We present the cross-correlation between the far-infrared background fluctuations as measured with the Herschel Space Observatory at 250, 350, and 500 {mu}m and the near-infrared background fluctuations with Spitzer Space Telescope at 3.6 {mu}m. The
cross-correlation between far and near-IR background anisotropies are detected such that the correlation coefficient at a few to ten arcminute angular scales decreases from 0.3 to 0.1 when the far-IR wavelength increases from 250 {mu}m to 500 {mu}m. We model the cross-correlation using a halo model with three components: (a) far-IR bright or dusty star-forming galaxies below the masking depth in Herschel maps, (b) near-IR faint galaxies below the masking depth at 3.6 {mu}m, and (c) intra-halo light, or diffuse stars in dark matter halos, that likely dominates fluctuations at 3.6 {mu}m. The model is able to reasonably reproduce the auto correlations at each of the far-IR wavelengths and at 3.6 {mu}m and their corresponding cross-correlations. While the far and near-IR auto-correlations are dominated by faint dusty, star-forming galaxies and intra-halo light, respectively, we find that roughly half of the cross-correlation between near and far-IR backgrounds is due to the same galaxies that remain unmasked at 3.6 {mu}m. The remaining signal in the cross-correlation is due to intra-halo light present in the same dark matter halos as those hosting the same faint and unmasked galaxies. In this model, the decrease in the cross-correlation signal from 250 {mu}m to 500 {mu}m comes from the fact that the galaxies that are primarily contributing to 500 {mu}m fluctuations peak at a higher redshift than those at 250 {mu}m.
