Hanbury Brown-Twiss effect with electromagnetic scattered field generated by a collection of particles of $\mathcal{L}$ types

A theoretical framework in the spherical polar coordinate system is developed to systematically treat the correlation between intensity fluctuations (CIF) of electromagnetic light waves on scattering from a collection of particles of $\mathcal{L}$ types. Two $\mathcal{L}\times \mathcal{L}$ matrices called pair-potential matrix (PPM) and pair-structure matrix (PSM) are introduced to jointly formulate the normalized CIF of the scattered field for the first time. We build a closed-form relation that associates the normalized CIF with the PPM and the PSM as well as the spectral degree of polarization $\mathcal{P}$ of the incident field, showing that the normalized CIF is closely related to the trace of the product of the PSM and the transpose of the PPM, and its dependence on $\mathcal{P}$ is completely determined by the scattering polar angle and azimuth angle. For a special case where the spatial distributions of scattering potentials of particles of different types are similar and the same is true of their density distributions, the PPM and the PSM will reduce to two new matrices whose elements separately quantify the degree of angular correlation of the scattering potentials of particles and their density distributions, and the number of species of particles in this special case appears as a scaled factor to ensure the normalization of the CIF. The effects of the off-diagonal elements of the PPM and the PSM on the normalized CIF and its dependence on $\mathcal{P}$ are illustrated by two numerical examples.