i suggest this paper

Article Numerical Modeling of Sub-Wavelength Anti-Reflective Structu...

Dear Sir

I recommend the following article which may be useful for you

https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=911529

The mixing rules for the real part of the index of refraction hold for the complex quanitity and thus for the imaginary part as well (or as bad). The problem is that this is a very complex problem without a clear solution. The names that are connected with this problem are Gladstone-Dale (Arago-Biot), Newton-Lagrange, Lorentz-Lorenz (Clausius-Mossotti), Maxwell-Garnett, Bruggeman, Loyenga... and there are nearly as many different models as names. If you want an overview I suggest Article Mixing Rules with Complex Dielectric Coefficient

Mahdi Motamedi

The Kramers–Kronig relations are mathematical relations, connecting the real and imaginary parts of any complex function. So, if we know the real part of the RI over sufficient part of the optical spectrum, we can calculate the imaginary component. It is the same as the Hilbert transformation and there is a Matlab function ‘Hilbert' for Hilbert transformation of discrete data

http://photonics.intec.ugent.be/education/IVPV/res_handbook/v2ch33.pdf

Also see:

P Kubelka F Munk (1931) "Ein beitrag zur optik der farbanstriche," Z. Tech. Phys. (Leipzig) 12, 593-601

Translation: An Article on Optics of Paint Layers Paul Kubelka Franz Munk August, 1931: http://www.graphics.cornell.edu/~westin/pubs/kubelka.pdf

and:

Kramers-Kronig Relations in Optical Materials Research Valerio Lucarini, Jarkko J. Saarinen, Kai-Erik Peiponen, Erik M. Vartiainen Springer-Verlag Berlin and Heidelberg GmbH Co. KG, Germany (2010)