  We show that the spatial coherence of thermal radiation can be manipulated in
time-modulated photonic systems supporting surface polaritons. We develop a
fluctuational electrodynamics formalism for such systems to calculate the
cross-spectral density tensor of the emitted thermal electromagnetic fields in
the near-field regime. Our calculations indicate that, due to time-modulation,
spatial coherence can be transferred between different frequencies, and
correlations between different frequency components become possible. All these
effects are unique to time-modulated systems. We also show that the decay rate
of optical emitters can be controlled in the proximity of such time-modulated
structure. Our findings open a promising avenue toward coherence control in
thermal radiation, dynamical thermal imaging, manipulating energy transfer
among thermal or optical emitters, efficient near-field radiative cooling, and
engineering spontaneous emission rates of molecules.
