Numerical Simulation of Mie Scattering

Mie scattering refers to the scattering phenomenon that occurs when light or electromagnetic waves encounter spherical particles, with wide applications in atmospheric science, biomedical fields, and nanomaterials. Numerical simulation of Mie scattering enables in-depth investigation of key parameters such as scattering intensity, angular distribution, and scattering coefficients.

Scattering intensity describes the energy distribution of scattered light in different directions, which is closely related to the wavelength of incident light, particle size, and refractive index. Numerical computation helps quantify how scattering intensity varies with scattering angle, typically analyzed across a 0° to 180° range where forward and backward scattering regions are of primary interest. Code implementations often calculate angular distributions using Legendre polynomial expansions and Bessel function evaluations through iterative algorithms.

Scattering coefficients measure the efficiency of scattering processes, including scattering cross-sections and extinction cross-sections. These parameters are derived from complex coefficient expansions in Mie theory, involving sophisticated mathematical functions like Bessel functions and Legendre polynomials. Numerical methods such as recurrence algorithms or Fast Fourier Transforms (FFT) are commonly employed to efficiently solve these equations, with implementations often optimizing computational loops for harmonic series convergence.

Through numerical simulation, researchers can model Mie scattering under varying conditions—such as adjusting particle size or incident wavelength—to optimize experimental designs or validate theoretical models. This simulation approach serves as a vital tool for understanding and predicting real-world scattering behavior, typically implemented through modular code structures separating core calculations from parameter sweeps and visualization routines.