Alternative to Mie Theory for Analysis of Homogenous Sphere

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Ox2
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I know that mie theory is used to analyze the absorption/scattering/extinction of a homogeneous sphere within a homogeneous dielectric medium. However, if I wanted to perform the same analysis on a sphere enclosed by two different media, is there an analytic solution to this?
 
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How by two different media? Do the media form shells? Or the lower half in one medium, the upper half in another?
 
One half of the sphere is embedded in a substrate, and the upper half is in air/vaccum.
 
maybe if you add additional boundary conditions to the equations in 3.5.2 (link below) you can get a solution suited to your needs... otherwise derive from maxwell...

http://evan.ucsd.edu/class/sioc251/Lecture_Notes_files/mie_detailed.pdf