Mie Theory Calculation for Spherical Particle Scattering Implemented in MATLAB

Mie scattering theory is a classical model describing how spherical particles scatter electromagnetic waves, with widespread applications in photonics, aerosol science, and biomedical optics. This MATLAB-based computational program implements the complete Mie theory solution process, accurately calculating scattering characteristics under various parameter conditions.

The core algorithm originates from Gustav Mie's 1908 analytical solution, primarily handling these key computational steps: First, it calculates the size parameter based on incident light wavelength, particle size, and refractive index. Then, it uses recurrence relations to solve ratios of Bessel functions and Hankel functions, ultimately obtaining scattering coefficients and extinction coefficients. The program outputs key parameters like scattering efficiency factors and absorption efficiency factors, which are crucial for analyzing particle-light interactions. The MATLAB implementation includes optimized recursive algorithms for calculating spherical Bessel functions and utilizes vectorization for efficient computation across multiple wavelength points.

In photonics applications, this Mie scattering calculation program is particularly suitable for simulating optical properties of nanoparticles, such as localized surface plasmon resonance effects in gold nanoparticles, or calculating light scattering patterns of biological cells. The program features optimized design with fast computation speed and excellent numerical stability, capable of handling broad spectral calculation requirements from ultraviolet to infrared wavelengths. The code incorporates stability checks for large size parameters and uses logarithmic derivatives to prevent numerical overflow in recursive calculations.

When using this program, researchers need only input four basic parameters: particle diameter, medium refractive index, environment refractive index, and incident wavelength. The program automatically completes all intermediate calculation steps and returns comprehensive scattering characteristic data. This convenience enables researchers to quickly evaluate particle scattering behaviors under different conditions, providing theoretical basis for optical device design and experimental scheme optimization. The MATLAB function includes parameter validation and automatically handles unit conversions between micrometers and nanometers for wavelength inputs.