Unraveling interference contributions to light scattering from concentrated colloids: A numerical study using density expansion

In dense colloidal suspensions, far-field interference between electric fields scattered by particles significantly influences light scattering properties. Previous studies using dependent scattering theory (DST), based on the first-order solution of the Foldy-Lax equations, have shown that destructive interference affects the scattering properties via the static structure factor. Meanwhile, the contributions of multiple interference and the relationship between interference and particle correlation remain unclear. We aim to clarify the interference effects and their relationship using a density expansion approach, which allows us to decompose the multiple interference contributions. We calculated the two scattering coefficients using the DST and the expansions with hard-sphere interaction in the volume fraction range up to 25% and the optical wavelength range of 600-1000 nm. Our numerical calculations showed that for particle diameters larger than approximately 300 nm, the second-order expansion for the reduced scattering coefficient agrees well with the DST results. This result reflects the destructive interference induced by the excluded volume between particles. For the scattering coefficient, the third-order expansion agrees with the DST results in the larger-diameter region. This agreement reveals a hidden constructive-interference contribution driven by an effective attractive interaction, even in the absence of any direct attractive force. For smaller diameters, higher-order expansions are necessary to accurately reproduce the DST results, as multiple interference contributions are involved. For the scattering coefficient, odd-order terms of expansion correspond to destructive interference, while even-order terms correspond to constructive interference. In contrast, the correspondence in the reduced scattering coefficient is more complex and depends on both particle diameter and wavelength. Our findings provide fundamental knowledge for developing nanotechnology to evaluate colloidal particle properties non-destructively using scattered light. • Analytic decomposition of interference in light scattering via density expansion. • Calculations of the scattering coefficients using the electromagnetic theory. • Small particle size case enhances the multiple interference in the coefficients. • This decomposition approach unveils hidden constructive interference. • Constructive interference correlates with the effective attraction between particles.