I am trying to compute the effective permittivity and permeability of a nanoparticle and a coated nanoparticle. Let's say I have a nanoparticle and simulate the scattering from the nanoparticle for the incident plane polarized light using COMSOL. I can calculate the scattering cross section and absorption as a function of wavelength. But I also want to calculate effective relative permittivity and permeability (both real and imaginary) as a function of wavelength. How to proceed with that.

I have tried to calculate by calculating the volume average of Dz, Ez, By, Hy (incident light is polarized along z direction) and by using the formula epsilon_r = Dz/Ez and mu_r=By/Hy, but it is not working.

Can someone please advise me how to do the calculation? Any kind of help is greatly appreciated.