Computational Analysis of Scattering in Spherical Shell Nanoparticles

The computational analysis of scattering in spherical shell nanoparticles involves the extension of electromagnetic scattering theory and Mie theory. Such problems hold significant value in fields including nanophotonics, optical sensing, and biomedical imaging.

Regarding fundamental principles, scattering analysis of spherical shell structures requires matching boundary conditions at multi-layer dielectric interfaces. Compared to homogeneous spheres, shell structures introduce additional refractive index interfaces, making analytical solutions for electromagnetic fields more complex. The core mathematical tool involves vector spherical harmonic expansions, where analytical expressions for scattering coefficients of various orders are obtained by solving Maxwell's equations in spherical coordinates.

Key parameters for computation include: inner/outer diameter dimensions, complex refractive indices of core-shell materials, and incident light wavelength. The construction of scattering coefficient matrices primarily involves recursive algorithms for calculating Mie coefficients, followed by series summation to obtain scattering field distributions. Extinction and absorption coefficients can be derived from specific combinations of scattering coefficient matrices, representing the particle's overall attenuation of incident light and internal absorption capacity respectively.

MATLAB implementation offers distinct advantages for such calculations due to its powerful matrix operations and extensive special function libraries. A typical program structure includes several core modules: parameter preprocessing, recursive computation module, field synthesis module, and visualization module. During debugging, special attention must be paid to series convergence and numerical stability issues, particularly for large size parameters or strongly absorbing materials.

In practical applications, these calculations can predict optical response characteristics of nanoparticles, guiding material design and experimental optimization. By adjusting shell thickness and material combinations, precise control over scattering properties can be achieved, which is particularly important in surface-enhanced spectroscopy and targeted therapy scenarios.