Comparison of Z-scan and THG derived nonlinear index of refraction in selected organic solvents

Ileana Rau; François Kajzar; Jérôme Luc; Bouchta Sahraoui; Georges Boudebs

doi:10.1364/JOSAB.25.001738

Journal of the Optical Society of America B
Vol. 25,
Issue 10,
pp. 1738-1747
(2008)
•https://doi.org/10.1364/JOSAB.25.001738

Comparison of Z-scan and THG derived nonlinear index of refraction in selected organic solvents

Ileana Rau, François Kajzar, Jérôme Luc, Bouchta Sahraoui, and Georges Boudebs

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Ileana Rau, François Kajzar, Jérôme Luc, Bouchta Sahraoui, and Georges Boudebs, "Comparison of Z-scan and THG derived nonlinear index of refraction in selected organic solvents," J. Opt. Soc. Am. B 25, 1738-1747 (2008)

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Abstract

Nonlinear index of refraction of a series of organic solvents, measured by the nonlinear imaging (z-scan) technique, is compared with the same values derived from optical third-harmonic generation (THG). The systematic differences in the values obtained from the z-scan measurements and from THG are attributed to three factors: the value of the standard used in THG measurements, important rotational contribution in z-scan measurements, and the difference in dispersion for $n_{2}$ derived from Kerr susceptibility and those derived from THG measurements. Using the recently proposed standard silica susceptibility value, one obtains a very good agreement for silica and significant differences for the solvents, particularly for $C S_{2}$ and chlorobenzene. A correction based on a three-level model for centrosymmetric media is applied for dispersion.

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Equations (17)

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Solvent	$n_{0}$	$χ_{THG}^{(3)}$ $\times 10^{- 14} esu$	$χ_{THG}^{(3)}$ $\times 10^{- 22}$ ${(m ∕ V)}^{2}$	$n_{2}$ $\times 10^{- 20} m^{2} ∕ W$ (calculated from $χ_{THG}^{(3)}$ )	$n_{2}$ $\times 10^{- 20} m^{2} ∕$ $W @ 1064 nm$ measured by z-scan	$χ_{Kerr}^{(3)}$ $\times 10^{- 22}$ ${(m ∕ V)}^{2}$	$χ_{Kerr}^{(3)} ∕ χ_{THG}^{(3)}$	$χ_{Kerr}^{(3)} ∕ χ_{THG}^{(3)}$ corrected for new silica value
Carbon tetrachloride	1.44678	7.96^a	11.1	15.0	28	$20.8 \pm 3.5$	$1.87 \pm 0.32$	$2.91 \pm 0.50$
Chloroform	1.43783	7.00^a	9.77	13.3	38	$27.8 \pm 5$	$2.85 \pm 0.51$	$4.43 \pm 0.79$
Dichloromethane	1.42862	6.13^a	8.56	11.8	37	$26.8 \pm 5$	$3.13 \pm 0.57$	$4.87 \pm 0.89$
Cyclohexane	1.44318	6.47^a	9.03	12.2	19	$14.0 \pm 3$	$1.55 \pm 0.32$	$2.41 \pm 0.50$
N-hexane	1.36500	4.42^a	6.17	9.35	17	$11.2 \pm 2.5$	$1.82 \pm 0.40$	$2.83 \pm 0.62$
Acetone	1.35347	4.69^a	6.55	10.1	23	$14.9 \pm 2.8$	$2.28 \pm 0.43$	$3.55 \pm 0.67$
Methanol	1.32000	2.98^a	4.16	6.74	18	$11.1 \pm 2.3$	$2.67 \pm 0.56$	$4.15 \pm 0.87$
Ethanol	1.33989	3.45^a	4.82	7.57	18	$11.5 \pm 3$	$2.38 \pm 0.63$	$3.70 \pm 0.98$
Dimetylformamide	1.41500	5.57^a	7.78	11.0	42	$29.8 \pm 5.1$	$3.83 \pm 0.66$	$5.96 \pm 1.00$
Water	1.32612	2.80^a	3.91	6.28	14	$8.7 \pm 2.1$	$2.23 \pm 0.54$	$3.47 \pm 0.84$
Chlorobenzene	1.52140	10.6^a	14.8	18.1	117	$95.9 \pm 12.0$	$6.48 \pm 0.81$	$10.07 \pm 1.26$
Toluene	1.49260	9.81^a	13.7	17.4	93	$73.4 \pm 10.5$	$5.36 \pm 0.77$	$8.33 \pm 1.19$
$C S_{2}$	1.62110	23^b	32.1	34.5	310	$288.9 \pm 56.8$	$9.00 \pm 1.77$	$14.00 \pm 2.75$
Silica	1.44967	3.11^a	4.34	5.83	3.7	$2.73 \pm 0.52$	$0.63 \pm 0.12$	$0.98 \pm 0.10$
Silica	1.44967	2.79^c	3.89	5.23	—	—	—	—
Silica	1.44967	$2.0 \pm 0.2$ ^d	2.79	3.75	—	—	—	—
Silica	1.44967	$1.6 \pm 0.2$ ^e	2.23	3.00	—	—	—	—

Damping factor Γ $({cm}^{- 1})$	Silica	Benzene
10	0.847	0.514
200	0.847	0.514
300	0.847	0.514
400	0.847	0.514
500	0.847	0.515
1000	0.847	0.517
2000	0.847	0.527
3000	0.850	0.543
4000	0.856	0.565
5000	0.861	0.592
8000	0.882	0.670
10000	0.904	0.791
15000	1.000	1.114
20000	1.091	1.817
50000	0.241	0.299

Solvent	Chemical formula	$n_{355}$	$n_{1064}$	$χ^{(3)}$ (355)/ $χ^{(3)}$ (1064)	$n_{2} (355) ∕ n_{2} (1064)$	$n_{1907}$	$χ^{(3)}$ (355)/ $χ^{(3)}$ (1907)	$n_{2} (355) ∕ n_{2} (1064)$
Benzene	$C_{6} H_{6}$	1.54976	1.48258	1.874	1.793	1.48008	1.921	1.835
Carbon tetrachloride	$C {Cl}_{4}$	1.48335	1.44678	1.454	1.418	1.44380	1.5	1.460
Chloroform	$C H {Cl}_{3}$	1.47194	1.43783	1.427	1.394	1.43492	1.473	1.436
Dichloromethane	$C H_{2} {Cl}_{2}$	1.45482	1.42862	1.323	1.300	1.42320	1.405	1.375
Dimethylformamide	$H C O N {(C H_{3})}_{2}$	1.45504	1.41500	1.543	1.501	1.41452	1.552	1.509
Cyclohexane	$C_{6} H_{12}$	1.47254	1.44318	1.356	1.329	1.44268	1.363	1.335
N-hexane	$C H_{3} {(C H_{2})}_{4} C H_{3}$	1.38957	1.36500	1.352	1.329	1.36450	1.361	1.336
Acetone	CH3COCH3	1.37933	1.35347	1.386	1.360	1.35056	1.439	1.409
Methanol	CH30H	1.34109	1.3200	1.338	1.317	1.31558	1.426	1.399
Ethanol	$C_{2} H_{5} O H$	1.36281	1.33989	1.317	1.297	1.33431	1.456	1.426
Silica	$Si O_{2}$	1.47642	1.44967	1.316	1.292	1.43953	1.466	1.429

Solvent	$n_{0}$	$χ_{THG}^{(3)}$ $\times 10^{- 14} esu$	$χ_{THG}^{(3)}$ $\times 10^{- 22}$ ${(m ∕ V)}^{2}$	$n_{2}$ $\times 10^{- 20} m^{2} ∕ W$ (calculated from $χ_{THG}^{(3)}$ )	$n_{2}$ $\times 10^{- 20} m^{2} ∕$ $W @ 1064 nm$ measured by z-scan	$χ_{Kerr}^{(3)}$ $\times 10^{- 22}$ ${(m ∕ V)}^{2}$	$χ_{Kerr}^{(3)} ∕ χ_{THG}^{(3)}$	$χ_{Kerr}^{(3)} ∕ χ_{THG}^{(3)}$ corrected for new silica value
Carbon tetrachloride	1.44678	7.96^a	11.1	15.0	28	$20.8 \pm 3.5$	$1.87 \pm 0.32$	$2.91 \pm 0.50$
Chloroform	1.43783	7.00^a	9.77	13.3	38	$27.8 \pm 5$	$2.85 \pm 0.51$	$4.43 \pm 0.79$
Dichloromethane	1.42862	6.13^a	8.56	11.8	37	$26.8 \pm 5$	$3.13 \pm 0.57$	$4.87 \pm 0.89$
Cyclohexane	1.44318	6.47^a	9.03	12.2	19	$14.0 \pm 3$	$1.55 \pm 0.32$	$2.41 \pm 0.50$
N-hexane	1.36500	4.42^a	6.17	9.35	17	$11.2 \pm 2.5$	$1.82 \pm 0.40$	$2.83 \pm 0.62$
Acetone	1.35347	4.69^a	6.55	10.1	23	$14.9 \pm 2.8$	$2.28 \pm 0.43$	$3.55 \pm 0.67$
Methanol	1.32000	2.98^a	4.16	6.74	18	$11.1 \pm 2.3$	$2.67 \pm 0.56$	$4.15 \pm 0.87$
Ethanol	1.33989	3.45^a	4.82	7.57	18	$11.5 \pm 3$	$2.38 \pm 0.63$	$3.70 \pm 0.98$
Dimetylformamide	1.41500	5.57^a	7.78	11.0	42	$29.8 \pm 5.1$	$3.83 \pm 0.66$	$5.96 \pm 1.00$
Water	1.32612	2.80^a	3.91	6.28	14	$8.7 \pm 2.1$	$2.23 \pm 0.54$	$3.47 \pm 0.84$
Chlorobenzene	1.52140	10.6^a	14.8	18.1	117	$95.9 \pm 12.0$	$6.48 \pm 0.81$	$10.07 \pm 1.26$
Toluene	1.49260	9.81^a	13.7	17.4	93	$73.4 \pm 10.5$	$5.36 \pm 0.77$	$8.33 \pm 1.19$
$C S_{2}$	1.62110	23^b	32.1	34.5	310	$288.9 \pm 56.8$	$9.00 \pm 1.77$	$14.00 \pm 2.75$
Silica	1.44967	3.11^a	4.34	5.83	3.7	$2.73 \pm 0.52$	$0.63 \pm 0.12$	$0.98 \pm 0.10$
Silica	1.44967	2.79^c	3.89	5.23	—	—	—	—
Silica	1.44967	$2.0 \pm 0.2$ ^d	2.79	3.75	—	—	—	—
Silica	1.44967	$1.6 \pm 0.2$ ^e	2.23	3.00	—	—	—	—

Damping factor Γ $({cm}^{- 1})$	Silica	Benzene
10	0.847	0.514
200	0.847	0.514
300	0.847	0.514
400	0.847	0.514
500	0.847	0.515
1000	0.847	0.517
2000	0.847	0.527
3000	0.850	0.543
4000	0.856	0.565
5000	0.861	0.592
8000	0.882	0.670
10000	0.904	0.791
15000	1.000	1.114
20000	1.091	1.817
50000	0.241	0.299

Abstract

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Figures (6)

Tables (3)

Equations (17)

Journal of the Optical Society of America B