Replica symmetry breaking reveals the emission mechanism of FRET-assisted random laser

Fȍrster resonance energy transfer (FRET) is a fundamental approach for fabricating widely tunable (≥100 nm) random lasers and cascaded ones, which are the fundamental direction for achieving applications breakthroughs of random lasers in multi-fields, such as speckle-free imaging and biosensing. However, it is challenging to realize due to a lack of method to investigate the emission mechanism and emission characteristics of FRET-assisted random laser. In this work, the replica symmetry breaking and the Lévy flight are introduced to investigate the dynamical emission mechanism of FRET-assisted random laser. It is revealed that FRET can induce the disorder in random laser to frustrate coherently oscillating modes, resulting in a non-trivial interaction between the modes, which generates discrete emission field. This emission field exhibits low spatiotemporal coherence, which is essential for using random laser in super-resolution spectroscopy and even photolithography. Meanwhile, the phase diagram of dynamics during the FRET is derived to reveal the dynamical evolution of the interaction between random laser modes during FRET, which illustrates how FRET influences the emissions properties of random laser. This work broadens not only the approach for exploring order physical principles in disorder random laser based on statistical analysis methods, but also provides the theoretical support for the design of complex energy level random lasers with special application properties.