Temperature dependence of thethird-order nonlinear susceptibility, X(3) Of CS2and dodecylbenzene

Dang Fu-xi and Wu Bai-shi

The dependence of the third-order nonlinear susceptibility, X(3), of CS2 and C18H30 (dodecylbenzene) ontemperature was measured by the method of degenerate four-wave mixing. The empirical formula forthis dependence was obtained. An explanation of this relationship was also given through theapplication of the model of a polar molecule moving in a viscous medium under the action of a laser beam.

Studies of the dependence of third-order nonlinearsusceptibility, X(3), on the temperature of the mediahave not been reported except in the case of the liquidcrystal in the isotropic phase."2 An experimentalstudy of the third-order nonlinear susceptibility ofliquid media CS 2 and C18H30 is presented here.

The arrangement of the experiment is shown inFig. 1.

The nonlinear reflectance of the degenerate four-wave mixing arrangement iS3

R = = tan2(BIl), (1)I3

in which I, is the intensity of the pumping beam andI3 and 14 are the intensities of the probing beam andthe reflected beam, respectively. The constant B isgiven by

3270rB = 3 (3 )qL (in electrostatic units), (2)

in which L is the interaction length between pumpingbeam and probing beam, n is the index of refraction,and 'T = (2/l)1/2.

From Eq. (2), we obtain the third-order nonlinear

The authors are with the Department of Physics, Xi'an JiaotongUniversity, 26 Xianning Road, 710049 China.

Received 30 July 1990; revised manuscript received 2 July 1993.0003-6935/94/245495-03$06.00/0.© 1994 Optical Society of America.

susceptibility:

(3) cn3X tan-l(R)l/ 2

X, 32rr 3 IlL

If we measure I,, I2, and R at the same time, wemay obtain X(3)- The experimental arrangement isshown in Fig. 2 (Ref. 4).

In Fig. 2, the angle between the pumping beam, El,and the probing beam, E3, is approximately 15 mrad,and the length of the sample cell is 1.45 mm. Theoptical-pulse energy is measured by an Rj-7200 en-ergy ratiometer manufactured by Laser PrecisionCorporation (Utica, New York). The output laser-pulse width is approximately 20 ns. The angle ofdivergence is smaller than 1.5 mrad.

The experimental points are shown in Figs. 3 and 4.From the experimental points and their tendency tovary, we suppose that the relationship between X(3)

Z=O Z=LFig. 1. Basic geometry of phase conjugation by degenerate four-wave mixing. The counterpropagating pump-wave amplitudes,E1 and E2, are assumed to be nondepleted. The probe wave, E3, is,in general, incident at an arbitrary angle to the nonlinear medium.As a result of the nonlinear optical interaction, the reflectedconjugate wave, E4, is generated.

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15

2 4 89

z I g 10 W yl~~~~~~~~~ 1

Fig. 2. Experimental apparatus for the observation of optical phase conjugation by degenerate four-wave mixing. 1, ruby laser; 2, colorfilter; 3, glan prism; 4, X/4 plate; 5, aperture; 6 and 13, dielectric multilayer film; 7, lens; 8, sample cell; 9 and 12, mirror; 10, p-i-n tube; 11,oscilloscope; 14 and 15, energy ratiometer Rj-7200.

0.40 -

0.35 F

0.3G

X(3) X 5.83X10-1 2 esu

CS2

0.25F .

T(k)

0.20 1 1 1 1 1200.0 220.0 240.0 260.0 280.0 300.0

Fig. 3. Variation of the third-order nonlinear susceptibility, X(3),in CS2 versus temperature T. The solid curve is derived from Eq.(3) with the constants listed in the text.

1.50

1.20

0.90

0.60 .

Z'3)X 1.67x10-12 esu

YH3 9 H3

CH3 -CH(-CH 2 -CH-)- 13

0.30

n nn

T(k)

270.0 290.0 310.0 330.0 350.0 370.0Fig. 4. Variation of the third-order nonlinear susceptibility, X(3),in C18H30 versus temperature T. The solid curve is derived fromEq. (3) with the constants listed in the text.

and T is given by the following:

x(3)(T) = C + D[1 + p(T - T1)u]exp(G/T), (3)

in which C, D, p, u, and G are constants and T1 is thetemperature of the first experimental point. Onemay fit Eq. (3) with the experimental points of x(3) (inelectrostatic units) - T of CS 2 and C18H30 by com-puter to find the constants C, D, p, u, and G; theresults are shown in Figs. 3 and 4 and in Table 1.

It can be seen from Figs. 3 and 4 that (a) thethird-order nonlinear susceptibility, X(3), of CS2 andC18H30 increases with increasing temperature; (b) thethird-order nonlinear susceptibility, X(3), of CS 2 andC18H30 has the tendency to saturate with increasingtemperature; and (c) the curve of X(3) - T of CS 2reaches saturation at approximately 250 K, but C18H30does not reach saturation even at 370 K.

Although CS 2 and C18H30 molecules are two differ-ent molecules in weight, structure, and stability, the

varying relationship of X(3) with T can be expressedwith the same formula. We think that this relation-ship is not accidental, and it may indicate that Eq. (3)has certain universal significance for liquid mediaunder the action of nanosecond laser pulses.

To explain qualitatively the experimental relation-ship between X(3) and T, we accept the so-called singlemolecule model. As we know, a number of physicalmechanisms can contribute to optical-induced refrac-tive indices, such as electronic contribution, exec-trostriction, thermal effects, and molecular reorienta-tion and redistribution,5 6 but with nanosecond laserpulses, molecular reorientation is often the dominantmechanism for the observed An (Ref. 7). C18H30 is ananisotropic polar molecule, if we neglect the induceddipole interaction between molecules and consideronly the reorientation effect; i.e., each C18H30 mol-ecule will independently turn and arrange along thedirection of electrical field. At the same time the

Table 1. Constants in Equation (3)

C D p u G

CS 2 (TI = 207.7 K) 0.4600 -0.4000 E - 2 1.548 E - 04 1.790 0.8000 E + 03C18H30 (T1 = 277.7 K) 1.322 -0.3679E - 10 1.198E - 02 1.600 0.6633 E + 04

5496 APPLIED OPTICS / Vol. 33, No. 24 / 20 August 1994

utuu w E | X s

thermal motion of the molecule and the viscousdamping of the liquid medium will oppose this ar-rangement. Because the mass of C18H30 molecule islarge, so the effect of the thermal motion is small andmay be neglected. The higher the temperature, thesmaller the influence of viscous resistance on thearrangement, and under the action of a laser pulsemolecules should be more easily arranged in order.Consequently X(3) increases with temperature. Asthe laser pulse becomes sufficiently strong, X(3) tendsto saturate. Because the moment inertia and theviscous resistance of C18H30 are much larger thanCS2, the tendency of saturation of X(3) for C18H30appears only at higher temperatures in comparisonwith CS 2.

The authors thank Zhang Guo-zhu for helpfuldiscussions on mathematics and computer calcula-tion.

References1. P. A. Madden, F. C. Saunders, and A. M. Scott, "Measurement

of the nonlinear susceptibility of liquid crystal material in theisotropic phase," Opt. Acta 33, 405-417 (1986).

2. G. K. L. Wong and Y. R. Shen, "Study of pretransitionalbehavior of laser-field-induced molecular alignment in isotropicnematic substance," Phys. Rev. A 10, 1277-1284 (1974).

3. A. Yariv, "Amplified reflection, phase conjugation, and oscilla-tion in degenerate four-wave mixing," Opt. Lett. 1, 16 (1977).

4. R. A. Fisher, Optical Phase Conjugation (Academic, New York,1983), Chap. 2, p. 57.

5. G. J. Rosasco and W. S. Hurst, "Measurement of resonant andnonresonant third-order nonlinear susceptibilities by coherentRaman spectroscopy," Phys. Rev. A 32, 281-299 (1985).

6. A. D. Buckingham and B. J. Orr, "Electric birefringence inmolecular hydrogen," Proc. R. Soc. London Ser. A 305,259-269(1968).

7. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, NewYork, 1984), Chap. 16, p. 291.

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