Phase angle encoded upconversion luminescent nanocrystals for multiplexing applicationsElectronic supplementary information (ESI) available: Theoretical analysis on the impulse response function of an upconversion dynamic system and the connection of the decay and rise time constants to the phase angle, numerical simulations of the phase angle, nanoparticle syntheses, fabrication of polymeric beads and films, inkjet printing of UCNPs, luminescence color decoding, a portable phase angle measureme

Lanthanide-doped upconversion nanoparticles (UCNPs) are increasingly used as luminescent candidates in multiplexing applications due to their excellent optical properties. In the past, several encoding identities have been proposed for UCNPs, including emission colour, intensity ratio between different emission bands, colour spatial distribution, and luminescence lifetime. In this paper, a new optical encoding dimension for upconversion nanomaterials is developed by exploring their luminescence kinetics, i.e. , the phase angle of upconversion luminescence in response to a harmonic-wave excitation. Our theoretical derivation shows that the phase angle is governed jointly by the rise and decay times, characterizing the upconversion luminescence kinetics. Experimentally, a full set of methods are developed to manage the upconversion luminescence kinetics, through which the rise and decay times can be manipulated dependently or independently. Furthermore, a large phase-angle space is achieved in which tens of unique codes can potentially be generated in the same colour channel. Our work greatly extends the multiplexing capacity of UCNPs, and offers new opportunities for their applications in a wide range such as microarray assays, bioimaging, anti-counterfeiting, deep tissue multiplexing labelling/detection and high-density data storage. In addition, the development of this luminescence kinetics-based optical encoding strategy is also instructive for developing multiplexing techniques using other cascade luminescent systems that inherently lack multi-spectral channels, such as triplet-triplet annihilation molecule pairs. A phase angle optical encoding dimension is developed by exploiting the luminescence kinetics of upconversion nanoparticles.