Thermal phenomena in quantum plasmonics

Plasmon nanolasers, also known as SPASERs, were suggested by Bergman and Stockman in 2003. Quantum plasmonics attract much attention in recent years due to the numerous potential applications in the plasmonics. We consider thermal effects in the metal nanoresonator immersed in the active, laser medium. The size of the resonator is much less than the wavelength. The plasmon field inside the nanoresonator operates as a quantum object. Due to the nanosize of the resonator, the internal plasmon electric field is about the atomic field even for few plasmon quants. The coupling between the plasmon field and plasmon resonator is anomalous strong. We develop the quantum dynamics of the plasmon field and show that the SPASER may be the subject of thermal instability. The loss in SPASER increases with increasing the temperature when the average number of the plasmons is maintained at the stationary level. Therefore, the heat generation increases with increasing the temperature. This positive feedback results in the thermal instability. When the energy, accumulated in the plasmon nanoresonator, exceeds the instability threshold the temperature increases exponentially. We find the increment of the temperature growth and lifetime as function of the loss in metal and the structure of the plasmon resonator. We consider how the thermal instability influences the luminescence and find how the lasing threshold is changed. The coherence of the light emitted by the plasmon laser is also considered. The thermal stability of the nanolaser is crucial for any practical application.