Matrix treatment for the correlation between intensity fluctuations of light waves on weak scattering from a...

We report a new approach to the correlation between intensity fluctuations (CIF) of light waves on weak scattering from a collection of particles with L types. Two L×L matrices called a pair-potential matrix (PPM) and a pair-structure matrix (PSM) are introduced to jointly formulate the CIF of the scattered field for the first time. We show that the CIF equals the squared modulus of the trace of the product of the PSM and the transpose of the PPM, and thus these two matrices provide sufficient amount of information to determine the CIF of the scattered field. Based on this, we further analyze the normalized version of the CIF of the scattered field. It is found that the expression of the normalized CIF can have pretty compact and profound forms in three special cases: (I) the spatial distributions of the scattering potentials of particles of different types are similar (II) the spatial distributions of the densities of particles of different types are similar (III) both the scattering potentials and the densities of particles of different types are similarly distributed in space. Finally, the effects of the off-diagonal elements of the PPM and the PSM on the normalized CIF of the scattered field are illustrated by two examples. The results show that the non-zero cross correlation between particles of different types can induce intense changes in the normalized CIF of the scattered field.