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I was wondering whether there is an equation that enables me to calculate the reflection, transmission, absorption and polarization, when the electric field everywhere is given?

Consider this: You have solved the full Mie scattering process, so incident field, the field in the sphere and the scattered field are known. How can one calculate those quantities then?

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For example, you can calculate absorption through integration of the Poynting vector over the surface of the sphere. I am not sure there are any standard general definitions of transmission and reflection for diffraction on a sphere.

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