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Diffusion-inspired time-varying phosphorescent decay in nanostructured environment

Structured environment controls dynamics of light-matter interaction processes via modified local density of electromagnetic states. In typical scenarios, where nanosecond-scale fluorescent processes are involved, mechanical conformational changes of the environment during the interaction processes can be safely neglected. However, slow decaying phosphorescent complexes (e.g. lanthanides) can efficiently sense micro- and millisecond scale motion via near-field interactions. As the result, lifetime statistics can inherit information about nano-scale mechanical motion. Here we study light-matter interaction dynamics of phosphorescent dyes, diffusing in a proximity of a plasmonic nanoantenna. The interplay between the time-varying Purcell enhancement and stochastic motion of molecules is considered via a modified diffusion equation, and collective decay phenomena is analysed. Fluid properties, such as local temperature and diffusion coefficient are mapped on phosphorescent lifetime distribution extracted with the help of inverse Laplace transform. We present rather simple photonic platform enabling contactless all-optical thermometry and diffusion measurement and paving a way for a plethora of possible applications. Among them, the proposed analysis can be used for detailed studies of nanofluidic processes in lab-on-a-chip devices, which are extremely hard or even impossible to analyse with other optical methods.