# Mie scattering simulation

### Mie Scattering: theory

Mie theory describes the electromagnetic fields inside and outside a dielectric sphere illuminated by a plane, monochromatic wave. It can be used to calculate the scattered fields when a sphere is interacting with electromagnetic radiation. The scattered fields are given as functions of the angles θ and φ, with &theta and &phi defined as in the scheme below.

### Simulation

The scattered fields are calculated using this C Code for Mie scattering simulation. The code implements two Fortran functions from SLATEC to calculate the Bessel function of complex arguments. The implementation was done by writing wrapper functions (see here for more details).

### Parameters

The parameters needed to describe the physical model are:

• The (complex) refractive index $m_{med}$ of the medium
• The (complex) refractive index $m_{sph}$ of the sphere
• The radius $R_0$ of the sphere
• The wavelength λ of the incoming plane wave

### Results

The simulation reports the values of $|S1|^2$ and $|S2|^2$
$|S1|^2 \sin^2(\phi)$ is proportional the intensity of the scattered field orthogonal to the scattering plane
$|S2|^2 \cos^2(\phi)$ is proportional the intensity of the scattered field parallel to the scattering plane
The simulation was performed using the following parameters:

$m_{med}=1.3 + 0i$
$m_{sph}=2 + 0.1i$
$R_0=10$ μm
λ=920 nm

With these parameters, the scattering is mostly in the forward direction.