MATLAB Source Code for Mie Theory with Application to Light Scattering by Metal Nanoparticles

Mie theory is a rigorous analytical method for describing electromagnetic wave scattering by spherical particles, particularly suitable for systems like metal nanoparticles where the particle size is comparable to the incident light wavelength. Through exact solutions of Maxwell's equations, this theory can calculate key optical parameters including scattering fields, absorption cross-sections, and extinction cross-sections. In light scattering studies of metal nanoparticles, the core of Mie theory lies in handling the dielectric function's dependence on particle size. For noble metal nanoparticles like gold and silver, one must account for dielectric function modifications due to size effects. The theoretical calculation involves key steps: first establishing electromagnetic field equations in spherical coordinates, then solving for coefficients of Bessel and Hankel functions through boundary condition matching, and finally obtaining analytical expressions for scattering coefficients. MATLAB serves as an ideal numerical computation tool for implementing Mie theory solutions. A typical implementation workflow includes: defining the incident light wavelength range, inputting particle dielectric constant parameters, calculating size parameters and relative refractive indices, constructing recursive computation modules for Bessel functions, and finally obtaining results like scattering efficiency through summation operations. The program can optimize computational efficiency through vectorized operations, particularly when handling batch calculations such as wavelength scans. Key MATLAB functions involved would include besselj() for Bessel functions, proper array indexing for recursive calculations, and vectorized operations for efficient parameter sweeps. Three technical details require attention in practical applications: First, the frequency dispersion relationship of metal dielectric constants should use experimental measurement data or the Drude model. Second, for larger size parameters, improved algorithms are needed to avoid numerical instability through techniques like logarithmic derivative methods. Third, the truncation order of multipole expansions must be properly selected based on accuracy requirements, typically determined by the size parameter magnitude. This theoretical model holds significant application value in surface-enhanced Raman spectroscopy, plasmonic sensors, and nanophotonic devices. By modifying geometric and material parameters of particles, researchers can study optical response characteristics of different nanostructures, providing theoretical guidance for nanophotonic device design. The MATLAB implementation allows parameterization of particle size, material properties, and wavelength ranges for systematic optical property analysis.