October 1, 1992 / Vol. 17, No. 19 / OPTICS LETTERS 1379

Simple technique to reveal a slow nonlinear mechanism in az-scanlike n2 measurement

Hiroyuki Toda* and Carl M. Verber

School of Electrical Engineering and Center for Optical Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332

Received April 6, 1992

We report a simple technique to determine whether the nonlinear mechanism that dominates the results of az-scan n2 measurement is slower than the duration of the exciting pulse. In this technique, the temporal wave-form of the beam transmitted through an aperture is observed, instead of total energy per pulse as in a normalz-scan measurement. Using a doubled Nd:YAG laser, we observed a slow response in index change in the ab-sorptive material methyl nitroaniline, whereas CS2 showed fast response compared with the laser pulse width of65 ns.

Sheik-Bahae et al.1'2 recently demonstrated a tech-nique for measuring the value of n2, the third-ordernonlinear refractive index. In this so-called z-scanmethod, the sample is illuminated by a single, fo-cused beam. An aperture is placed some distancefrom the sample, and the light transmitted throughthe aperture is monitored as the sample is scannedalong the optic axis through the focal region. Theamplitude of the signal is influenced by the fact thatthe nonlinear material acts as a positive (n2 > 0) or anegative (n2 < 0) lens, so a plot of the power trans-mitted through the aperture versus the position ofthe sample with respect to the focal point can be in-terpreted to yield the sign and the magnitude of n2.Typical z-scan data for a positive n2 material areshown in Fig. 1.

This z-scan method, based on the beam-distortioneffect in a nonlinear sample, has advantages com-pared with other methods in that the optical configu-ration is quite simple and that the method permitsthe determination of the sign as well as the magni-tude of n2. However, since the z-scan method re-quires a long interaction length (>103 wavelengths),it tends to be influenced by thermal effects, espe-cially if nanosecond pulses are used as the probebeam.3 Once a z-scan measurement is performed, itmay be necessary to determine whether the mea-sured photoinduced index change is caused by a slowmechanism, such as the thermal effect, or by a fastelectronic mechanism. We describe a simple tech-nique to determine whether the time response ofthe dominant photoinduced index change is longerthan the width of the laser pulse used in the z-scanmeasurement.

The modified z-scan configuration is depicted inFig. 2. Instead of detecting time-averaged trans-mitted power through an aperture while scanningthe sample along the beam axis as in the normal z-scan technique, one derives temporal informationfrom the measurement of the shape of the transmit-ted pulse when the sample is fixed at positions zi andZ2 , respectively. z1 and Z2 are the sample positionswhere the transmission extrema occur in the conven-

tional z-scan measurement. The trailing edge of thepulse acts as a probe that senses the nonlinearity in-duced by the more intense, preceding part of thepulse, provided that the recovery of the nonlinearityis slower than the pulse duration. If the nonlinear-ity is fast, then the weak tail will sense only the smallperturbation that is due to its own effect on thesample. The waveform amplitude deviates fromthat of the original laser pulse in proportion to themagnitude of the index change.

To determine whether the index change is due to aslow mechanism, we compare the waveforms gener-ated with the sample at positions z1 and Z2- If theindex changes faster than the laser pulse decay time,the tails of the two waveforms converge before theend of the pulse. On the other hand, if the indexchange results from a slow mechanism, the wave-

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1380 OPTICS LETTERS / Vol. 17, No. 19 / October 1, 1992

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forms remain separated on the trailing edge of thepulse, which indicates that the index change remainsafter the sample is irradiated by the pulse.

In the experiment, a Q-switched Nd:YAG laserwith a KDP crystal for second-harmonic generationwas used to generate 532-nm pulses with a width of65 nsec. We set the pulse repetition rate at 10 Hz toavoid the accumulation of slow effects. A lens witha focal length of 250 mm was used to produce a 33-,m-radius spot. 28% of the beam was transmittedthrough the 3-mm-diameter aperture located infront of the detector.

To find the sample positions z1 and Z2 , we per-formed a z-scan measurement on a CS2 sample in a10-mm-length quartz cell, which was mounted upona stepper-motor-driven linear-translation stage. In-stead of the detector and the oscilloscope shown inFig. 2, we used an energy meter to measure thetransmitted beam energy through the aperture whilethe sample was scanned along the beam axis. Toreduce the influence of the laser power fluctuation,the laser beam was sampled with a beam splitter be-fore the focusing lens, and this sample was used as areference. The ratio of the reference energy and thetransmitted beam energy was calculated on a pulse-to-pulse basis by an energy ratiometer. Further-more, the measurement at each sample position wasmade by taking an average of 10 pulses. Figure 1shows a typical CS2 z-scan plot, which exhibits apositive nonlinear index. From the transmittancechange of 0.18 in this result, n2 was calculated tobe 2.5 X 1018 m2/W, which is fairly consistent withthe reported value2 of (1.2 ± 0.2) X 10-1' esu (3.1 ±0.5 X 10-18 M2/W).

Having found the sample positions z1 and z2 thatshow the transmission extrema in the z-scan mea-surement, we recorded the temporal waveform of thetransmitted beam when the sample was fixed at eachof these two positions. An avalanche photodiodewith a rise time of approximately 1 ns was used as adetector. The detected signal was displayed on a40-GHz-bandwidth sampling oscilloscope. Todemonstrate the capability of the proposed tech-nique, we investigated the temporal responses of twosamples. The first sample, CS2, has a well-knownfast nonlinearity and was used as a standard. Thesecond sample was a solution of methyl nitroaniline(MNA) in chloroform, which has an absorption coef-ficient of 3.6 m-1 at 532 nm. A 10-mm-length MNAsample thus absorbs 3.5% of the beam energy andshould exhibit a slow thermal effect.

Figures 3(a) and 3(b) show the waveforms ob-tained at sample positions z1 and Z2 , for CS2 andMNA, respectively. Note that, although z1 and z2are the same for both cases, the relative positions ofthe z1 and z2 curves are reversed since the sign of

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(b)Fig. 3. Temporal waveforms of a beam transmittedthrough an aperture, where the sample and the peak in-tensity are (a) CS2 , 90 MW/cm2 and (b) MNA, 22 MW/cm2 .The curves are labeled z1 and Z2 to indicate the position ofthe samples. Note that the relative positions of the z, andZ2 curves differ in the two cases since the sign of the non-linearity is positive for CS2 and negative for MNA.

October 1, 1992 / Vol. 17, No. 19 / OPTICS LETTERS 1381

the index change is positive for CS2 and negative forMNA. The spikes in the waveforms are characteris-tic of the laser used. As Fig. 3(a) shows, when thesample is the transparent nonlinear material CS2the tails of the two waveforms coalesce well beforethe end of the pulse. On the other hand, as is shownin Fig. 3(b), when the sample is an absorptive MNAsolution it is clearly seen that the dominant indexchange has a slower rise time than that of CS2 andthat the relaxation time is slower than the pulse du-ration. A quantitative estimate of the responsetime could be made if different probe-pulse widthswere used. No attempt was made to model this phe-nomenon to see how accurate a measurement of re-sponse time could be derived from the presentmeasurements.

It has been shown that a simple modification ofthe z-scan technique can yield qualitative informa-tion about the speed of the mechanism responsiblefor the optical nonlinearity observed during the con-

ventional z-scan experiment if the speed is close toor greater than the width of the probe beam.

The authors are grateful to Daniel P. Campbellfor providing materials and John Buck for helpfuldiscussions.

*Present address, Department of CommunicationEngineering, Faculty of Engineering, Osaka Univer-sity, 2-1 Yamada-Oka, Suita, Osaka 565 Japan.

References

1. M. Sheik-Bahae, A. A. Said, and E. W Van Stryland,Opt. Lett. 14, 955 (1989).

2. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, andE. W Van Stryland, IEEE J. Quantum Electron. 26,760 (1990).

3. P. N. Prasad and D. J. Williams, Introduction to Non-linear Optical Effects in Molecules and Polymers(Wiley, New York, 1991), p. 211.