The interaction of a core and different modes of a hollow shell in a core-shell structure can be modelled using Mie theory, which provides a mathematical framework for calculating the electromagnetic scattering properties of spherical particles. The basic Mie scattering theory describes the interaction between a plane wave and a single spherical particle, and the theory can be extended to consider the interaction between a core and multiple modes of a hollow shell by incorporating the appropriate boundary conditions for each layer of the structure. The resulting equations will depend on the specific geometry and material properties of the core and shell and may require numerical simulations to accurately predict the electromagnetic properties of the core-shell structure.

Mohsin Ali Marwat

As I have gone through some papers on this hybridization modes, I have found that there is a simple equation that can give modes for a hollow shell.

some groups have also carried out for multishelll and even for core-shell. For that first they have calculated modes of different shells and then found out the interaction.

But no where I have found the formulation to get particular wavelength.

I want to know how to get that equations which will give wavelengths of different coupled modes after interaction. I know the equation to calculate modes of plasmon for single hollow nanoparticle.