How can I calculate the complex refractive index of non absorbing nanoparticles in an absorbing medium?
You can try FDTD software. My understanding is that there are several free codes available. That will be a brute force approach. Some codes break or don't handle evanescent waves well. This has probably gotten better since there has been a lot of interest in plasmonics lately.
Second option would be to calculate the transmission (absorption) and reflection as a function of wavelength, then use the krammer-kronig relation to obtain the refractive index.
In both cases I think the film needs to be thin, so there is sufficient light going through it for best results. If you are only going to measure reflection, you will need to measure both the energy and the phase of the signal.
This frames the question as an experimentalist, but should give some ideas how to approach from a math perspective.
In the limits of the nanoparticles being unfilled holes and when the nanoparticles match the real part of the dielectric constant, you should be able to see if the answers make sense.
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