Depolarized correlation function of light double scattered from a system of Brownian particles

We consider the multiply scattered electric field from a system of noninteracting Brownian scatterers. We show that the lowest-order contribution to the depolarized correlation spectrum of the scattered light is due to double scattering. We find an expression in the far-field approximation for the electric-field correlation function double scattered from a system of pointlike particles. We show that while the correlation function is slightly nonexponential, the $t=0\mathrm{}$ slope of the correlation function is independent of scattering angle and equal to the single scattered correlation time corresponding to a scattering angle of 180°. We then generalize our result to include larger, Rayleigh-Debye particles of radius $l\lesssim \lambda$ where $\lambda$ is the wavelength of the incident light. The results for larger particles are qualitatively similar to those for pointlike particles in that there is a lack of a large scattering-angle dependence in the correlation time of the double-scattered light, and the magnitude of the correlation time is slightly greater than the correlation time for single-scattered light at 180°. We then perform intensity autocorrelation experiments on two systems of polystyrene microspheres of radii $l=0.055\mathrm{} \mathrm{and} 0.117$ μm. We measure the depolarized scattered light correlation time and compare it to our theoretical results for double scattering. The agreement of theory and data is seen to be good. We discuss potential applications of this work to other phenomena.