# Complex permeability and permittivity

1. Apr 4, 2012

### M.Eng

Hello All,

I have a question regarding complex permeability and permittivity, in particular, regarding their use with the complex refractive index in Mie theory.

If the material is not dielectric, the permeability/permittivity needs to be accounted for while calculating the scattering coefficients. I have the material properties (complex refractive index and complex dielectric function) at the given wavelength. Yet, I do not have the complex permittivity or permeability. I know you can use LLG equation and derive the complex permeability, but I was wondering if there was an alternative way.

Or let's say that since I do have this complex refractive index, can I simply ignore the relative permeability in the scattering coefficients? My logic says no since some materials could have a permeability of several thousand or more. I checked Kittel, Jackson, and even my trusted source in anything related to physics, Landau's books. Unless I missed something, I could not find something helpful.

Can someone start me along the right path perhaps??

2. Apr 5, 2012

### DrDu

How can a material not be dielectric but have a permittivity?

At optical frequencies, permeability is encoded in the wavenumber dependence of the dielectric tensor. In lowest order, this is taken care off by the distinction between longitudinal and transversal dielectric constant. I wonder that you did not find anything in Landau, as he discusses it at length in "Electrodynamics of continua".

3. Apr 9, 2012

### M.Eng

DrDu,

Thank you for your reply. Upon your instructions, I actually revisited Electrodynamics of Continua and found what I was looking for. Additionally, I went ahead and did a numerical/asymptotic solutions for the LLG equations and found the value of the permeability I needed.