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

While passing laser radiation through a crystal, local temperature increases also increases local energy  inside the material. Due fact spatial distribution of intensity formed in crystal as a result  spatial distribution of refractive index is formed inside the crystal. In some cryatals along axis intensity of beam will be maximum due to high refractive index compared with other places in the material. So this self focussing effect was only due to high intense laser beam. Without laser one can't make material to act like focusing lens.

Dear Prof.Krishnakumar Muthusamy,

So, from your point of view, these effects are nonlinear optics effecs.

I don't know enough about the materials you are dealing with to say one way or another, but I think there are some experimental paths that could clarify the situation.

In principle, you should be able to estimate thermal changes in linear index of refraction by using constant, low intensity probe and externally heating the sample to various temperatures.

If you know absorption (and let's assume, for the moment, that absorption itself is linear, and doesn't involve multi-photon or cooperative absorption processes), then you should be able to estimate local heating due to absorption, and with previous data thus estimate the thermal lensing effect. If it is insufficient to explain the amount of lensing observed at high intensities, you may be dealing with a non-trivial non-linear refractive index.

You might also explore process dynamics:

n2 has a polynomial dependence on intensity. Thermal lensing should, more or less, scale linearly with intensity.

In another way, n2 is instantaneous (in effect - the time scales are extremely fast), while thermal lensing might display some much longer time constant. For example, if you are dealing with a pulsed source, then if n2 dominates, then every pulse will look identical. If thermal effects dominate, you might observe a monotonic amplification of the effect from pulse to pulse.

In all of these cases, we are assuming that absorption itself is linear. How assured are you of this assumption for your material?

Dear Prof.Boris L. Glebov,

Thank you for your answers. We are studying some organic materials such as Oil Red O in paper of Prof.Rekha, Acid blue 29 and Aniline Blue.

What kind of power densities are you achieving with your illumination?

Intensity of Laser in my work is 13.1 W/mm^2, waist 26 micro met, Rayleigh length 4 mm.

I come at these questions and answers from an entirely different background and perspective, knowing essentially nothing of too much. ;-) But I did win (not to brag, but to share some of where I've been) the Data Art category of this >https://www.lpl.arizona.edu/art> art show&contest, and you can see my display at . The winning image is at , but I've learned a great deal since that image was created.

Without giving away too much about results that I am currently working into a paper for possible publication, I can say: Via statistical modeling I have been able to filter out results that seem to be attributable to the play of heat and light in the samples, so as better to be able to map the probability levels of the RI signals themselves. I hope that my results might provide insights for others who know much more about lasers and such as Raman Spectroscopy that I ever will. I have used a mere student-model petrographic microscope that was modified closely to hold chosen stage Temperatures, together with monochromatic visual-light illumination that seems to induce low-power lasing.

All best wishes, -Steve-

Please forgive the typo; this works:

-Steve-

At least in optical materials, a rule of thumb for Kerr-type nonlinearities is power density of 1 MW / cm2. You are well short of that. I'm going to guess you're mostly looking at thermal lensing.

Dear Prof.Boris L. Glebov,

Thank you for your reply. It was very kind of you. And I understand what you say. I agree with you entirely.

However, in my work, I don't focus on Kerr-type nonlinearities, I focus on thermal lesing-type nonlinearities of organic with CW laser for opptical limitting applacations. Then, I want to know differences differences between absorption in thermal lesing-type nonlinearities and trivial absorption in material such as glass, Orange G. As far as I know, Orange G also absorb strongly 532 nm but thermal lesing effect don't occur in Orange G when illuminating by my Green laser.

I discussed this issue with Prof.Svetlana Lukishova. Prof.Svetlana Lukishova suppose that:"Your effects is definitely NONLINEAR, this is thermal self-focusing, nonlinear effect. Many years ago Akhmanov and Khokhlov wrote a theoretical review on thermal self-focusing."

Besides, if they are not important, why are there  many works focus on them?

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.

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It is clear you have a thermal effect that manifests as a change in refractive index due to the application of a light field. In this sense it is a nonlinear effect, exactly the same as one produced by electronic response. The only difference is the response time, which is going to be governed by thermal diffusion, which is slow. For this reason, it is important when reporting the nonlinear response of a material, to clarify whether it is thermal or electronic (or a mixture of both) in origin. Even using fs pulses a thermal response can be present (see: B. Can-Uc, R. Rangel-Rojo, L. Rodriguez-Fernandez, and A. Oliver, "Polarization selectable nonlinearities in elongated silver nanoparticles embedded in silica," Opt. Mater. Express 3, 2012-2021 (2013))

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