Simulation of light scattering from a colloidal droplet using a polarized Monte Carlo method: application to the time-shift technique

This study is devoted to the development and application of a Monte Carlo ray-tracing model to simulate light scattering when a colloid suspension droplet passes through a highly focused Gaussian laser sheet. Within this study, a colloidal suspension droplet refers to a spherical droplet containing multiple spherical inclusions. Such scattering scenarios arise when using the time-shift measurement technique for particle sizing. The incident laser sheet is treated as a large number of polarized light rays: the Stokes vector of each light ray is tracked, achieved by multiplication of the rotation matrix and the Mueller matrix after each scattering event. For the Monte Carlo simulation of light scattering, a very important issue is to generate the deflection angle and azimuthal angle after each scattering event. The scattering from embedded inclusions is computed using the Lorenz-Mie theory and by employing the rejection sampling technique to update the new propagation direction. Multi-reflection and refraction within the droplet is accounted for, as is total reflection at the drop interface. For this, the Mueller matrix formulation is invoked at the drop surface to update the Stokes vector. To validate this simulation code, the scattering diagram from a nanoparticle is computed with this Monte Carlo method and compared with the scattering diagram computed with the Lorenz-Mie theory, the agreement is excellent. This Monte Carlo code is then applied to simulate signals arising from a time-shift device, when a colloid suspension droplet passes through a focused polarized laser sheet, with the objective of measuring the concentration of colloidal particles in the droplet. Measurements verify the ability of the code to properly simulate this light scattering scenario.