Spatial correlations of the spontaneous decay rate as a probe of dense and correlated disordered materials

We study theoretically and numerically a new kind of spatial correlation for waves in disordered media. We define $C_{\mathrm{\Gamma }}$ as the correlation function of the fluorescent decay rate of an emitter at two different positions inside the medium. We show that the amplitude and the width of $C_{\mathrm{\Gamma }}$ provide decoupled information on the structural correlation of the disordered medium and on the local environment of the emitter. This result may stimulate the emergence of new imaging and sensing modalities in complex media.