The femtosecond open-aperture Z-scan of standard sample CS2 at 800 and 780 nm is present here by using thinner sample length and an integrating sphere. The open-aperture Z-scan signal is verified to arise mainly from nonlinear scattering, not from two- or three-photon absorption as reported in literature. And the two- and three-photon absorption coefficients of CS2 are negligible. Therefore, around 800 nm the femtosecond open-aperture Z-scan of CS2 cannot be used to calibrate Z-scan measurement system, but the closed-aperture Z-scan is capable.
©2010 Optical Society of America
Until now, there are lots of works using femtosecond open-aperture (OA) Z-scan to measure the two-photon absorption (2PA) coefficient of standard sample CS2 around 800 nm [1–5]. Among these works, the 2PA coefficient β(CS2) from OA Z-scan trace fitting is widely considered to be (1~5) × 10−11 cm/W. It seems that the OA Z-scan signal undoubtedly arises from two-photon absorption.
However, according to the electronic spectroscopy of CS2, the longer wavelength absorption band ranges from 290 to 390 nm (there is other absorption bands at shorter wavelength for CS2, because we discuss the nonlinear absorption only around 800 nm, the absorption spectrum focused here is restricted to the absorption bands with a peak at about 318 nm) . Thus, under the energy conservation requirement of 2PA rule [7,8], the probability of 2PA for CS2 around 800 nm should be extremely small, and it is hard to observe obvious 2PA around 800 nm. Indeed, the β(CS2) from the time evolution of the closed aperture (CA) Z-scan measurements conducted by Falconieri  and Gnoli et al  is really small at 770 nm ((4.5,1.2) × 10−13 cm/W). Their results are about two orders smaller than these from OA Z-scan measurements. The much larger value of β(CS2) from OA Z-scan was attributed to the contribution of stimulated Raman scattering (SRS) processes which generate radiation at angles wider than the collection angle by Gnoli et al . However, no explicit experimental verification of the scattering explanation was previously reported to the best of our knowledge. If SRS really contributes to the valley of OA Z-scan trace, the stimulated Rayleigh-wing scattering (SRWS) may also exist since the threshold for SRWS in CS2 is really low [11–13].
As we know, one absorptive peak of CS2 is around 318 nm [6,14], three-photon absorption (3PA) process may take place around 800 nm since the requirement of wavelength (i.e., energy) for 3PA is met. Thus, the signal of OA Z-scan may be from 3PA, and the OA Z-scan experimental data could not be easily dealt with by 2PA model. In fact, the OA Z-scan signal at 800 nm has been considered arising from 3PA and dealt with 3PA model .
Although the femtosecond OA Z-scan signal of CS2 around 800 nm has not been solidly determined, it has been used to calibrate the Z-scan measurement system [16–18] and the value of β(CS2) from OA Z-scan measurements has been used as referenced value for validating other methods of 2PA measurements . If the signal is mainly from nonlinear scattering or 3PA but we still use CS2 as a referenced material of 2PA in OA Z-scan to calibrate Z-scan measurement system, we could not obtain right parameters of the measurement system because of the wrong fitting model used and the randomicity caused by nonlinear scattering in measurement. For example, wrong beam waist radius will be obtained if OA Z-scan trace of 3PA and nonlinear scattering is fit by 2PA model, and different β(CS2) will be gotten under the same Z-scan scheme if the position of the lens (which is placed after sample and used to collect the transmitted light) with respective to sample is changed. It is probable bring errors for new materials measurements or ignore influence of other signal to new 2PA measurements. Thus, it is very necessary to determine the origin of femtosecond OA Z-scan signal of the standard material CS2 around 800 nm from experimental aspect.
In this letter, the femtosecond OA Z-scan measurements of CS2 at 800 and 780 nm were carried out by using different sample length and an integrating sphere (IS). From the comparisons of OA Z-scan traces for 1mm-thick sample at different intensity, different sample length at the same intensity and with/without IS at the same sample length and intensity respectively, the OA Z-scan signal is determined to arise from nonlinear scattering. And then the nonlinear scattering is attributed to SRS and SRWS from the spectrums of forward transmitted light and backward scattering light.
2. Experimental results and discussions
In the experiment we used a mode-locked Ti: Sapphire laser (Spitfire Pro, Spectra-Physics) to provide 120-fs (FWHM) pulses at 800 nm with 1 KHz repetition rate. The spatial distribution of the linearly polarized incidence pulses after passing through a spatial filter was nearly Gaussian. The laser beam was focused onto sample by using a 250 mm focal-length lens with a beam waist radius w0 of 33 ± 2 μm. The beam waist was obtained from CCD camera when the CCD camera was placed at focus. The measurement system was calibrated by both OA and CA Z-scan measurements of other samples, i.e., OA Z-scan of 2PA materials (1mm-thick ZnSe  at low intensity and a piece of amorphous silicon film ) and CA Z-scan of toluene . The Z-scan traces of these materials could be well fit with the beam waist radius. The energies of referenced and transmitted pulses were simultaneously measured by two detectors (Ophir). In all the OA Z-scan measurements present here, no measurable nonlinear absorption or nonlinear scattering signal from the quartz cell near focus was observed.
Because the linear absorption spectrum of CS2 is not consistent in [1,2,6,9,10], the linear absorption spectrum was still measured in order to check the linear absorption edge of CS2 and make sure no impurities in CS2. The absorption spectrum (measured using a U-4100 HITACHI spectrophotometer) above 300 nm is shown in Fig. 1(c) . As shown in the figure the absorption of CS2 below 380 nm is really large and out of the ability of the equipment, the shape of absorption spectrum had to be determined by measuring diluted CS2 in ethanol (the effect of ethanol has been subtracted). From the figure we find that the absorption peak is at 317 nm, and absorption edge is at about 411 nm. The absorption peak and the absorption edge are consistent with the measurement results given in  and theoretical analysis in , respectively. So, the 2PA of CS2 around 800 nm is not against conservation of energy, but the 2PA could not be obvious around 800 nm due to it matches the absorption edge. And there may be 3PA around 800 nm.
The dependence of Z-scan trace on on-axis peak intensity I 0 (calculated using Eq. (32) in ) is shown in Fig. 1(a,b). The sample length was set to be 1 mm not 2 mm as in [1–3,15] because we tried to reduce the self-focusing effect which would cause nonlinear scattering at low energy [12,23]. There is no visible signal in these traces for I 0≤183 GW/cm2 (see Fig. 1(b,d)), however, a valley abruptly appears in the Z-scan trace for I 0 = 292 GW/cm2. As comparison, the calculated Z-scan curves for 2PA from others’ values and 3PA were also plotted. The value of β(CS2) used for calculation was set to be 3 × 10−11 cm/W (a compromised value of [1–5], indicated as normal) and 1.2 × 10−13 cm/W (indicated as Gnoli’s ). The value of 3PA coefficient γ was set to be 1.4 × 10−22 cm3/W2 (from 3PA fitting in Fig. 1(d)). From the figure we find that these curves could be fitted by neither 2PA with normal β(CS2) nor 3PA . All the Z-scan traces calculated from Gnoli’s value are like a beeline, the signal of 2PA at focus is extremely small and hard to be observed. And they could fit the experimental traces well for I 0≤153 GW/cm2. At 292 GW/cm2, the great discrepancy between the experimental trace and 2PA/3PA fitting indicates that the signal of the valley is from neither 2PA nor 3PA. From the evolution of Z-scan traces, we can conclude that the 2PA and 3PA is negligible and it is probable that the signal of the valley is from nonlinear scattering at 800 nm.
The Z-scan traces for 1mm- and 2mm-thick sample at 183 GW/cm2 are shown in Fig. 1(d). We find that there is an obvious valley for 2mm-thick case, however, there is no any observable signal of nonlinear absorption for 1mm-thick case. For 2mm-thick case, the calculated Z-scan trace by β(CS2) = 3 × 10−11 cm/W greatly deviates from the experimental data. And then the valley of Z-scan trace was fitted by 2PA model , the nominal 2PA coefficient is determined to be about 1.55 × 10−11 cm/W. Although the from fitting is consistent with the result in [5,16], there is obvious discrepancy between experimental data and 2PA fitting. Thus, the signal of the valley could not arise from pure 2PA. To directly verify that there is the contribution of nonlinear scattering to the valley, an IS attached behind the sample was used to collect the transmitted light when the sample was moved along Z axis. As shown in the figure, the valley of Z-scan trace for the case with IS is shallower than that without IS. Therefore, it is certain that there was nonlinear scattering in Z-scan process for 2mm-thick case. Then the Z-scan trace with IS was dealt with 2PA (not shown) and 3PA models . 2PA model could not fit well the experimental data like the case without IS, however, 3PA could fit most of the experimental data well as shown in the figure. It seems that the signal of valley for the case with IS was from 3PA. To further verify that the signal was not mainly from 3PA but nonlinear scattering, the value of γ from 3PA fitting was used to calculate the Z-scan trace of 3PA for 1mm-thick case (Fig. 1(a,b,d)). If the signal was indubitably from 3PA, the valley of experimental Z-scan trace for 1mm-thick should be a little deeper than that from calculation (because 1mm-thick case was measured without IS, there may be some nonlinear scattering for 1mm-thick case, thus, the valley will become a little deeper compared with pure 3PA). However, there are no valleys in experimental traces for 1mm-thick (Fig. 1(b,d)). So, the valley in the trace of 2mm-thick case with IS could not arise from 3PA, the signal of the valley is attributed to backward scattering and leak of the IS (the port of IS was much larger than the sample width, and the IS could not collect all the transmitted light). In fact, the nonlinear scattering could be viewed from forward and backward directions with the help of an infrared viewing (FJW, find-R-scope). Because the OA Z-scan were carried out at same I 0 for 1mm-thick and 2mm-thick case, the intensity threshold assumption for 2PA or 3PA could be eliminated.
The 2PA and 3PA was separately used to analyze the traces in above discussion, 2PA and 3PA may simultaneously take place in the Z-scan process. But from the evolution of Z-scan traces for 1mm-thick sample (Fig. 1(a,d)) and the extremely different trace for 1mm- and 2mm-thick sample (Fig. 1(d)), the conclusion that the signal is mainly from scattering should be correct.
In order to verify the existence of nonlinear scattering from spectrum aspect and determine the nonlinear scattering type, we used a fiber optic spectrometer (USB4000, Ocean Optics) to measure the forward transmitted spectrum and backward scattering spectrum. The spectra are shown in Fig. 2 . From the comparison of forward transmitted spectra at different sample position we find that there is a new peak around 830 nm and new spectrum band around 820 nm when the sample was placed near focus. The new peak and band were not found in the forward transmitted spectrum or backward scattering spectrum of quartz cell, so the new peak and band in spectra are from CS2. The new peak is away from the wavelength of incident light and is attributed to Stokes SRS, which is predicted by Gnoli et al . The frequency shift of the scattering is about 452 cm−1, which almost agrees with the SRS frequency shift of CS2 at 694 nm [22,24]. The new spectrum band around 820 nm may be from Stokes SRWS, it is not attributed to stimulated Brillouin scattering (SBS) because it is usually observed only in the backwards direction . In order to check that the new spectrum band is from SRWS not from the incident light or SRS, the measurement of backward scattering spectrum was also carried out. The schematic diagram of experimental setup for backward scattering spectrum measurement was the same as that in Fig. 3 , except that the polarizing beam splitter was replaced by a polarizer-lens combination. The polarizer was parallel to the polarization of incident light. So, only the scattering light with phase conjugation could be measured. From the comparison of the backward scattering spectra at different position we find that the new spectrum band still exists. As we know, SRWS is the light scattering process resulting from the tendency of anisotropic molecules to become aligned along the electric field vector of an applied optical wave . For anisotropic molecule CS2, the response time of molecular orientation is about 1.66 ps, which is much slower than the pulse used here. So, the SRWS may be due to molecular collision, whose relaxation time is in order of 100~200 fs. The molecular collision can distort electronic cloud, and then change the polarizability of molecular. The collision-induced polarizability can scatter the light in a large spectral band . No matter what type of nonlinear scattering is, forward and backward nonlinear scattering processes undoubtedly exist and contribute to valley of Z-scan traces.
In order to check whether the OA Z-scan signals of CS2 is from nonlinear scattering only at 800 nm, the experiment was also carried out at 780 nm. The 780 nm femtosecond laser pulses were generated by a light conversion (TOPAS). The Z-scan traces for 1mm- and 2mm-thick cases are shown in Fig. 3(a). As for 800 nm in Fig. 1(d), there is obvious valley for 2mm-thick case but there is no visible valley for 1mm-thick case. And the signal of the valley can be reduced by using an IS. So, the situation of CS2 OA Z-scan at 780 nm is the same as that at 800 nm, the signal is mainly from nonlinear scattering.
The CA Z-scan traces of CS2 are shown in Fig. 3(b). There is small nonlinear refraction signal of cell in the Z-scan trace of 122 GW/cm2, and it could be ignored compared with the nonlinear refraction of CS2. It is seen that these traces can by well fitted by theory with large nonlinear phase shift . The fitting results are listed in the figure and consistent with previous reports [2,5,9]. Therefore, the CA Z-scan of CS2 can be used to calibrate Z-scan measurement system. However, as the 2PA and 3PA fitting in Fig. 1(d) the OA Z-scan trace cannot be fitted by 2PA or 3PA. The nonlinear absorption signal is hard to be directly measured because of nonlinear scattering and the noise in experiments, thus, it is not a reliable way to measure the β and γ by using OA Z-scan for CS2. So, the OA Z-scan of CS2 cannot be used to calibrate Z-scan measurement system.
Although we have not observed any measurable signal from 2PA or 3PA, we cannot conclude that there is no 2PA and 3PA around 800 nm. In other words, both the 2PA and 3PA around 800nm is negligible. Maybe, the β(CS2) from Gnoli’s measurement can be an candidate of referenced value of CS2, thus, the value from [1–5,15] cannot be used to validate other methods for measuring 2PA or 3PA coefficient.
The signal of femtosecond OA Z-scan arises mainly from Stokes stimulated Raman scattering and Stokes stimulated Rayleigh-wing scattering around 800 nm, and the two-photon absorption and three-photon absorption of CS2 is negligible. The OA Z-scan of CS2 cannot be used to calibrate Z-scan measurement system, but CA Z-scan is capable.
We acknowledge the help of Yasheng Ma and Boyang Liu in the femtosecond laser operation. This research was supported by NSFC (grant 60708020, 10974103), the Program for New Century Excellent Talents in University (NCET-09-0484), and Chinese National Key Basic Research Special Fund (grant 2006CB921703).
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