Interference between two independent multi-mode thermal fields

We study the property of the field which is a mixing of two multi-mode thermal fields. We accomplish a general theoretical analysis and show that the mode of the mixed field, characterized by its intensity correlation function $g^{(2)}$, is determined by the two-photon interference between the two independent multi-mode thermal fields. Our analysis reveals that the mode structures of the two thermal fields play an important role in the interference. Comparing with $g^{(2)}$ for one of the individual field with less average mode number, $g^{(2)}$ of the mixed field always decreases due to the change of mode distribution, but the amount of drop depends on the relative overlap between the mode structures of the two thermal fields and their relative strength. Moreover, we verify the theoretical analysis by performing the experiments when the modes of two multi-mode thermal fields are identical, orthogonal and partially overlapped, respectively. The experimental results agree with theoretical predictions. Our investigation is useful for analyzing the signals carried by the intensity correlation of multi-mode thermal fields.