum Semiclassic. Opt. 10(1), 283–292 (1998). [CrossRef]

]. Furthermore, the value of

Im (χ_{x y y x}^{(3)})

could be calculated by subtracting

Im (2 χ_{x y x y}^{(3)})

from

Im (χ_{x x x x}^{(3)})

. The normalized transmittance traces for I ₀ = 38 GW/cm² are shown in Fig. 3 . From the figure we could not find any observable nonlinear absorption for all the polarized lights within experimental error. We have checked the polarized lights OA Z-scan at other intensities, which are up to 183 GW/cm², and have not found any observable nonlinear absorption for the three polarized lights [22

]. So, both

Im (χ_{x y y x}^{(3)})

and

Im (χ_{x y x y}^{(3)})

are negligible. The value of

β_{l i n}

from measurements of Falconieri and Gnoli et al is about 1.2 × 10⁻¹³ cm/W [34

M. Falconieri and G. Salvetti, “Simultaneous measurement of pure-optical and thermo-optical nonlinearities induced by high-repetition-rate, femtosecond laser pulses: application to CS₂ ,” Appl. Phys. B 69(2), 133–136 (1999). [CrossRef]

,35

A. Gnoli, L. Razzari, and M. Righini, “Z-scan measurements using high repetition rate lasers: how to manage thermal effects,” Opt. Express 13(20), 7976–7981 (2005). [CrossRef] [PubMed]

], which means

Im (χ_{x x x x}^{(3)})

= 5.1 × 10⁻¹⁷ esu. According to their results,

Im (χ_{x x x x}^{(3)})

is also negligible compared with

Re (χ_{x x x x}^{(3)})

. The polarized lights OA Z-scan were also carried out at higher intensity, but it was found that the signal at the valley of Z-scan trace was mainly from nonlinear scattering for the three polarized lights. The polarized lights OA Z-scan was repeated at 780 nm, there was no observable nonlinear absorption signal before the nonlinear scattering appeared [22

]. Therefore, the imaginary parts of susceptibility components are negligible around 800 nm, and the assumption of no-imaginary is reliable and available. But there is nonlinear absorption for CS₂ in the shorter wavelength region [36

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 a short-wavelength region,” J. Opt. Soc. Am. B 24(5), 1101–1104 (2007). [CrossRef]

]. And, the aged CS₂ (yellow color) gives an absorption peak at 350 nm, with probable two-photon absorption around 700 nm [37

K. Fujiwara and K. Fuwa, “Liquid Core Optical Fiber Total Reflection Cell as a Colorimetric Detector for Flow Injection Analysis,” Anal. Chem. 57(6), 1012–1016 (1985). [CrossRef]

]. So,

Im (χ_{i j k l}^{(3)})

may be non-negligible for aged CS₂ around 700 nm.

Fig. 3 OA Z-scan experimental data of different polarized lights.

The reference value

Based on the values of susceptibility tensor elements, the reference value for non-aged CS₂ is suggested to be (9.8 ± 0.7) × 10⁻¹⁴ esu for

| χ_{x x x x}^{(3)} |

in DFWM, (7.2 ± 0.8) × 10⁻¹⁴ esu for

| χ_{x y x y}^{(3)} + χ_{x y y x}^{(3)} |

in OKG/OKE and OHD-OKE, and (4.6 ± 0.8) × 10⁻¹⁴ esu for

| χ_{x y y x}^{(3)} |

in the ellipse rotation measurements when fs laser pulse is in near infrared range.

3. Conclusions

We have systematically studied the real and imaginary parts of third-order susceptibility independent components of CS₂ by using polarized lights Z-scan method. The real parts of tensor elements arising from different mechanisms have separately been determined, and the imaginary parts are negligible. The ratio of

Re (χ_{x y y x}^{(3)})

Re (χ_{x y x y}^{(3)})

is about 1.8, which means both nonresonant electron and fast non-instantaneous nuclear contribute to the third-order nonlinear susceptibility. Based on the values of these susceptibility elements, the reference value of non-aged CS₂ is suggested to be (9.8 ± 0.7) × 10⁻¹⁴ esu for .. in DFWM, (7.2 ± 0.8) × 10⁻¹⁴ esu for

| χ_{x y x y}^{(3)} + χ_{x y y x}^{(3)} |

in OKG/OKE and (4.6 ± 0.8) × 10⁻¹⁴ esu for

| χ_{x y y x}^{(3)} |

in the ellipse rotation measurements respectively when experiments are carried out by using near infrared fs pulsed laser.

Acknowledgements

We thank Boyang Liu and Yasheng Ma for femtosecond laser operation. This work was supported by the Natural Science Foundation of China (grant 10974103), the Program for New Century Excellent Talents in University (NCET-09-0484), Chinese National Key Basic Research Special Fund (grant 2011CB922003), the Natural Science Foundation of Tianjin (09JCYBJC04300), and the Key Project of Chinese Ministry of Education (109039).

References and links

1.	Z. B. Cai, J. R. Gao, X. N. Li, and B. Xiang, “Synthesis and characterization of symmetrical benzodifuranone compounds with femtosecond time-resolved degenerate four-wave mixing technique,” Opt. Commun. 272(2), 503–508 (2007). [CrossRef]
2.	Z. Y. Li, Z. H. Chen, S. Xu, L. H. Niu, Z. Zhang, F. S. Zhang, and K. Kasatani, “Off-resonant third-order optical nonlinearities of novel diarylethene–phthalocyanine dyads,” Chem. Phys. Lett. 447(1-3), 110–114 (2007). [CrossRef]
3.	G. Heng-Qun and W. Qi-Ming, “Nonlinear Optical Response of nc-Si-SiO₂ Films Studied with Femtosecond Four-Wave Mixing Technique,” Chin. Phys. Lett. 23(11), 2989–2992 (2006). [CrossRef]
4.	H. B. Liao, R. F. Xiao, H. Wang, K. S. Wong, and G. K. L. Wong, “Large third-order optical nonlinearity in Au:TiO2 composite films measured on a femtosecond time scale,” Appl. Phys. Lett. 72(15), 1817 (1998). [CrossRef]
5.	H. B. Liao, R. F. Xiao, J. S. Fu, H. Wang, K. S. Wong, and G. K. L. Wong, “Origin of third-order optical nonlinearity in Au:SiO(2) composite films on femtosecond and picosecond time scales,” Opt. Lett. 23(5), 388–390 (1998). [CrossRef]
6.	H. L. Yang, X. Q. Wang, Q. Ren, G. H. Zhang, X. B. Sun, L. Feng, S. F. Wang, and Z. W. Wang, “Study on the third-order nonlinear optical properties of bis(tetrabutylammonium)bis(1,3-dithiole-2-thione- 4,5-dithiolato)cadium,” Opt. Commun. 256(4-6), 256–260 (2005). [CrossRef]
7.	L. Tamayo-Rivera, R. Rangel-Rojo, Y. Mao, and W. H. Watson, “Ultra fast third-order non-linear response of amino-triazole donor-acceptor derivatives by optical Kerr effect,” Opt. Commun. 281(20), 5239–5243 (2008). [CrossRef]
8.	S. F. Wang, W. T. Huang, H. Yang, Q. H. Gong, Z. J. Shi, X. H. Zhou, D. Qiang, and Z. N. Gu, “Large and ultrafast third-order optical non-linearity of single-wall carbon nanotubes at 820 nm,” Chem. Phys. Lett. 320(5-6), 411–414 (2000). [CrossRef]
9.	S. S. Chu, F. M. Li, H. Z. Tao, H. Yang, S. F. Wang, C. G. Lin, X. J. Zhao, and Q. H. Gong, “SbS₃ enhanced ultrafast third-order optical nonlinearities of Ge-S chalcogenide glasses at 820 nm,” Opt. Mater. 31(2), 193–195 (2008). [CrossRef]
10.	Z. W. Wang, C. L. Liu, H. Xiang, Z. Li, Q. H. Gong, Y. J. Qin, Z. X. Guo, and D. B. Zhu, “Ultrafast third-order nonlinear optical response of two soluble multi-wall carbon nanotubes,” J. Phys. D Appl. Phys. 37(7), 1079–1082 (2004). [CrossRef]
11.	Y. Liu, D. Li, R. Y. Zhu, G. J. You, S. X. Qian, Y. Yang, and J. L. Shi, “Third-order nonlinear optical response of Au-core CdS-shell composite nanoparticles embedded in BaTiO₃ thin films,” Appl. Phys. B 76(4), 435–439 (2003). [CrossRef]
12.	Q. Liu, C. Gao, H. Zhou, B. Lu, X. He, Q. Shixiong, and X. Zhao, “Ultrafast third-order optical non-linearity of 0.56GeS₂-0.24Ga₂S₃-0.2KX(X=Cl, Br, I) chalcohalide glasses by femtosecond optical Kerr effect,” Opt. Mater. 32(1), 26–29 (2009). [CrossRef]
13.	Q. M. Liu, X. J. Zhao, F. X. Gan, J. Mi, and S. X. Qian, “Femtosecond optical Kerr effect study of Ge₁₀As₄₀S₃₀Se₂₀ film,” Solid State Commun. 134(8), 513–517 (2005). [CrossRef]
14.	Q. M. Liu, B. Lu, X. J. Zhao, F. X. Gan, J. Mi, and S. X. Qian, “Ultrafast non-linear optical properties of Ge₂₀As₂₅Se₅₅ chalcogenide films,” Opt. Commun. 258(1), 72–77 (2006). [CrossRef]
15.	R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker Inc, New York, 1996) Chapter 7.
16.	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(4), 760–769 (1990). [CrossRef]
17.	R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “nonlinear refraction in CS₂ ,” Appl. Phys. B 78(3-4), 433–438 (2004). [CrossRef]
18.	R. A. Ganeev, A. I. Ryasnyansky, N. Ishizawa, M. Baba, M. Suzuki, M. Turu, S. Sakakibara, and H. Kuroda, “Two- and three-photon absorption in CS₂ ,” Opt. Commun. 231(1-6), 431–436 (2004). [CrossRef]
19.	R. A. Ganeev, A. I. Ryasnyanskiĭ, and H. Kuroda, “Nonlinear optical characteristics of carbon disulfide,” Opt. Spectrosc. 100(1), 108–118 (2006). [CrossRef]
20.	S. Couris, M. Renard, O. Faucher, B. Lavorel, R. Chaux, E. Koudoumas, and X. Michaut, “An experimental investigation of the nonlinear refractive index (n ₂) of carbon disulfide and toluene by spectral shearing interferometry and z-scan techniques,” Chem. Phys. Lett. 369(3-4), 318–324 (2003). [CrossRef]
21.	B. Gu, W. Ji, and X. Q. Huang, “Analytical expression for femtosecond-pulsed Z scans on instantaneous nonlinearity,” Appl. Opt. 47(9), 1187–1192 (2008). [CrossRef] [PubMed]
22.	X. Q. Yan, Z. B. Liu, S. Shi, W. Y. Zhou, and J. G. Tian, “Analysis on the origin of the ultrafast optical nonlinearity of carbon disulfide around 800 nm,” Opt. Express 18(25), 26169–26174 (2010). [CrossRef] [PubMed]
23.	K. Minoshima, M. Taiji, and T. Kobayashi, “Femtosecond time-resolved interferometry for the determination of complex nonlinear susceptibility,” Opt. Lett. 16(21), 1683–1685 (1991). [CrossRef] [PubMed]
24.	R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic Press, San Diego, 2003) Chapter 1.
25.	I. J. Bigio and J. F. Ward, “Measurement of the hyperpolarizability ratio X_{y y y y}(-2ω;0,ω,ω)/X_{y y x x}(-2ω;0,ω,ω) for the inert gases,” Phys. Rev. A 9(1), 35–39 (1974). [CrossRef]
26.	J. Burgin, C. Guillon, and P. Langot, “Femtosecond investigation of the non-instantaneous third-order nonlinear suceptibility in liquids and glasses,” Appl. Phys. Lett. 87(21), 211916 (2005). [CrossRef]
27.	P. Langot, S. Montant, and E. Freysz, “Measurement of non-instantaneous contribution to the χ⁽³⁾ in different liquids using femtosecond chirped pulses,” Opt. Commun. 176(4-6), 459–472 (2000). [CrossRef]
28.	Y. Sato, R. Morita, and M. Yamashita, “Study on ultrafast dynamic behaviors of different nonlinear refractive index components in CS₂ using a femtosecond interferometer,” Jpn. J. Appl. Phys. 36(Part 1, No. 4A), 2109–2115 (1997). [CrossRef]
29.	C. Kalpouzos, W. T. Lotshaw, D. McMorrow, and G. A. Kenney-Wallace, “Femtosecond laser-induced Kerr responses in liquid carbon disulfide,” J. Phys. Chem. 91(8), 2028–2030 (1987). [CrossRef]
30.	T. D. Krauss, J. K. Ranka, F. W. Wise, and A. L. Gaeta, “Measurements of the tensor properties of third-order nonlinearities in wide-gap semiconductors,” Opt. Lett. 20(10), 1110–1112 (1995). [CrossRef] [PubMed]
31.	X. Q. Yan, Z. B. Liu, X. L. Zhang, W. Y. Zhou, and J. G. Tian, “Polarization dependence of Z-scan measurement: theory and experiment,” Opt. Express 17(8), 6397–6406 (2009). [CrossRef] [PubMed]
32.	T. D. Krauss and F. W. Wise, “Femtosecond measurement of nonlinear absorption and refraction in CdS, ZnSe, and ZnS,” Appl. Phys. Lett. 65(14), 1739 (1994). [CrossRef]
33.	M. Lefkir, X. N. Phu, and G. Rivoire, “Existence of a bistable polarization state in a Kerr medium in the presence of two-photon absorption,” Quantum Semiclassic. Opt. 10(1), 283–292 (1998). [CrossRef]
34.	M. Falconieri and G. Salvetti, “Simultaneous measurement of pure-optical and thermo-optical nonlinearities induced by high-repetition-rate, femtosecond laser pulses: application to CS₂ ,” Appl. Phys. B 69(2), 133–136 (1999). [CrossRef]
35.	A. Gnoli, L. Razzari, and M. Righini, “Z-scan measurements using high repetition rate lasers: how to manage thermal effects,” Opt. Express 13(20), 7976–7981 (2005). [CrossRef] [PubMed]
36.	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 a short-wavelength region,” J. Opt. Soc. Am. B 24(5), 1101–1104 (2007). [CrossRef]
37.	K. Fujiwara and K. Fuwa, “Liquid Core Optical Fiber Total Reflection Cell as a Colorimetric Detector for Flow Injection Analysis,” Anal. Chem. 57(6), 1012–1016 (1985). [CrossRef]

OCIS Codes
(120.6710) Instrumentation, measurement, and metrology : Susceptibility
(190.4400) Nonlinear optics : Nonlinear optics, materials
(320.7110) Ultrafast optics : Ultrafast nonlinear optics

ToC Category:
Nonlinear Optics

History
Original Manuscript: December 13, 2010
Revised Manuscript: January 30, 2011
Manuscript Accepted: January 31, 2011
Published: March 10, 2011

Citation
Xiao-Qing Yan, Xiao-Liang Zhang, Shuo Shi, Zhi-Bo Liu, and Jian-Guo Tian, "Third-order nonlinear susceptibility tensor elements of CS₂ at femtosecond time scale," Opt. Express 19, 5559-5564 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-6-5559

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References

Z. B. Cai, J. R. Gao, X. N. Li, and B. Xiang, “Synthesis and characterization of symmetrical benzodifuranone compounds with femtosecond time-resolved degenerate four-wave mixing technique,” Opt. Commun. 272(2), 503–508 (2007). [CrossRef]
Z. Y. Li, Z. H. Chen, S. Xu, L. H. Niu, Z. Zhang, F. S. Zhang, and K. Kasatani, “Off-resonant third-order optical nonlinearities of novel diarylethene–phthalocyanine dyads,” Chem. Phys. Lett. 447(1-3), 110–114 (2007). [CrossRef]
G. Heng-Qun and W. Qi-Ming, “Nonlinear Optical Response of nc-Si-SiO2 Films Studied with Femtosecond Four-Wave Mixing Technique,” Chin. Phys. Lett. 23(11), 2989–2992 (2006). [CrossRef]
H. B. Liao, R. F. Xiao, H. Wang, K. S. Wong, and G. K. L. Wong, “Large third-order optical nonlinearity in Au:TiO2 composite films measured on a femtosecond time scale,” Appl. Phys. Lett. 72(15), 1817 (1998). [CrossRef]
H. B. Liao, R. F. Xiao, J. S. Fu, H. Wang, K. S. Wong, and G. K. L. Wong, “Origin of third-order optical nonlinearity in Au:SiO(2) composite films on femtosecond and picosecond time scales,” Opt. Lett. 23(5), 388–390 (1998). [CrossRef]
H. L. Yang, X. Q. Wang, Q. Ren, G. H. Zhang, X. B. Sun, L. Feng, S. F. Wang, and Z. W. Wang, “Study on the third-order nonlinear optical properties of bis(tetrabutylammonium)bis(1,3-dithiole-2-thione- 4,5-dithiolato)cadium,” Opt. Commun. 256(4-6), 256–260 (2005). [CrossRef]
L. Tamayo-Rivera, R. Rangel-Rojo, Y. Mao, and W. H. Watson, “Ultra fast third-order non-linear response of amino-triazole donor-acceptor derivatives by optical Kerr effect,” Opt. Commun. 281(20), 5239–5243 (2008). [CrossRef]
S. F. Wang, W. T. Huang, H. Yang, Q. H. Gong, Z. J. Shi, X. H. Zhou, D. Qiang, and Z. N. Gu, “Large and ultrafast third-order optical non-linearity of single-wall carbon nanotubes at 820 nm,” Chem. Phys. Lett. 320(5-6), 411–414 (2000). [CrossRef]
S. S. Chu, F. M. Li, H. Z. Tao, H. Yang, S. F. Wang, C. G. Lin, X. J. Zhao, and Q. H. Gong, “SbS3 enhanced ultrafast third-order optical nonlinearities of Ge-S chalcogenide glasses at 820 nm,” Opt. Mater. 31(2), 193–195 (2008). [CrossRef]
Z. W. Wang, C. L. Liu, H. Xiang, Z. Li, Q. H. Gong, Y. J. Qin, Z. X. Guo, and D. B. Zhu, “Ultrafast third-order nonlinear optical response of two soluble multi-wall carbon nanotubes,” J. Phys. D Appl. Phys. 37(7), 1079–1082 (2004). [CrossRef]
Y. Liu, D. Li, R. Y. Zhu, G. J. You, S. X. Qian, Y. Yang, and J. L. Shi, “Third-order nonlinear optical response of Au-core CdS-shell composite nanoparticles embedded in BaTiO3 thin films,” Appl. Phys. B 76(4), 435–439 (2003). [CrossRef]
Q. Liu, C. Gao, H. Zhou, B. Lu, X. He, Q. Shixiong, and X. Zhao, “Ultrafast third-order optical non-linearity of 0.56GeS2-0.24Ga2S3-0.2KX(X=Cl, Br, I) chalcohalide glasses by femtosecond optical Kerr effect,” Opt. Mater. 32(1), 26–29 (2009). [CrossRef]
Q. M. Liu, X. J. Zhao, F. X. Gan, J. Mi, and S. X. Qian, “Femtosecond optical Kerr effect study of Ge10As40S30Se20 film,” Solid State Commun. 134(8), 513–517 (2005). [CrossRef]
Q. M. Liu, B. Lu, X. J. Zhao, F. X. Gan, J. Mi, and S. X. Qian, “Ultrafast non-linear optical properties of Ge20As25Se55 chalcogenide films,” Opt. Commun. 258(1), 72–77 (2006). [CrossRef]
R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker Inc, New York, 1996) Chapter 7.
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(4), 760–769 (1990). [CrossRef]
R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “nonlinear refraction in CS2,” Appl. Phys. B 78(3-4), 433–438 (2004). [CrossRef]
R. A. Ganeev, A. I. Ryasnyansky, N. Ishizawa, M. Baba, M. Suzuki, M. Turu, S. Sakakibara, and H. Kuroda, “Two- and three-photon absorption in CS2,” Opt. Commun. 231(1-6), 431–436 (2004). [CrossRef]
R. A. Ganeev, A. I. Ryasnyanskiĭ, and H. Kuroda, “Nonlinear optical characteristics of carbon disulfide,” Opt. Spectrosc. 100(1), 108–118 (2006). [CrossRef]
S. Couris, M. Renard, O. Faucher, B. Lavorel, R. Chaux, E. Koudoumas, and X. Michaut, “An experimental investigation of the nonlinear refractive index (n2) of carbon disulfide and toluene by spectral shearing interferometry and z-scan techniques,” Chem. Phys. Lett. 369(3-4), 318–324 (2003). [CrossRef]
B. Gu, W. Ji, and X. Q. Huang, “Analytical expression for femtosecond-pulsed Z scans on instantaneous nonlinearity,” Appl. Opt. 47(9), 1187–1192 (2008). [CrossRef] [PubMed]
X. Q. Yan, Z. B. Liu, S. Shi, W. Y. Zhou, and J. G. Tian, “Analysis on the origin of the ultrafast optical nonlinearity of carbon disulfide around 800 nm,” Opt. Express 18(25), 26169–26174 (2010). [CrossRef] [PubMed]
K. Minoshima, M. Taiji, and T. Kobayashi, “Femtosecond time-resolved interferometry for the determination of complex nonlinear susceptibility,” Opt. Lett. 16(21), 1683–1685 (1991). [CrossRef] [PubMed]
R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic Press, San Diego, 2003) Chapter 1.
I. J. Bigio and J. F. Ward, “Measurement of the hyperpolarizability ratio X_{y y y y}(-2ω;0,ω,ω)/X_{y y x x}(-2ω;0,ω,ω) for the inert gases,” Phys. Rev. A 9(1), 35–39 (1974). [CrossRef]
J. Burgin, C. Guillon, and P. Langot, “Femtosecond investigation of the non-instantaneous third-order nonlinear suceptibility in liquids and glasses,” Appl. Phys. Lett. 87(21), 211916 (2005). [CrossRef]
P. Langot, S. Montant, and E. Freysz, “Measurement of non-instantaneous contribution to the χ(3) in different liquids using femtosecond chirped pulses,” Opt. Commun. 176(4-6), 459–472 (2000). [CrossRef]
Y. Sato, R. Morita, and M. Yamashita, “Study on ultrafast dynamic behaviors of different nonlinear refractive index components in CS2 using a femtosecond interferometer,” Jpn. J. Appl. Phys. 36(Part 1, No. 4A), 2109–2115 (1997). [CrossRef]
C. Kalpouzos, W. T. Lotshaw, D. McMorrow, and G. A. Kenney-Wallace, “Femtosecond laser-induced Kerr responses in liquid carbon disulfide,” J. Phys. Chem. 91(8), 2028–2030 (1987). [CrossRef]
T. D. Krauss, J. K. Ranka, F. W. Wise, and A. L. Gaeta, “Measurements of the tensor properties of third-order nonlinearities in wide-gap semiconductors,” Opt. Lett. 20(10), 1110–1112 (1995). [CrossRef] [PubMed]
X. Q. Yan, Z. B. Liu, X. L. Zhang, W. Y. Zhou, and J. G. Tian, “Polarization dependence of Z-scan measurement: theory and experiment,” Opt. Express 17(8), 6397–6406 (2009). [CrossRef] [PubMed]
T. D. Krauss and F. W. Wise, “Femtosecond measurement of nonlinear absorption and refraction in CdS, ZnSe, and ZnS,” Appl. Phys. Lett. 65(14), 1739 (1994). [CrossRef]
M. Lefkir, X. N. Phu, and G. Rivoire, “Existence of a bistable polarization state in a Kerr medium in the presence of two-photon absorption,” Quantum Semiclassic. Opt. 10(1), 283–292 (1998). [CrossRef]
M. Falconieri and G. Salvetti, “Simultaneous measurement of pure-optical and thermo-optical nonlinearities induced by high-repetition-rate, femtosecond laser pulses: application to CS2,” Appl. Phys. B 69(2), 133–136 (1999). [CrossRef]
A. Gnoli, L. Razzari, and M. Righini, “Z-scan measurements using high repetition rate lasers: how to manage thermal effects,” Opt. Express 13(20), 7976–7981 (2005). [CrossRef] [PubMed]
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 a short-wavelength region,” J. Opt. Soc. Am. B 24(5), 1101–1104 (2007). [CrossRef]
K. Fujiwara and K. Fuwa, “Liquid Core Optical Fiber Total Reflection Cell as a Colorimetric Detector for Flow Injection Analysis,” Anal. Chem. 57(6), 1012–1016 (1985). [CrossRef]

Anal. Chem.

K. Fujiwara and K. Fuwa, “Liquid Core Optical Fiber Total Reflection Cell as a Colorimetric Detector for Flow Injection Analysis,” Anal. Chem. 57(6), 1012–1016 (1985). [CrossRef]

Appl. Opt.

B. Gu, W. Ji, and X. Q. Huang, “Analytical expression for femtosecond-pulsed Z scans on instantaneous nonlinearity,” Appl. Opt. 47(9), 1187–1192 (2008). [CrossRef] [PubMed]

Appl. Phys. B

M. Falconieri and G. Salvetti, “Simultaneous measurement of pure-optical and thermo-optical nonlinearities induced by high-repetition-rate, femtosecond laser pulses: application to CS2,” Appl. Phys. B 69(2), 133–136 (1999). [CrossRef]
Y. Liu, D. Li, R. Y. Zhu, G. J. You, S. X. Qian, Y. Yang, and J. L. Shi, “Third-order nonlinear optical response of Au-core CdS-shell composite nanoparticles embedded in BaTiO3 thin films,” Appl. Phys. B 76(4), 435–439 (2003). [CrossRef]
R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “nonlinear refraction in CS2,” Appl. Phys. B 78(3-4), 433–438 (2004). [CrossRef]

Appl. Phys. Lett.

H. B. Liao, R. F. Xiao, H. Wang, K. S. Wong, and G. K. L. Wong, “Large third-order optical nonlinearity in Au:TiO2 composite films measured on a femtosecond time scale,” Appl. Phys. Lett. 72(15), 1817 (1998). [CrossRef]
T. D. Krauss and F. W. Wise, “Femtosecond measurement of nonlinear absorption and refraction in CdS, ZnSe, and ZnS,” Appl. Phys. Lett. 65(14), 1739 (1994). [CrossRef]
J. Burgin, C. Guillon, and P. Langot, “Femtosecond investigation of the non-instantaneous third-order nonlinear suceptibility in liquids and glasses,” Appl. Phys. Lett. 87(21), 211916 (2005). [CrossRef]

Chem. Phys. Lett.

S. Couris, M. Renard, O. Faucher, B. Lavorel, R. Chaux, E. Koudoumas, and X. Michaut, “An experimental investigation of the nonlinear refractive index (n2) of carbon disulfide and toluene by spectral shearing interferometry and z-scan techniques,” Chem. Phys. Lett. 369(3-4), 318–324 (2003). [CrossRef]
Z. Y. Li, Z. H. Chen, S. Xu, L. H. Niu, Z. Zhang, F. S. Zhang, and K. Kasatani, “Off-resonant third-order optical nonlinearities of novel diarylethene–phthalocyanine dyads,” Chem. Phys. Lett. 447(1-3), 110–114 (2007). [CrossRef]
S. F. Wang, W. T. Huang, H. Yang, Q. H. Gong, Z. J. Shi, X. H. Zhou, D. Qiang, and Z. N. Gu, “Large and ultrafast third-order optical non-linearity of single-wall carbon nanotubes at 820 nm,” Chem. Phys. Lett. 320(5-6), 411–414 (2000). [CrossRef]

Chin. Phys. Lett.

G. Heng-Qun and W. Qi-Ming, “Nonlinear Optical Response of nc-Si-SiO2 Films Studied with Femtosecond Four-Wave Mixing Technique,” Chin. Phys. Lett. 23(11), 2989–2992 (2006). [CrossRef]

IEEE J. Quantum Electron.

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(4), 760–769 (1990). [CrossRef]

J. Opt. Soc. Am. B

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 a short-wavelength region,” J. Opt. Soc. Am. B 24(5), 1101–1104 (2007). [CrossRef]

J. Phys. Chem.

C. Kalpouzos, W. T. Lotshaw, D. McMorrow, and G. A. Kenney-Wallace, “Femtosecond laser-induced Kerr responses in liquid carbon disulfide,” J. Phys. Chem. 91(8), 2028–2030 (1987). [CrossRef]

J. Phys. D Appl. Phys.

Z. W. Wang, C. L. Liu, H. Xiang, Z. Li, Q. H. Gong, Y. J. Qin, Z. X. Guo, and D. B. Zhu, “Ultrafast third-order nonlinear optical response of two soluble multi-wall carbon nanotubes,” J. Phys. D Appl. Phys. 37(7), 1079–1082 (2004). [CrossRef]

Jpn. J. Appl. Phys.

Y. Sato, R. Morita, and M. Yamashita, “Study on ultrafast dynamic behaviors of different nonlinear refractive index components in CS2 using a femtosecond interferometer,” Jpn. J. Appl. Phys. 36(Part 1, No. 4A), 2109–2115 (1997). [CrossRef]

Opt. Commun.

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Other

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Third-order nonlinear susceptibility tensor elements of CS2 at femtosecond time scale

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Abstract

1. Introduction

2. Experiments and results

The real parts

The imaginary parts

The reference value

3. Conclusions

Acknowledgements

References and links

References

Anal. Chem.

Appl. Opt.

Appl. Phys. B

Appl. Phys. Lett.

Chem. Phys. Lett.

Chin. Phys. Lett.

IEEE J. Quantum Electron.

J. Opt. Soc. Am. B

J. Phys. Chem.

J. Phys. D Appl. Phys.

Jpn. J. Appl. Phys.

Opt. Commun.

Opt. Express

Opt. Lett.

Opt. Mater.

Opt. Spectrosc.

Phys. Rev. A

Quantum Semiclassic. Opt.

Solid State Commun.

Other

Cited By

Figures

Third-order nonlinear susceptibility tensor elements of CS₂ at femtosecond time scale