Abstract

It has long been known that nonlinear refraction in solvents can depend on pulse width, and this along with experimental uncertainties has led to orders-of-magnitude disagreements in nonlinear refractive coefficients reported in the literature. To resolve this issue, we perform beam-deflection (BD) measurements of the rigorously defined nonlinear impulse response function for 24 commonly used solvents selected from various classes of molecules. Using this polarization-resolved BD, the bound-electronic and the three major nuclear contributions are separately measured by determining the magnitudes, symmetry, and temporal dynamics of each mechanism. This allows us to construct the response functions that we use to accurately establish self-consistent references for predicting and interpreting the outcomes of other experiments performed on these materials over the temporal range from 10 fs to 1 ns. The results also provide insight into relating solvent nonlinearities with their molecular structures and exploring the effects of the Lorentz–Lorenz local field. We find that nonconjugated molecules with small polarizability anisotropy exhibit negligible reorientational response, and hence the nonlinear refraction is almost independent of pulse width. Knowledge of the response functions also allows engineering the transient nonlinear refractive properties of solutions of organic dyes, for example, materials with effectively zero nonlinear refraction.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  66. Z. A. Li, P. Zhao, S. Tofighi, R. Sharma, T. R. Ensley, S.-H. Jang, D. J. Hagan, E. W. Van Stryland, and A. K.-Y. Jen, “Zwitterionic cyanine-cyanine salt: structure and optical properties,” J. Phys. Chem. C 120, 15378–15384 (2016).
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    [Crossref]

2018 (1)

2017 (2)

M. L. Miguez, T. G. B. De Souza, E. C. Barbano, S. C. Zilio, and L. Misoguti, “Measurement of third-order nonlinearities in selected solvents as a function of the pulse width,” Opt. Express 25, 3553–3565 (2017).
[Crossref]

M. Chemnitz, M. Gebhardt, C. Gaida, F. Stutzki, J. Kobelke, J. Limpert, A. Tünnermann, and M. A. Schmidt, “Hybrid soliton dynamics in liquid-core fibres,” Nat. Commun. 8, 42 (2017).
[Crossref]

2016 (8)

M. Reichert, P. Zhao, J. M. Reed, T. R. Ensley, D. J. Hagan, and E. W. Van Stryland, “Beam deflection measurement of bound-electronic and rotational nonlinear refraction in molecular gases: erratum,” Opt. Express 24, 19122 (2016).
[Crossref]

P. Zhao, M. Reichert, D. J. Hagan, and E. W. Van Stryland, “Dispersion of nondegenerate nonlinear refraction in semiconductors,” Opt. Express 24, 24907–24920 (2016).
[Crossref]

T. R. Ensley, H. Hu, M. Reichert, M. R. Ferdinandus, D. Peceli, J. M. Hales, J. W. Perry, Z. A. Li, S.-H. Jang, A. K. Y. Jen, S. R. Marder, D. J. Hagan, and E. W. Van Stryland, “Quasi-three-level model applied to measured spectra of nonlinear absorption and refraction in organic molecules,” J. Opt. Soc. Am. B 33, 780–796 (2016).
[Crossref]

Z. A. Li, P. Zhao, S. Tofighi, R. Sharma, T. R. Ensley, S.-H. Jang, D. J. Hagan, E. W. Van Stryland, and A. K.-Y. Jen, “Zwitterionic cyanine-cyanine salt: structure and optical properties,” J. Phys. Chem. C 120, 15378–15384 (2016).
[Crossref]

L. G. Holmen and M. W. Haakestad, “Optical limiting properties and z-scan measurements of carbon disulfide at 2.05  μm wavelength,” J. Opt. Soc. Am. B 33, 1655–1660 (2016).
[Crossref]

E. C. Barbano, T. G. Bezerra de Souza, S. C. Zilio, and L. Misoguti, “Comparative study of electronic and orientational nonlinear refractive indices with nonlinear ellipse rotation measurements,” J. Opt. Soc. Am. B 33, E40–E44 (2016).
[Crossref]

P. Zhao, M. Reichert, T. R. Ensley, W. M. Shensky, A. G. Mott, D. J. Hagan, and E. W. Van Stryland, “Nonlinear refraction dynamics of solvents and gases,” Proc. SPIE 9731, 97310F (2016).
[Crossref]

M. Reichert, H. Hu, M. R. Ferdinandus, M. Seidel, P. Zhao, T. R. Ensley, D. Peceli, J. M. Reed, D. A. Fishman, S. Webster, D. J. Hagan, and E. W. Van Stryland, “Temporal, spectral, and polarization dependence of the nonlinear optical response of carbon disulfide: erratum,” Optica 3, 657–658 (2016).
[Crossref]

2015 (5)

S. Kakinuma and H. Shirota, “Dynamic Kerr effect study on six-membered-ring molecular liquids: benzene, 1,3-cyclohexadiene, 1,4-cyclohexadiene, cyclohexene, and cyclohexane,” J. Phys. Chem. B 119, 4713–4724 (2015).
[Crossref]

M. L. Miguez, E. C. Barbano, J. A. Coura, S. C. Zílio, and L. Misoguti, “Nonlinear ellipse rotation measurements in optical thick samples,” Appl. Phys. B 120, 653–658 (2015).
[Crossref]

M. Reichert, P. Zhao, J. M. Reed, T. R. Ensley, D. J. Hagan, and E. W. Van Stryland, “Beam deflection measurement of bound-electronic and rotational nonlinear refraction in molecular gases,” Opt. Express 23, 22224–22237 (2015).
[Crossref]

K. Iliopoulos, D. Potamianos, E. Kakkava, P. Aloukos, I. Orfanos, and S. Couris, “Ultrafast third order nonlinearities of organic solvents,” Opt. Express 23, 24171–24176 (2015).
[Crossref]

Z. A. Li, T. R. Ensley, H. Hu, Y. Zhang, S.-H. Jang, S. R. Marder, D. J. Hagan, E. W. Van Stryland, and A. K. Y. Jen, “Conjugated polycyanines: a new class of materials with large third-order optical nonlinearities,” Adv. Opt. Mater. 3, 900–906 (2015).
[Crossref]

2014 (5)

H. Hu, T. R. Ensley, M. Reichert, M. R. Ferdinandus, D. Peceli, O. V. Przhonska, S. R. Marder, A. K. Y. Jen, J. M. Hales, J. W. Perry, D. J. Hagan, and E. W. Van Stryland, “Optimization of the electronic third-order nonlinearity of cyanine-like molecules for all optical switching,” Proc. SPIE 8983, 898303 (2014).
[Crossref]

S. Shahin, K. Kieu, J. M. Hales, H. Kim, Y. A. Getmanenko, Y. Zhang, J. W. Perry, S. R. Marder, R. A. Norwood, and N. Peyghambarian, “Third-order nonlinear optical characterization of organic chromophores using liquid-core optical fibers,” J. Opt. Soc. Am. B 31, 2455–2459 (2014).
[Crossref]

F. Zhao, Z. Pan, C. Wang, Y. Zhou, and M. Qin, “Third-order nonlinear optical properties of an azobenzene-containing ionic liquid crystalline polymer,” Opt. Quantum Electron. 46, 1491–1498 (2014).
[Crossref]

S. Kedenburg, A. Steinmann, R. Hegenbarth, T. Steinle, and H. Giessen, “Nonlinear refractive indices of nonlinear liquids: wavelength dependence and influence of retarded response,” Appl. Phys. B 117, 803–816 (2014).
[Crossref]

M. Reichert, H. Hu, M. R. Ferdinandus, M. Seidel, P. Zhao, T. R. Ensley, D. Peceli, J. M. Reed, D. A. Fishman, S. Webster, D. J. Hagan, and E. W. Van Stryland, “Temporal, spectral, and polarization dependence of the nonlinear optical response of carbon disulfide,” Optica 1, 436–445 (2014).
[Crossref]

2013 (2)

M. Bala Murali Krishna and D. Narayana Rao, “Influence of solvent contribution on nonlinearities of near infra-red absorbing croconate and squaraine dyes with ultrafast laser excitation,” J. Appl. Phys. 114, 133103 (2013).
[Crossref]

M. R. Ferdinandus, H. Hu, M. Reichert, D. J. Hagan, and E. W. Van Stryland, “Beam deflection measurement of time and polarization resolved ultrafast nonlinear refraction,” Opt. Lett. 38, 3518–3521 (2013).
[Crossref]

2012 (1)

2008 (1)

2004 (2)

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, 431–436 (2004).
[Crossref]

J. M. Hales, D. J. Hagan, E. W. Van Stryland, K. J. Schafer, A. R. Morales, K. D. Belfield, P. Pacher, O. Kwon, E. Zojer, and J. L. Bredas, “Resonant enhancement of two-photon absorption in substituted fluorene molecules,” J. Chem. Phys. 121, 3152–3160 (2004).
[Crossref]

2003 (2)

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, 318–324 (2003).
[Crossref]

N. Thantu and R. S. Schley, “Ultrafast third-order nonlinear optical spectroscopy of chlorinated hydrocarbons,” Vib. Spectrosc. 32, 215–223 (2003).
[Crossref]

2002 (2)

R. A. Negres, J. M. Hales, A. Kobyakov, D. J. Hagan, and E. W. Van Stryland, “Experiment and analysis of two-photon absorption spectroscopy using a white-light continuum probe,” IEEE J. Quantum Electron. 38, 1205–1216 (2002).
[Crossref]

C. J. Fecko, J. D. Eaves, and A. Tokmakoff, “Isotropic and anisotropic Raman scattering from molecular liquids measured by spatially masked optical Kerr effect spectroscopy,” J. Phys. Chem. 117, 1139–1154 (2002).
[Crossref]

2001 (3)

Q.-H. Xu, Y.-Z. Ma, and G. R. Fleming, “Heterodyne detected transient grating spectroscopy in resonant and non-resonant systems using a simplified diffractive optics method,” Chem. Phys. Lett. 338, 254–262 (2001).
[Crossref]

S. Constantine, J. A. Gardecki, Y. Zhou, L. D. Ziegler, X. Ji, and B. Space, “A novel technique for the measurement of polarization-specific ultrafast Raman responses,” J. Phys. Chem. A 105, 9851–9858 (2001).
[Crossref]

D. McMorrow, N. Thantu, V. Kleiman, J. S. Melinger, and W. T. Lotshaw, “Analysis of intermolecular coordinate contributions to third-order ultrafast spectroscopy of liquids in the harmonic oscillator limit,” J. Phys. Chem. A 105, 7960–7972 (2001).
[Crossref]

2000 (1)

K. Kiyohara, K. Kamada, and K. Ohta, “Orientational and collision-induced contribution to third-order nonlinear optical response of liquid CS2,” J. Chem. Phys. 112, 6338–6348 (2000).
[Crossref]

1999 (1)

T. Kawazoe, H. Kawaguchi, J. Inoue, O. Haba, and M. Ueda, “Measurement of nonlinear refractive index by time-resolved z-scan technique,” Opt. Commun. 160, 125–129 (1999).
[Crossref]

1998 (1)

Q.-h. Gong, J.-l. Li, T.-q. Zhang, and H. Yang, “Ultrafast third-order optical nonlinearity of organic solvents investigated by subpicosecond transient optical Kerr effect,” Chin. Phys. Lett. 15, 30–31 (1998).
[Crossref]

1997 (3)

A. Tokmakoff, M. J. Lang, D. S. Larsen, G. R. Fleming, V. Chernyak, and S. Mukamel, “Two-dimensional Raman spectroscopy of vibrational interactions in liquids,” Phys. Rev. Lett. 79, 2702–2705 (1997).
[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, 2109–2115 (1997).
[Crossref]

A. Dogariu, T. Xia, D. J. Hagan, A. A. Said, E. W. Van Stryland, and N. Bloembergen, “Purely refractive transient energy transfer by stimulated Rayleigh-wing scattering,” J. Opt. Soc. Am. B 14, 796–803 (1997).
[Crossref]

1996 (3)

H. Tzer-Hsiang, H. Chia-Chen, W. Tai-Huei, S. Chang, Y. Shih-Ming, T. Chi-Pin, L. Ray-Tang, C. Kuo, X. Tong, T. Wan-Sun, and C. Chihta, “The transient optical Kerr effect of simple liquids studied with an ultrashort laser with variable pulsewidth,” IEEE J. Sel. Top. Quantum Electron. 2, 756–768 (1996).
[Crossref]

G. Boudebs, M. Chis, and J. P. Bourdin, “Third-order susceptibility measurements by nonlinear image processing,” J. Opt. Soc. Am. B 13, 1450–1456 (1996).
[Crossref]

S. Couris, E. Koudoumas, F. Dong, and S. Leach, “Sub-picosecond studies of the third-order optical nonlinearities toluene solutions,” J. Phys. B 29, 5033–5041 (1996).
[Crossref]

1995 (1)

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]

1994 (1)

D. P. Shelton and J. E. Rice, “Measurements and calculations of the hyperpolarizabilities of atoms and small molecules in the gas phase,” Chem. Rev. 94, 3–29 (1994).
[Crossref]

1993 (2)

H.-S. Albrecht, P. Heist, J. Kleinschmidt, and D. V. Lap, “Ultrafast beam-deflection method and its application for measuring the transient refractive index of materials,” Appl. Phys. B 57, 193–197 (1993).
[Crossref]

J. S. Friedman and C. Y. She, “The effects of molecular geometry on the depolarized stimulated gain spectra of simple liquids,” J. Chem. Phys. 99, 4960–4969 (1993).
[Crossref]

1992 (1)

A. Willetts, J. E. Rice, D. M. Burland, and D. P. Shelton, “Problems in the comparison of theoretical and experimental hyperpolarizabilities,” J. Chem. Phys. 97, 7590–7599 (1992).
[Crossref]

1991 (2)

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, 760–769 (1990).
[Crossref]

K. J. Miller, “Calculation of the molecular polarizability tensor,” J. Am. Chem. Soc. 112, 8543–8551 (1990).
[Crossref]

1988 (2)

C. Kalpouzos, D. McMorrow, W. T. Lotshaw, and G. A. Kenney-Wallace, “Femtosecond laser-induced optical Kerr dynamics in CS2/alkane binary solutions,” Chem. Phys. Lett. 150, 138–146 (1988).
[Crossref]

D. McMorrow, W. T. Lotshaw, and G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443–454 (1988).
[Crossref]

1985 (1)

F. Kajzar and J. Messier, “Third-harmonic generation in liquids,” Phys. Rev. A 32, 2352–2363 (1985).
[Crossref]

1984 (1)

N. Phu Xuan, J.-L. Ferrier, J. Gazengel, and G. Rivoire, “Picosecond measurements of the third order susceptibility tensor in liquids,” Opt. Commun. 51, 433–437 (1984).
[Crossref]

1983 (1)

M. Thalhammer and A. Penzkofer, “Measurement of third-order nonlinear susceptibilities by non-phase matched third-harmonic generation,” Appl. Phys. B 32, 137–143 (1983).
[Crossref]

1980 (1)

A. K. Burnham and T. D. Gierke, “A comparison of effective polarizabilities from electro-optical experiments using microscopic and macroscopic theories of the local electric field,” J. Chem. Phys. 73, 4822–4831 (1980).
[Crossref]

1979 (2)

R. J. Bartlett and G. D. Purvis, “Molecular hyperpolarizabilities. I. Theoretical calculations including correlation,” Phys. Rev. A 20, 1313–1322 (1979).
[Crossref]

P. P. Ho and R. R. Alfano, “Optical Kerr effect in liquids,” Phys. Rev. A 20, 2170–2187 (1979).
[Crossref]

1975 (2)

G. R. Alms, A. K. Burnham, and W. H. Flygare, “Measurement of the dispersion in polarizability anisotropies,” J. Chem. Phys. 63, 3321–3326 (1975).
[Crossref]

B. F. Levine and C. G. Bethea, “Second and third order hyperpolarizabilities of organic molecules,” J. Chem. Phys. 63, 2666–2682 (1975).
[Crossref]

1974 (1)

M. D. Levenson and N. Bloembergen, “Dispersion of the nonlinear optical susceptibilities of organic liquids and solutions,” J. Chem. Phys. 60, 1323–1327 (1974).
[Crossref]

1972 (1)

J. Applequist, J. R. Carl, and K.-K. Fung, “Atom dipole interaction model for molecular polarizability. Application to polyatomic molecules and determination of atom polarizabilities,” J. Am. Chem. Soc. 94, 2952–2960 (1972).
[Crossref]

1959 (1)

R. Bramley, C. G. Le Fevre, R. J. W. Le Fevre, and B. P. Rao, “232. Molecular polarisability. The anisotropy of the C=C bond,” J. Chem. Soc. (Resumed) 0, 1183–1188 (1959).
[Crossref]

Albrecht, H.-S.

H.-S. Albrecht, P. Heist, J. Kleinschmidt, and D. V. Lap, “Ultrafast beam-deflection method and its application for measuring the transient refractive index of materials,” Appl. Phys. B 57, 193–197 (1993).
[Crossref]

Alfano, R. R.

Alms, G. R.

G. R. Alms, A. K. Burnham, and W. H. Flygare, “Measurement of the dispersion in polarizability anisotropies,” J. Chem. Phys. 63, 3321–3326 (1975).
[Crossref]

Aloukos, P.

Applequist, J.

J. Applequist, J. R. Carl, and K.-K. Fung, “Atom dipole interaction model for molecular polarizability. Application to polyatomic molecules and determination of atom polarizabilities,” J. Am. Chem. Soc. 94, 2952–2960 (1972).
[Crossref]

Baba, M.

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, 431–436 (2004).
[Crossref]

Bala Murali Krishna, M.

M. Bala Murali Krishna and D. Narayana Rao, “Influence of solvent contribution on nonlinearities of near infra-red absorbing croconate and squaraine dyes with ultrafast laser excitation,” J. Appl. Phys. 114, 133103 (2013).
[Crossref]

Barbano, E. C.

Bartlett, R. J.

R. J. Bartlett and G. D. Purvis, “Molecular hyperpolarizabilities. I. Theoretical calculations including correlation,” Phys. Rev. A 20, 1313–1322 (1979).
[Crossref]

Belfield, K. D.

J. M. Hales, D. J. Hagan, E. W. Van Stryland, K. J. Schafer, A. R. Morales, K. D. Belfield, P. Pacher, O. Kwon, E. Zojer, and J. L. Bredas, “Resonant enhancement of two-photon absorption in substituted fluorene molecules,” J. Chem. Phys. 121, 3152–3160 (2004).
[Crossref]

Benis, S.

S. Benis, D. J. Hagan, and E. W. Van Stryland, “Cross-propagating beam-deflection measurements of third-order nonlinear optical susceptibility,” in SPIE LASE (SPIE, 2017), p. 6.

Bethea, C. G.

B. F. Levine and C. G. Bethea, “Second and third order hyperpolarizabilities of organic molecules,” J. Chem. Phys. 63, 2666–2682 (1975).
[Crossref]

Bezerra de Souza, T. G.

Bloembergen, N.

A. Dogariu, T. Xia, D. J. Hagan, A. A. Said, E. W. Van Stryland, and N. Bloembergen, “Purely refractive transient energy transfer by stimulated Rayleigh-wing scattering,” J. Opt. Soc. Am. B 14, 796–803 (1997).
[Crossref]

M. D. Levenson and N. Bloembergen, “Dispersion of the nonlinear optical susceptibilities of organic liquids and solutions,” J. Chem. Phys. 60, 1323–1327 (1974).
[Crossref]

Boudebs, G.

Bourdin, J. P.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

Bramley, R.

R. Bramley, C. G. Le Fevre, R. J. W. Le Fevre, and B. P. Rao, “232. Molecular polarisability. The anisotropy of the C=C bond,” J. Chem. Soc. (Resumed) 0, 1183–1188 (1959).
[Crossref]

Bredas, J. L.

J. M. Hales, D. J. Hagan, E. W. Van Stryland, K. J. Schafer, A. R. Morales, K. D. Belfield, P. Pacher, O. Kwon, E. Zojer, and J. L. Bredas, “Resonant enhancement of two-photon absorption in substituted fluorene molecules,” J. Chem. Phys. 121, 3152–3160 (2004).
[Crossref]

Burland, D. M.

A. Willetts, J. E. Rice, D. M. Burland, and D. P. Shelton, “Problems in the comparison of theoretical and experimental hyperpolarizabilities,” J. Chem. Phys. 97, 7590–7599 (1992).
[Crossref]

Burnham, A. K.

A. K. Burnham and T. D. Gierke, “A comparison of effective polarizabilities from electro-optical experiments using microscopic and macroscopic theories of the local electric field,” J. Chem. Phys. 73, 4822–4831 (1980).
[Crossref]

G. R. Alms, A. K. Burnham, and W. H. Flygare, “Measurement of the dispersion in polarizability anisotropies,” J. Chem. Phys. 63, 3321–3326 (1975).
[Crossref]

Butcher, P. N.

P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge University, 1990).

Carl, J. R.

J. Applequist, J. R. Carl, and K.-K. Fung, “Atom dipole interaction model for molecular polarizability. Application to polyatomic molecules and determination of atom polarizabilities,” J. Am. Chem. Soc. 94, 2952–2960 (1972).
[Crossref]

Chang, S.

H. Tzer-Hsiang, H. Chia-Chen, W. Tai-Huei, S. Chang, Y. Shih-Ming, T. Chi-Pin, L. Ray-Tang, C. Kuo, X. Tong, T. Wan-Sun, and C. Chihta, “The transient optical Kerr effect of simple liquids studied with an ultrashort laser with variable pulsewidth,” IEEE J. Sel. Top. Quantum Electron. 2, 756–768 (1996).
[Crossref]

Chaux, R.

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, 318–324 (2003).
[Crossref]

Chemnitz, M.

M. Chemnitz, C. Gaida, M. Gebhardt, F. Stutzki, J. Kobelke, A. Tünnermann, J. Limpert, and M. A. Schmidt, “Carbon chloride-core fibers for soliton mediated supercontinuum generation,” Opt. Express 26, 3221–3235 (2018).
[Crossref]

M. Chemnitz, M. Gebhardt, C. Gaida, F. Stutzki, J. Kobelke, J. Limpert, A. Tünnermann, and M. A. Schmidt, “Hybrid soliton dynamics in liquid-core fibres,” Nat. Commun. 8, 42 (2017).
[Crossref]

Chen, D. Y.

Chernyak, V.

A. Tokmakoff, M. J. Lang, D. S. Larsen, G. R. Fleming, V. Chernyak, and S. Mukamel, “Two-dimensional Raman spectroscopy of vibrational interactions in liquids,” Phys. Rev. Lett. 79, 2702–2705 (1997).
[Crossref]

Chia-Chen, H.

H. Tzer-Hsiang, H. Chia-Chen, W. Tai-Huei, S. Chang, Y. Shih-Ming, T. Chi-Pin, L. Ray-Tang, C. Kuo, X. Tong, T. Wan-Sun, and C. Chihta, “The transient optical Kerr effect of simple liquids studied with an ultrashort laser with variable pulsewidth,” IEEE J. Sel. Top. Quantum Electron. 2, 756–768 (1996).
[Crossref]

Chihta, C.

H. Tzer-Hsiang, H. Chia-Chen, W. Tai-Huei, S. Chang, Y. Shih-Ming, T. Chi-Pin, L. Ray-Tang, C. Kuo, X. Tong, T. Wan-Sun, and C. Chihta, “The transient optical Kerr effect of simple liquids studied with an ultrashort laser with variable pulsewidth,” IEEE J. Sel. Top. Quantum Electron. 2, 756–768 (1996).
[Crossref]

Chi-Pin, T.

H. Tzer-Hsiang, H. Chia-Chen, W. Tai-Huei, S. Chang, Y. Shih-Ming, T. Chi-Pin, L. Ray-Tang, C. Kuo, X. Tong, T. Wan-Sun, and C. Chihta, “The transient optical Kerr effect of simple liquids studied with an ultrashort laser with variable pulsewidth,” IEEE J. Sel. Top. Quantum Electron. 2, 756–768 (1996).
[Crossref]

Chis, M.

Constantine, S.

S. Constantine, J. A. Gardecki, Y. Zhou, L. D. Ziegler, X. Ji, and B. Space, “A novel technique for the measurement of polarization-specific ultrafast Raman responses,” J. Phys. Chem. A 105, 9851–9858 (2001).
[Crossref]

Cotter, D.

P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge University, 1990).

Coura, J. A.

M. L. Miguez, E. C. Barbano, J. A. Coura, S. C. Zílio, and L. Misoguti, “Nonlinear ellipse rotation measurements in optical thick samples,” Appl. Phys. B 120, 653–658 (2015).
[Crossref]

Couris, S.

K. Iliopoulos, D. Potamianos, E. Kakkava, P. Aloukos, I. Orfanos, and S. Couris, “Ultrafast third order nonlinearities of organic solvents,” Opt. Express 23, 24171–24176 (2015).
[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, 318–324 (2003).
[Crossref]

S. Couris, E. Koudoumas, F. Dong, and S. Leach, “Sub-picosecond studies of the third-order optical nonlinearities toluene solutions,” J. Phys. B 29, 5033–5041 (1996).
[Crossref]

De Souza, T. G. B.

Dogariu, A.

Dong, F.

S. Couris, E. Koudoumas, F. Dong, and S. Leach, “Sub-picosecond studies of the third-order optical nonlinearities toluene solutions,” J. Phys. B 29, 5033–5041 (1996).
[Crossref]

Eaves, J. D.

C. J. Fecko, J. D. Eaves, and A. Tokmakoff, “Isotropic and anisotropic Raman scattering from molecular liquids measured by spatially masked optical Kerr effect spectroscopy,” J. Phys. Chem. 117, 1139–1154 (2002).
[Crossref]

Ensley, T. R.

P. Zhao, M. Reichert, T. R. Ensley, W. M. Shensky, A. G. Mott, D. J. Hagan, and E. W. Van Stryland, “Nonlinear refraction dynamics of solvents and gases,” Proc. SPIE 9731, 97310F (2016).
[Crossref]

T. R. Ensley, H. Hu, M. Reichert, M. R. Ferdinandus, D. Peceli, J. M. Hales, J. W. Perry, Z. A. Li, S.-H. Jang, A. K. Y. Jen, S. R. Marder, D. J. Hagan, and E. W. Van Stryland, “Quasi-three-level model applied to measured spectra of nonlinear absorption and refraction in organic molecules,” J. Opt. Soc. Am. B 33, 780–796 (2016).
[Crossref]

Z. A. Li, P. Zhao, S. Tofighi, R. Sharma, T. R. Ensley, S.-H. Jang, D. J. Hagan, E. W. Van Stryland, and A. K.-Y. Jen, “Zwitterionic cyanine-cyanine salt: structure and optical properties,” J. Phys. Chem. C 120, 15378–15384 (2016).
[Crossref]

M. Reichert, P. Zhao, J. M. Reed, T. R. Ensley, D. J. Hagan, and E. W. Van Stryland, “Beam deflection measurement of bound-electronic and rotational nonlinear refraction in molecular gases: erratum,” Opt. Express 24, 19122 (2016).
[Crossref]

M. Reichert, H. Hu, M. R. Ferdinandus, M. Seidel, P. Zhao, T. R. Ensley, D. Peceli, J. M. Reed, D. A. Fishman, S. Webster, D. J. Hagan, and E. W. Van Stryland, “Temporal, spectral, and polarization dependence of the nonlinear optical response of carbon disulfide: erratum,” Optica 3, 657–658 (2016).
[Crossref]

Z. A. Li, T. R. Ensley, H. Hu, Y. Zhang, S.-H. Jang, S. R. Marder, D. J. Hagan, E. W. Van Stryland, and A. K. Y. Jen, “Conjugated polycyanines: a new class of materials with large third-order optical nonlinearities,” Adv. Opt. Mater. 3, 900–906 (2015).
[Crossref]

M. Reichert, P. Zhao, J. M. Reed, T. R. Ensley, D. J. Hagan, and E. W. Van Stryland, “Beam deflection measurement of bound-electronic and rotational nonlinear refraction in molecular gases,” Opt. Express 23, 22224–22237 (2015).
[Crossref]

M. Reichert, H. Hu, M. R. Ferdinandus, M. Seidel, P. Zhao, T. R. Ensley, D. Peceli, J. M. Reed, D. A. Fishman, S. Webster, D. J. Hagan, and E. W. Van Stryland, “Temporal, spectral, and polarization dependence of the nonlinear optical response of carbon disulfide,” Optica 1, 436–445 (2014).
[Crossref]

H. Hu, T. R. Ensley, M. Reichert, M. R. Ferdinandus, D. Peceli, O. V. Przhonska, S. R. Marder, A. K. Y. Jen, J. M. Hales, J. W. Perry, D. J. Hagan, and E. W. Van Stryland, “Optimization of the electronic third-order nonlinearity of cyanine-like molecules for all optical switching,” Proc. SPIE 8983, 898303 (2014).
[Crossref]

M. R. Ferdinandus, M. Reichert, T. R. Ensley, H. Hu, D. A. Fishman, S. Webster, D. J. Hagan, and E. W. Van Stryland, “Dual-arm Z-scan technique to extract dilute solute nonlinearities from solution measurements,” Opt. Mater. Express 2, 1776–1790 (2012).
[Crossref]

Faucher, O.

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, 318–324 (2003).
[Crossref]

Fecko, C. J.

C. J. Fecko, J. D. Eaves, and A. Tokmakoff, “Isotropic and anisotropic Raman scattering from molecular liquids measured by spatially masked optical Kerr effect spectroscopy,” J. Phys. Chem. 117, 1139–1154 (2002).
[Crossref]

Ferdinandus, M. R.

T. R. Ensley, H. Hu, M. Reichert, M. R. Ferdinandus, D. Peceli, J. M. Hales, J. W. Perry, Z. A. Li, S.-H. Jang, A. K. Y. Jen, S. R. Marder, D. J. Hagan, and E. W. Van Stryland, “Quasi-three-level model applied to measured spectra of nonlinear absorption and refraction in organic molecules,” J. Opt. Soc. Am. B 33, 780–796 (2016).
[Crossref]

M. Reichert, H. Hu, M. R. Ferdinandus, M. Seidel, P. Zhao, T. R. Ensley, D. Peceli, J. M. Reed, D. A. Fishman, S. Webster, D. J. Hagan, and E. W. Van Stryland, “Temporal, spectral, and polarization dependence of the nonlinear optical response of carbon disulfide: erratum,” Optica 3, 657–658 (2016).
[Crossref]

M. Reichert, H. Hu, M. R. Ferdinandus, M. Seidel, P. Zhao, T. R. Ensley, D. Peceli, J. M. Reed, D. A. Fishman, S. Webster, D. J. Hagan, and E. W. Van Stryland, “Temporal, spectral, and polarization dependence of the nonlinear optical response of carbon disulfide,” Optica 1, 436–445 (2014).
[Crossref]

H. Hu, T. R. Ensley, M. Reichert, M. R. Ferdinandus, D. Peceli, O. V. Przhonska, S. R. Marder, A. K. Y. Jen, J. M. Hales, J. W. Perry, D. J. Hagan, and E. W. Van Stryland, “Optimization of the electronic third-order nonlinearity of cyanine-like molecules for all optical switching,” Proc. SPIE 8983, 898303 (2014).
[Crossref]

M. R. Ferdinandus, H. Hu, M. Reichert, D. J. Hagan, and E. W. Van Stryland, “Beam deflection measurement of time and polarization resolved ultrafast nonlinear refraction,” Opt. Lett. 38, 3518–3521 (2013).
[Crossref]

M. R. Ferdinandus, M. Reichert, T. R. Ensley, H. Hu, D. A. Fishman, S. Webster, D. J. Hagan, and E. W. Van Stryland, “Dual-arm Z-scan technique to extract dilute solute nonlinearities from solution measurements,” Opt. Mater. Express 2, 1776–1790 (2012).
[Crossref]

Ferrier, J.-L.

N. Phu Xuan, J.-L. Ferrier, J. Gazengel, and G. Rivoire, “Picosecond measurements of the third order susceptibility tensor in liquids,” Opt. Commun. 51, 433–437 (1984).
[Crossref]

Fishman, D. A.

Fleming, G. R.

Q.-H. Xu, Y.-Z. Ma, and G. R. Fleming, “Heterodyne detected transient grating spectroscopy in resonant and non-resonant systems using a simplified diffractive optics method,” Chem. Phys. Lett. 338, 254–262 (2001).
[Crossref]

A. Tokmakoff, M. J. Lang, D. S. Larsen, G. R. Fleming, V. Chernyak, and S. Mukamel, “Two-dimensional Raman spectroscopy of vibrational interactions in liquids,” Phys. Rev. Lett. 79, 2702–2705 (1997).
[Crossref]

Flygare, W. H.

G. R. Alms, A. K. Burnham, and W. H. Flygare, “Measurement of the dispersion in polarizability anisotropies,” J. Chem. Phys. 63, 3321–3326 (1975).
[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]

Friedman, J. S.

J. S. Friedman and C. Y. She, “The effects of molecular geometry on the depolarized stimulated gain spectra of simple liquids,” J. Chem. Phys. 99, 4960–4969 (1993).
[Crossref]

Fung, K.-K.

J. Applequist, J. R. Carl, and K.-K. Fung, “Atom dipole interaction model for molecular polarizability. Application to polyatomic molecules and determination of atom polarizabilities,” J. Am. Chem. Soc. 94, 2952–2960 (1972).
[Crossref]

Gaida, C.

M. Chemnitz, C. Gaida, M. Gebhardt, F. Stutzki, J. Kobelke, A. Tünnermann, J. Limpert, and M. A. Schmidt, “Carbon chloride-core fibers for soliton mediated supercontinuum generation,” Opt. Express 26, 3221–3235 (2018).
[Crossref]

M. Chemnitz, M. Gebhardt, C. Gaida, F. Stutzki, J. Kobelke, J. Limpert, A. Tünnermann, and M. A. Schmidt, “Hybrid soliton dynamics in liquid-core fibres,” Nat. Commun. 8, 42 (2017).
[Crossref]

Ganeev, R. A.

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, 431–436 (2004).
[Crossref]

Gardecki, J. A.

S. Constantine, J. A. Gardecki, Y. Zhou, L. D. Ziegler, X. Ji, and B. Space, “A novel technique for the measurement of polarization-specific ultrafast Raman responses,” J. Phys. Chem. A 105, 9851–9858 (2001).
[Crossref]

Gazengel, J.

N. Phu Xuan, J.-L. Ferrier, J. Gazengel, and G. Rivoire, “Picosecond measurements of the third order susceptibility tensor in liquids,” Opt. Commun. 51, 433–437 (1984).
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Supplementary Material (1)

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Figures (9)

Fig. 1.
Fig. 1. Survey of literature values reported for CS2. The letters represent references of [319], i.e., a: [3], c–f: [47], and h–s: [819].
Fig. 2.
Fig. 2. (a) Schematics of BD setup; (b) spatial irradiance distribution of the excitation beam (red) and overlapping geometry with the probe beam (blue) at the sample plane; (c) positions of probe beam on segmented quad-cell detector without and with deflection.
Fig. 3.
Fig. 3. (a) Data (circles) and fit (curves) of BD measurement of benzene for parallel (black), perpendicular (red), and magic-angle (blue) polarizations; (b) response function for each nuclear mechanism using the fit parameters of benzene in Table 1.
Fig. 4.
Fig. 4. BD measurements (circles) with fits (lines) of benzene derivatives including (a) toluene, (b) p-xylene, (c) pyridine, (d) nitrobenzene, (e) o-dichlorobenzene and (f) butyl salicylate for parallel (black), perpendicular (red), and magic-angle (blue) polarizations.
Fig. 5.
Fig. 5. BD measurements (circles) with fits (lines). (a) Dichloromethane, (b) chloroform, and (c) CCl4 for parallel (black), perpendicular (red), and magic-angle (blue) polarizations; (d) measured CCl4 response excited with shorter pulse width with parallel polarization (circles), with a fit including the vibrational response (inset shows the vibrational component enlarged).
Fig. 6.
Fig. 6. BD measurements (circles) with fits (lines). (a) Cyclohexane and (b) 1-octanol for parallel (black), perpendicular (red), and magic-angle (blue) polarizations.
Fig. 7.
Fig. 7. Predictions of pulse-width dependent n2,eff of (a) CS2 using parameters in Table 1, which is compared to Z-scan measurements in [20,25], as well as literature values a–s from references specified in the caption of Fig. 1; (b),(c) predictions of the other 23 solvent molecules using parameters in Table 1.
Fig. 8.
Fig. 8. Predictions (blue) of pulse-width dependent n2,eff of (a) toluene and (b) chloroform using parameters in Table 1, which are compared to literature values a–s from references specified in the caption of Fig. 1.
Fig. 9.
Fig. 9. BD measurements of (a) AJBC3701 in DMF solution with a fit, and (b) YZ-V-69 in CCl4 solution (blue). The responses from the solvents with cuvette (black) are measured under identical experimental conditions. The solute signal (red circles) is from subtraction of solvent background from solution response, with a fit (red lines) considering only bound-electronic NLR. Inset shows molecular structures. (c) Predictions of pulse-width dependent n2,eff of AJBC3701 solutions with different concentrations.

Tables (2)

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Table 1. Fit Parameters of Nonlinear Response Function of Solventsa

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Table 2. Reorientational n2,d Comparison between Theoretical and Experimental Valuesa

Equations (4)

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n2,el=34Nnpneϵ02cf(3)Re[γ],
n2,d=Nnpneϵ02c[fp(1)fe(1)]2ΔαeΔαp45kBT,
Δn(t)=2n2,elIe(t)+m(n2,mrm(tt)Ie(t)dt).
n2,eff=n2,el+I(t)R(tt)I(t)dtdtI2(t)dt.

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