Dear Sumeet Sonvane ,

For the conversion of ß[m/W] --> ß[esu] you may have a look at page 5 equation (6) of:

Article Third-order nonlinear optical properties of the small-molecu...

The authors have taken the formula from ref [42] therein.

But unfortunately I found no full-text of that reference. You may have access via your institution...

You may also see for example eq. 4 on page 5 of:

Article Research on nonlinear absorption effect in KDP and 70%-DKDP crystals

These authors cite [16], [18] and [20] therein.

But only [16] has full-text (see eq. 6):

https://www.iosrjournals.org/iosr-jap/papers/Vol6-issue1/Version-1/G06114246.pdf

Good luck and

best regards

G.M.

Dear Sumeet Sonvane

In the nonlinear optics literature beta can be used for different physical quantities. The most common is the nonlinear (two photon) absorption coefficient that is a generalization of Beer's law I (z) = I_0*exp(-Beta*I_0*z), assuming small absorption. The conversion from SI units (m/W) to esu units (the cgs system) is a factor of 10^-9. See the Wikipedia article

https://en.wikipedia.org/wiki/Two-photon_absorption

Hope this helps

Best regards

Michael