MATLAB Implementation for Mie Scattering Calculation

Mie scattering is a fundamental theory for studying light interaction with microscopic particles, widely applied in atmospheric optics, nanomaterials, and biomedical fields. Based on user requirements for MATLAB implementation, this section introduces core computational concepts and key parameter processing methods.

Basic Theoretical Framework The core of Mie scattering calculation involves solving analytical solutions of Maxwell's equations under spherical particle boundary conditions, requiring handling of these key parameters: Size parameter x=2πa/λ (where a is particle radius, λ is incident light wavelength) Complex refractive index m=n+ik (n being the real refractive index part, k representing the extinction coefficient)

Calculation Process Breakdown Typical MATLAB implementation includes these steps: (1) Calculate relative size parameters through input wavelength, particle size, and medium refractive index (2) Iteratively solve coefficients for Bessel and Hankel functions using series expansion methods (3) Compute key indicators like scattering efficiency Qsca and absorption efficiency Qabs through series summation (4) Handle complex refractive index by separately calculating real and imaginary parts' effects on scattering fields

Numerical Optimization Points Series truncation: Automatically determine calculation terms using Wiscombe's criterion Large parameter handling: Apply asymptotic formulas for x>100 cases to prevent numerical overflow Vectorization operations: Utilize MATLAB matrix operations to enhance complex number computation efficiency

Result Visualization Extensions Calculation programs typically output: Angular distribution of scattering intensity (polar plots) Extinction spectra curves at different wavelengths Trends of efficiency factors versus size parameters

This implementation requires special attention to energy absorption effects caused by the imaginary part of complex refractive index, and special phenomena like surface plasmon resonance at nanoscale. For polydisperse systems, integral calculations combining particle size distribution functions are necessary.