dear Lam

in my experience the main source of error in z-scan measurement is the uncertainty in the laser beam fluence measurements, or in other words in the beam shape. As a matter of fact the laser beam is often assumed to be a TEM 00 which is not always realistic. I think this fact can explain the reported differences in the published values and add large uncertainty in the results.

Following Rajeev Gandhi reply, I think it is worth to stress here that measurements using cw sources cannot be compared to pulsed ones since in the first case only the thermo-optical properties are probed. In  fact in this case the signal is originated by the thermo-optical coefficient dn/dT which is not a true third order nonlinear coefficient.

Finally, other techniques for third-order nonlinear characterization may probe other components of the chi^3 tensor, so that the measurements results may be not directly comparable to z-scan results.

It depends on your experimental configuration.  If you are averaging many pulses (or cw) then your errors will come down. If you use second detector and normalize the signal then your errors due to input pulse fluctuations will reduce.  If you sample has scattering or highly inhomogeneous then the signal will fluctuate accordingly. Then there are errors in the estimation of I0 (peak intensity) which determines the NLO coefficient.

Typically 5-10% is what people report and is acceptable.  Even other techniques have errors depending on experimental configurations.

Hope this helps.

Best Wishes

Venugopal Rao Soma

Dear Prof.Venugopal Rao Soma,

Thank you for your answer. But in paper of Prof.Mansoor Sheik-Bahae, I see that error of n2 i up to 40% (1,5+-0,6).

In my Ph.D. research I measured nonlinear refractive indexes on  different growth planes of pure and doped crystals by Z-scan method using a cw (continuous wave) He–Ne laser at 632.8 nm. The measured values of nonlinear refraction of different planes were in the order of 10−12cm2/W, which are too large compared to those determined using Nd:YAG pulsed laser. Higher values of nonlinear refractive indices maybe due to thermal effects by continuous wave He-Ne laser.

Go through the following papers

1. H.P. Li, C.H. Kam, Y.L. Lam, W. Ji, Femtosecond Z-scan measurement of nonlinearrefraction in nonlinear optical materials, Opt. Mater. 15 (2001) 237–242.

2. Chongkyu Shin, Hoosung Lee, Comparative study of third-order electronic andthermally induced optical nonlinearity in a polythiophene thin film, J. Kor. Phys.Soc. 36 (2000) 356–359.

3. I.P. Khristov, I.V. Tomov, S.M. Saltiel, Self-heating effects in electro-optic lightmodulators, Opt. Quantum Electron. 15 (1983) 289–295.

dear Lam

in my experience the main source of error in z-scan measurement is the uncertainty in the laser beam fluence measurements, or in other words in the beam shape. As a matter of fact the laser beam is often assumed to be a TEM 00 which is not always realistic. I think this fact can explain the reported differences in the published values and add large uncertainty in the results.

Following Rajeev Gandhi reply, I think it is worth to stress here that measurements using cw sources cannot be compared to pulsed ones since in the first case only the thermo-optical properties are probed. In  fact in this case the signal is originated by the thermo-optical coefficient dn/dT which is not a true third order nonlinear coefficient.

Finally, other techniques for third-order nonlinear characterization may probe other components of the chi^3 tensor, so that the measurements results may be not directly comparable to z-scan results.

Thank Prof.Rajeev Gandhi and Mauro Falconieri. I understand that n2 is not compared in two different experimental conditions (CW laser and pulsed laser). So, we assume that both experiments use CW lasers, so which range is error of nonlinear index n2 in ?

I suggest you that to use wave-front sensor based methods to measure refractive index varying in present of pump laser, then it able you to measure n2 with more accuracy than z-scan method. We use moire'deflectometey based wave-front sensor for this reason.

Dear Prof.Mohammad Yeganeh,

I understand that there are many other methods to measure n2. However, in my lab, we have a laser beam profiler. So, I do Z-scan according to Prof.G. Tsigaridas:

https://www.researchgate.net/publication/226556943_Z_-scan_technique_through_beam_radius_measurements

And I see that many papers on Z-Scan measurements have error in the range of 25 to 40%.Then,I wonder which range the error of the Z-scan method lies in is acceptable? And how many order of magnitude do results of measuring nonlinear index n2 by Z-scan method and other methods different?

Article Z -scan technique through beam radius measurements

dear Lam

if you use CW lasers then you are measuring a thermo-optical effect which cannot be analysed using the z-scan theory for purely optical nonlinearities. For thermo-optical "nonnlinearities" the relationships derived in the Sheikh-Bahae paper do not hold. You can find some details on this topic on the attached paper. 

On the other hand I think the best way to reduce the errors due to inaccurate laser fluence is to calibrate the system with a well-known nonlinear material like CS2.

best 

Mauro

Dear Prof.Mauro Falconieri,

Thank you for your excellent paper. I understand that you are taking about very strict and high accuracy method in your paper to analyse Z -scan signal.

But I also see that there are many works measuring a thermo-optical effect with CW laser and analyse data by Z-scan theory of Prof.Sheikh-Bahae, such as:

1.Wang, J., Aihara, Y., Kinoshita, M., Mamiya, J. I., Priimagi, A., & Shishido, A. (2015), Laser-pointer-induced self-focusing effect in hybrid-aligned dye-doped liquid crystals, Scientific reports, 5.

2. G.Balaji, R.K.Rekha, A.Ramalingam (2011), Nonlinear characterization of safranin O dye for application in optical limiting, Acta Phys. Pol. A, 119, 359-363.

3. T. R. Kumar, R. J. Vijay, R. Jeyasekaran, S. Selvakumar, M. A. Arockiaraj, P. Sagayaraj (2011), Growth, linear and nonlinear optical and, laser damage threshold studies of organometallic crystal of MnHg(SCN)4, Opt. Mater. 33, pp.1654-1660.

4. P. V. Dhanaraj, N. P. Rajesh, G. Vinitha, G. Bhagavannarayana (2011), Crystal structure and characterization of a novel organic optical crystal:2-Aminopyridinium trichloroacetate, Mater. Research Bull. 46, pp.726-731.

5. P. V. Dhanaraja, N. P. Rajesh, J. K. Sundar, S. Natarajan, G. Vinitha (2011), Studies on growth, crystal structure and characterization of novel organic nicotinium trifluoroacetate single crystals, Mater. Chem. Phys. 129, pp.457-463.

6.S.Dhanuskodi, T.S.Girisun, S.Vinitha (2011), Optical limiting behavior of certain thiourea metal complexes under CW laser excitation, Current Applied Physics, 11(3), 860-864.

7.. M. D. Zidan, A. W. Allaf, Z. Ajji, A. Allahham (2011), Investigation of the optical limiting properties of acid blue29 in various solvents, Opt. Laser Technol. 43, pp.1347-1350.

8.. N. Ramamurthy, S. Dhanuskodi, M. V. Manjusha, J. Philip (2011), Low power CW optical limiting properties of bis (2-aminopyridinium)-succinate-succinic acid (2APS) single crystal, Opt. Mater. 33, pp.607-612.

9. H.A.Badran, Q.M.A.Hassan, A.Y. Al-Ahmad, C.A. Emshary (2011), Laser-induced optical nonlinearities in Orange G dye: polyacrylamide gel, Canadian Journal of Physics, 89(12), 1219-1224.

10.R.K.H.Manshad, Q.M.A.Hassan (2012), Optical limiting properties of magenta doped PMMA under CW laser illumination, Adv. Appl. Sci. Res, 3(6), 3696-3702.

...............................................................

For pulsed lasers errors are arise from pulse shape Gaussian shapre which is important may improved by a pin hole and other source of errore is enrgy flactuation per puls averaging  reduces errors for cw and nano second the effect is  thermal and depend on the coductivity of the materal i think 10% would be acceptable 

Dear Prof.Fryad Henari,

Thank you for your useful advice. We are talking about errors in the same measurement technique, it't about 10% is acceptable.

However, for two different measurement techniques, I see that difference in n2 is large, more than one order of magnitude (attached picture, C60 and C70 measured by different techniques).

dear Lam

I know that Sheik-Bahae theory has been used to analyse CW z-scan measurements, but nevertheless this procedure is not always correct, and actually is wrong in the majority of cases.

To convince yourself please consider the simple fact that thermal nonlinearities are due to the temperature profile established in the sample because of laser heating. The temperature profiles originates the refractive index profile, which is then measured by the z-scan technique. Now the point is that the temperature profile is not stationary but it evolves according to the heat diffusion in the sample. So the refractive index lens profile is not stationary also. Therefore the z-scan trace cannot be calculated using the instantaneous nonlinearity theory which assumes instead a stationary (gaussian) lens profile.

Therefore, for thermal nonlinearities and CW lasers  the peak-valley distance is not equal to 1.72 z0, and the peak valley amplitude is not equal to 0.406 times the phase shift.

Mauro

Thank you for your useful advice, Prof.Mauro Falconieri. This issue is still open for more opinions.

If the material you are testing shows strong nonlinear effect then you have no problem because the error is small.  However, if the sample you are test with weak nonlinear effect then in this case examine your graph, if it in general shows a typical nonlinear behavior, then you can accept the data otherwise there it is not acceptable. Once I was reviewing a paper and I notice that the data scattered randomly and I advise the authors to repeat the z-scan, and they found that they were measuring noise as one of the connection was lose and when repeated the measurement they got reasonable result.

Thank you for your positive comments, Prof.Ahmed AlSaie. The material we are studying is organic show strong nonlinear effect.

you could use the z-scan as a relative measurement, measure your sample and then measure a reference sample with well known nonlinearities under the same conditions. One such sample is CS2, which has been extensively studied, and being a liquid, there are no structure issues. In this way, the major source of uncertainty in the data is in the actual fit that can be done to the experimental data.

Thank you for your positive comments, Prof.Raul Rangel-Rojo.

Dear Lam, please see the attached manuscript. It describes an experiment based on z-scan and how the uncertainty can be reduced. I hope it can help.

Best

The advantage with Z-scan technique is that it provides sign and magnitude of n2/chi_3 at the same time. However, things get complicated when working with cw, nsec pulses due to thermal nonlinearities. Further, the nonlinearities measured in liquids (concentration dependent) are not fully accurate. One needs to normalize for the concentration used. It generally provides an order of magnitude. The errors will vary depending on the sample uniformity, homogeneity, scattering etc. (thin film, colloidal suspension, clear solutions, etc.). 10-20% is acceptable while in some cases 20-30 % is also acceptable. It is always better to compare with other standard samples or the values obtained with other techniques. If some one reports a new molecules/crystal/film nonlinearity ensure they do with minimal complications. Usually 100 fsec, 1 KHz data is very reliable. Even with 100 fs, 100 MHz data one records high nonlinearities. One needs to understand the origin of nonlinearity and then analyze the data accordingly. There are applications of cw, nsec nonlinearities in optical limiting etc.

The other common techniques available are THG and DFWM, which are little complicated experiments to perform.

Dear, in my point of view, to obtain the electronic n2 with high accuracy by using the close-aperture Z-scan technique it is necessary to use the femtosecond pulses with low repetition rate (1-100 kHz). In addition, several papers have reporting the electronic n2 of chromophores in solutions but the authors do not remove the Z-scan signal from the solvent. In a solution, there are much more solvent molecules than chromophores (~10000). In addition, it is know that solvent molecules present considerable electronic n2. To overcome this effect, it is necessary obtain the n2 ratio between the solution/solvent. Therefore, to measure electronic n2 of chromophores in solution through the conventional close-aperture Z-scan it is practically impossible. Unfortunately, many reviewers have accepted this kind of manuscript containing several mistakes.

Thank you very much for your answers, Prof.Venugopal Rao Soma and Prof.Marcelo G Vivas.

Hi Mr nguyen,

I am having difficulties in finding the standard n2 and beta value for CS2 as standard sample precisely for 532nm of CW beam. Do you happened to found it anywhere? Thanks for your attention. I’m looking forward to your reply.

Dear M. Abdella,

n2 and beta value of CS2 for pulsed laser can found at the end of this paper (Table 1):

http://www.phys.unm.edu/msbahae/publications/z-scan.pdf

I can not find these values for CW laser.

I think that studies on third order nonlinear optical effect of material mainly focused on the pulsed laser because CW laser produces a thermal effect. And we can not manage these effects.

Dear Nguyen,

Thank for your reply. The values of n2 for CS2 measured from my CW setup is much higher that the values reported in the paper since CW beam will cause addition of thermal nonlinear effect in the signal. So theres no way i can compare it with the standard. By the way, have you checked this paper? They included the thermal effect in their analysis.

Dear M. Abdella ,

Thank you for sharing me excellent paper. I will read this work and discuss with you.