Quantum theory of dipole nanolasers

Abstract

We generalize the semiclassical model of the dipole nanolaser (DNL) based on the Heisenberg–Langevin approach, taking into account spontaneous emission of plasmons into the generation mode, nonlinearity of generation, and noises. We find a “thresholdless” smooth transition from the spontaneous emission to the stimulated emission and the threshold conditions for such a transition and determine the spectrum of generation and its linewidth. We show that, in spite of the very low quality of the DNL generation mode, the linewidth of a DNL with many M ∼ 104 − 105 emitters decreases, with the pump increase, to quite small values ~ 10−2 of the width 2Γ2 of the lasing transition at modest pump rates, about 30 times larger that the decay rate of the emitter upper lasing state. This fact confirms the practical possibilities of realizing DNLs with narrow-line stimulated emission. Otherwise, the linewidth of DNLs with small M ∼ 1 number of emitters is larger than 2Γ2 and increases with the pump rate. In addition our results on DNLs can be applied to other lasers, such as nanolasers, microlasers, and LEDs for lighting, also with a low-quality cavity and strong spontaneous emission into the generation mode.