I think when nonlinear refraction is dominant, you can extract the nonlinear parameters from the closed z-scan with some confidence. However, there are cases , for example when either NL refraction or absorption are dominant, that you cannot do that without ambiguity, so that is why it is customary to run the open z-scan to get the NL absorption parameters first, and then used them in the closed-aperture results. Experimentally all you need is a beam splitter in the far field, and an extra detector yo obtain both the open and closed-zscan traces at the same time

Your results are quite convincing. From your analysis, it is quite evident that Matlab alone can provide the required parameters. As you said, most of the works pertain to Open Z-scan measurements. May be Open Z scan provide more constraints than the other one.

Regards,

Dear Dr.Rajib Biswas and colleagues,

I have clearly explained this method in the presentation:

https://www.researchgate.net/publication/323069521_A_comparison_of_third_order_nonlinear_parameters_n2_and_b_calculated_by_closed_aperture_Z-scan_data_open_aperture_Z-scan_data_AND_closed_aperture_Z-scan_data_Matlab

I think when nonlinear refraction is dominant, you can extract the nonlinear parameters from the closed z-scan with some confidence. However, there are cases , for example when either NL refraction or absorption are dominant, that you cannot do that without ambiguity, so that is why it is customary to run the open z-scan to get the NL absorption parameters first, and then used them in the closed-aperture results. Experimentally all you need is a beam splitter in the far field, and an extra detector yo obtain both the open and closed-zscan traces at the same time

Dear Dr.Raul Rangel-Rojo ,

Thank you for your answer.

In the work of Prof.Sheik-Bahae et al [1], the authors suggest that we can use computer fits to calculate nonlinear refractive indices and nonlinear absorption coefficients, but these methods are complex . However, computer fits methods are consistent with my experimental conditions. Therefore, we have studied computer fits as well as the numerical methods for analyzing Z-scan data. We found that the result calculated from closed aperture Z-scan data+ matlab are in excellent agreement with the results calculated from the closed Z-scan data+ open-aperture Z-scan data. In addition, in some Z-scan methods such as beam radius based Z-scan [2], if the open-aperture Z-scan measurement is required, in addition to the two detectors in the traditional Z-scan, the experimental setup need more Laser Beam Profiler. Such experimental setup will be more complex and costly.

[1] Sheik-Bahae, M., Said, A. A., Wei, T. H., Hagan, D. J., & Van Stryland, E. W. (1990). Sensitive measurement of optical nonlinearities using a single beam. IEEE journal of quantum electronics, 26(4), 760-769.

[2] Tsigaridas, G., Fakis, M., Polyzos, I., Persephonis, P., & Giannetas, V. (2003). Z-scan technique through beam radius measurements. Applied Physics B, 76(1), 83-86.

Dear Nguyễn Thanh Lâm,

It is a nice idea to explore the asymmetry of the closed-aperture Z-scan to separate the Nonlinear Index Refraction (Real X(3)) and the nonlinear absorption (Im X(3)) contributions without the necessity of two arms (beam split).

However, there are different artifacts in the experimental setup that introduce asymmetry in the Z-scan curves as well, that maybe you are not considering in your discussion.

1. The closed aperture position. The Z-scan curve symmetry is extremely sensitive to the aperture position (x-y plane), aperture shifts of a few micrometers can introduce peak intensity variations around 20% (in the peak or the valley). The same artifact is still more critical if you are in the Eclipse-Zscan Variation.

2. A non-perfect Gaussian Beam. Although nowadays the laser has a nice quality of the Gaussian profile, it is inevitable to introduce wavefront distortions (ex. astigmatism, coma) in the experimental setup.

If you are measuring samples for Optical Switching applications, it is quite common to be in a condition of a small nonlinear absorption (almost null) and a considerable self-defocus effect, in that case both artifacts plays an important role in the measurement quality, they are avoided using the open-aperture setup.

Cheers,

Diego R.

Dear Dr. Diego Rativa,

Thanks for your great answer. I also performed beam radius based Z-scan experiment with the same setup as open-aperture setup [1]. I think that under such experimental conditions, the artifacts you mentioned above can be avoided.

[1] Z -scan technique through beam radius measurements

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

Dear Nguyễn Thanh Lâm,

I´m in total agreement.

However, in the conventional z-scan using a closed-aperture (blocking most of the beam) you can obtain a sensitivity of lambda/300 for the wavefront distortion (self-defocus), and more sensitive with the variation eclipse Z-scan (4 -10 times more sensitive).

Using a CCD camera or analyzing all the laser beam, much of the intensity variations are masked by (almost) saturated detectors, reducing dramatically the sensitivity of the technique.

In that case, measuring by using a webcam, it should be easier to measure the area under the histogram curve of the images, you can obtain the total intensity for different "z" positions (absorption), without get worried with the symmetry of the self-focus curve.

Thank you very much for your useful information, Dr.Diego Rativa.