MATLAB Computation of Mie Scattering Coefficients

This text discusses Mie scattering coefficients and their MATLAB computational implementation. Mie scattering occurs when particle dimensions are comparable to the wavelength of incident light. Under these conditions, the three-dimensional distribution of charges within scattering particles must be considered. Scattering particles can be modeled as aggregates of complex molecules that form oscillating multipoles under the influence of incident electromagnetic fields. The electromagnetic waves radiated by these multipoles superimpose to form scattered waves. Since particle size is comparable to wavelength, the phase of the incident wave becomes non-uniform across the particle, creating spatial and temporal phase differences among secondary waves. At locations where scattered waves combine, interference patterns emerge due to these phase differences. These interference effects depend on the wavelength of incident light, particle size, refractive index, and scattering angle. As particle size increases, the interference effects causing variations in scattering intensity become more pronounced. Consequently, the relationship between scattering intensity and these parameters is more complex than Rayleigh scattering, requiring expression through infinite series with relatively slow convergence rates. This relationship was first derived by German scientist Gustav Mie, hence the phenomenon's name. MATLAB implementations typically utilize Bessel function expansions and recursive algorithms to handle the computational complexity of these series solutions.