Alternative to Mie Theory for Analysis of Homogenous Sphere

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SUMMARY

The discussion centers on the limitations of Mie Theory for analyzing the absorption, scattering, and extinction of a homogeneous sphere when it is enclosed by two different media. Participants explore the possibility of applying additional boundary conditions to the equations outlined in section 3.5.2 of the provided lecture notes to derive an analytic solution. The scenario involves a sphere with its lower half embedded in a substrate and the upper half in air or vacuum. The conversation emphasizes the need to consider Maxwell's equations for a comprehensive solution.

PREREQUISITES
  • Understanding of Mie Theory and its applications in scattering analysis.
  • Familiarity with Maxwell's equations and boundary conditions.
  • Knowledge of dielectric media and their properties.
  • Basic concepts of electromagnetic wave propagation.
NEXT STEPS
  • Research methods for applying boundary conditions in electromagnetic theory.
  • Study the derivation of solutions for spheres in multilayer media.
  • Explore advanced topics in scattering theory beyond Mie Theory.
  • Investigate numerical simulations for complex geometries in optics.
USEFUL FOR

Researchers, physicists, and engineers working in optics, particularly those focused on scattering phenomena and the analysis of particles in heterogeneous media.

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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
 

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