nonlinear refractive index is independent of sample thickness as like linear refractive index. origin of nonlinear refractive index comes due to enharmonic nature of light mater interaction. for more detail you can see the nonlinear optics book by Robert W Boyd (he has shown how the non linearity cames in the refractive index from Lorenz model). In experiments like z-scan, we measure the nonlinear refractive index by phase distortion in the beam, were we will use the optical path length contributed by linear and nonlinear refractive indices (optical path length=(n0+∆n(I))L)

Yes, nonlinear refractive index is a feature of material, and, in general, does not depend on dimensions of material. But conversion efficiency is a characteristic of process and depends on many parameters, in particular, on interaction length, light power, nonlinear refraction index, etc.

Third order nonlinear susceptibility is independent of the sample dimensionality, hence both absorption and refractive indices also the same. These properties may change with excitation source parameters like pulse width, repetition rate of the lasers due to contributions of various nonlinear effects.

Conversion efficiency of the second harmonic generation depends upon the various factor such as phase matching angle, strength of NLO response of the material as well as crystal thickness.

Comments and suggestions are welcome!!!!!!

Hello colleague,

I think that the nonlinear refractive index is nearly constant in the material sample, because the typical conversion efficiency of third-harmonic generation is relatively small.

Dependence on the square of sample length of the conversion efficiency has been derived with the pump depletion being negligible or no pump depletion approximation, and therefore the characteristics of the square dependence means that the conversion efficiency is small.

For very high peak power optical pulse pumping and high conversion efficiency, I think that the nonlinear refractive index may vary as the material sample length increases.

The details are quantitatively described in the attached file, NLRindex.pdf.

Please find the file, NLRindex.pdf.

I wish the details helpful to you. 

Hi,

In optics, indices are defined as to be intrinsic characteristics of materials, to be geometry invariant.

The conversion efficiency, the intensity of the light converted  after some propagation along a length L, depends on this length. For second harmonic generation it varies as the square of this length while it changes as the cube for third harmonic generation.

This is clearly demonstrated in Zung-Shik Suh paper above.

You could read also:

« Femtosecond laser pulses », 2nd edition, C. Rullière Ed., Springer Verlag, 2003. Page 38-55.

So that, even if your reasoning is not right, the final result is right: if you double the thickness of a doubling crystal the second harmonic generation is multiplied by 4.

First of all, I would like to thank Prof. A S V Rao, Aleksandr A. Tarasov,  Sudhakar Reddy Bongu, Charles Hirlimann, especially Prof. Zung-Shik Suh. We appreciate the valuable comments from you. Through discussion and attached file of Prof. Zung-Shik Suh, I totally agree  that nonlinear refractive index is independent of sample thickness .

However, I and another authors measured the nonlinear refractive index (due to thermal nonlinear optical effect) of same organic sample by CW He-Ne laser 632 nm.  The sample which he et al used in their work had a thickness  (length) of 2 mm, He-Ne laser 3 mW and we used 1 mm thick sample,  He-Ne laser 3,6 mW. But, nonlinear refractive index measured by him is 2,89 times larger than that measured by us.

The method we used is Z -scan technique through beam radius measurements (Prof.Georgios N Tsigaridas et al), while he used transmittance Z-scan (Prof.Sheik-Bahae et al). However, according Prof.Georgios N Tsigaridas et al, authors of Z -scan technique through beam radius measurements, both of techniques give same result on standard nonlinear optical sample CS2. So we think that the difference between two above nonlinear refractive indexes  does not result from  difference in techniques. We do not understand the reason of this too large difference and need to comment further on the results from you. Thank you again.

Dear Lam Thanh Nguyen,

You did not indicate, which kind of crystals you study. May be the difference in the measured data results from different or incompleted orientation of  crystal samples ?

For example, ferroelectric crystals, like KTP, require monodomenization, otherwise effective nonlinearlity reduces. For liquid crystals we must be very careful with surface induced orientation, especially for thick (2 mm) samples.

Hello colleague,

Please let me know more details on your experiments on the measurement of the nonlinear refractive index: the experimental scheme, apparatus, organic sample, etc...

I would also like to know the details of thermal nonlinear optical effect you mentioned, and the paper of prof. Georgios N Tsigaridas et al. is available(in the form of file) ?

Dear Prof. Zung-Shik Suh and Prof. Aleksandr A. Tarasov,

We measured the nonlinear optical index of organic solution (Acid Blue 29 + ethanol, concentration 0.05 mM ) in 1 mm cuvette by CW He-Ne laser, waist w0= 34,7 micro meter through beam radius Z-scan (attached file). He-Ne laser in my lab had maximum power output 10 mW. However, It’s lifetime is over twenty years old, so, power is decreased to 3,6 mW. Thank you for your comments.

Hello colleague,

I wonder if the experimental measurements of the team with the 2[mm] sample violate the fundamental assumption of the z-scan technique.

More details are in the attached file, NLRindex2.pdf.

Please find the file, NLRindex2.pdf.

Dear Prof.Zung-Shik Suh,

Thank you for your helpful comments. I will discuss with this team about Experimental setup.

Best regard.

I agree with ASV Rao. Convential definitions state, that the nonlinear refractive is a material parameter and does not depend on on the sample thickness.

However, it may be that you evaluate from your experiment a nonlinear refractice which depends on the length. If the happens, the theoretical model you used for evaluation of your data is not correct, probably.

Bonjour,

The Z-scan technique is a simple way for measuring the non-linear index of refraction and the non-linear absorption. It is a tricky technique though, sensitive to the translation misalignment with the beam axis, as well as to the beam geometry. The result of the measurement can be totally spoiled out when the beam is not strictly Gaussian, or if the Gaussian beam axis is tilted against the translation axis.

I would suggest you to perform the following three measurements: closed aperture, open aperture, beam diameter measurement and check the coherence of the results. You mentioned non-linear thermal effect. From the measurements you should also calculate the non-linear absorption coefficient.

Perhaps more important. Acid blue 29 strongly absorbs the 632.8 nm red light of He-Ne lasers. So you should expect a strong linear absorption. How do you distinguish the linear and non-linear absorption contribution to the beam changes?

Please find joined a nice paper on Z-scan.

Thank Prof.Hans Joachim Eichler for your helpful comments And thank Prof.Charles Hirlimann for sending me paper. I think that the difference maybe come from the instability of intensity I0 and we must measure accurately the value of the beam intensity (through maximum power output) again.

Dear Dr. Lam Thanh Nguyen

The nonlinear optical response can occur when there is a sufficiently intense illumination. The non-linearity is exhibited in the polarization of the material, which is often represented by a power series expansion of the total applied optical field. The third-order nonlinear optical susceptibility can be evaluated from the following equation:

                                                 Exi3 = B((n2 - 1)/ 4Pi)4                                    

where B is a constant value for all materials equals to 1.7 x 10-10 esu and is neither dependent upon the frequency nor the thickness of the sample, while n is the refractive index of samples which is independent also upon the length or the thickness of samples.

For more detail please see the appended articles

Good luck.

https://www.researchgate.net/publication/294426798_Studies_on_dielectric_properties_opto-electrical_parameters_and_electronic_polarizability_of_thermally_evaporated_amorphous_Cd50S50-xSex_thin_films

https://www.researchgate.net/publication/304150361_Study_of_optical_properties_of_thermally_evaporated_ZnSe_thin_films_annealed_at_different_pulsed_laser_powers

Article Studies on dielectric properties, opto-electrical parameters...

Article Study of optical properties of thermally evaporated ZnSe thi...

 Dear Prof. Lam Thanh

Thank you very much for your recommendations for my answer and my articles.

Thanks a lot Dr.

You're welcome, Prof.Ahmed Saeed Hassanien.

Dear doctors,

Kindly, I want to extend the question from the experimental phase to the theoretical phase. The question is: what is the Relation between the nonlinear refractive index and third-order susceptibility?

For example that is obtained in the following paper "

All-optical flip-flop circuit composed of coupled two-port resonant tunneling filter in two-dimensional photonic crystal slab"

(i.e. how the parameter n2 is calculated on page 2?).

Thanks

Tamer S. Mostafa

[email protected]