beta (nonlinear absorption coefficient) and chi3 are the material intrinsic properties. These two parameters are constant with respect to intensity, concentration and sample thickness. However they will change with respect to the excitation wavelength.

For same material and excitation wavelength, these two parameters can differ when comparing between the solution and solid phases.

Thank you Akbar..

What about Is, do you think it will change.

According to your answer it should change then only bet and Chi3 can be intrinsic because of Is=-alp0/Beta

Also we can see in this attached paper. Variation in Beta with RB concentration at constant excitation and iraadiance.

All these coefficients change with material concentration (if you are speaking about the final values for the mixed material). χ(3) is proportional to β, while Is is just the relation between two coefficients: Is=-α0/β.

Thanks, Solnsev

But as mentioned above Akbar ali, he is saying that Beta and Chi3 are independent on the sample concentration and thickness of the samples? Recently I got one reviewer comments in that he mentioned all alpha, Is, Beta and Chi3 are intrinsic properties of the material. I don,t know how can he say that.

In my opinion your answer is correct and can explain correctly based on the theory.

β = -Delta (Si)/(I0*Leff)

Let us consider two case one low and one higher concentration

For lower concentration case:

OD low>>Alpha low>>Leff is more

At same I0 low concentration molecules shows low SA beviour So Delta (Si) from Z-scan fitting come low.

For High concentration case:

OD high>>Alpha high>>Leff is lower than previous case

And more SA behaviour giving higer Delta (Si),

Here, Delta (Si) more and denominator leff is low gives more B that the previous one.

Note: take in both the cases I0 is constant

Then how can Beta become same in two case?

If I am the wrong please correct me?

Chi3 is the intrinsic property of the material, but when you mix your material with something else, the total effective Chi3 of the mixture will change and in turn change beta. I am not familiar with the formula in your last reply.

All the quantities you are mentioning are intrinsic quantities that are only dependant on the material they characterize.

They have been explicitly designed to be constants that do not depend on the thickness, concentration. What depends on these parameters is the extinction (absorption +  diffusion + diffraction of light) of a sample, the quantity of light that does not cross the sample. There is then a diffusion coefficient that is also intrinsic.

The absorption in itself contains the absorption coefficient and the length of the medium, but also quantities that depend on the solvent and the solute in the case of gases and liquids.

The absorption of light is the result of the promotion of an electron of the medium to an upper level, the kinetic energy of light is changed into potential energy of electrons. The number of electrons in the lower level is finite. When the intensity of light is large enough the electrons falling down back to the lower level can be excited up again with no delay: there are more photon present than absorbing electrons and the medium becomes partly transparent again (bleaching). Is is a parameter measuring the number of photons necessary for starting the dynamical bleaching process.

For even higher light intensities the probability for two photons to impinge a material at the same time becomes significant. Then light can then be absorbed in a transparent material, the energy of two photons being changed into the potential energy of a unique electron promoted to an upper level. This effect is characterized by a two photon absorption coefficient. This two photon absorption can also saturate when the intensity of light still increases provided the material is not destroyed, see joined file.

Hope it helped you.

Thanks, Charles

You said all the quantities are intrinsic.  Lets come to the linear absorption coefficient

Which is given by α0 = O.D/path length. Here optical density proportional to the concentration of the sample. Consider path length is constant. My question is if I change the concentration of the sample how can α0 becomes constant. As I know molar extinction coefficient of the samples is constant but not the linear absorption coefficient. If I am the wrong please correct me.

Dear Sudhakar,

your equation is the definition of the optical density from the Beer-Lambert equation for a solid. For liquids and gases the equation writes as :

I/I0 = exp-(a0.C.x), a0 is the intrinsic molar absorptivity, C the molar concentration, and x the path-length.

a0 is intrinsic of a material and it depends on the wavelength of the light used for the measurement. Two solutions of a same compound with two different concentrations are two different materials.

Could that answer your question?