Journal of Russian Laser Research, Volume 33, Number 6, November, 2012 QUANTUM THEORY OF DIPOLE NANOLASERS Igor E. Protsenko 2 P. N. Lebedev Physical Institute, Russian Academy of Sciences Leninskii Prospect 53, Moscow 119991, Russia Advanced Energy Technologies Ltd. Novaya Street 100, Skolkovo, Moscow Region 143025, Russia e-mail: protsen @ sci.lebedev.ru 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 ∼ 10 4 − 10 5 emitters decreases, with the pump increase, to quite small values ∼ 10 −2 of the width 2Γ 2 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 2Γ 2 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. Keywords: nanolasers, plasmonics. 1. Introduction Miniature lasers find many applications in microelectronics, information processing, and telecommu- nications [1]. Several microlasers have been suggested such as, for example, polymer-thin-film lasers [2], microwire lasers [3], and Bregg-mirror-cavity lasers [4]. Microlasers have the Fabry–Perot or a whispering gallery-mode cavity [3], so their size cannot be smaller than λ/(2n), where λ is the wavelength of the cavity mode and n is the refractive index of the lasing medium. Spasers and dipole nanolasers (DNLs) have been suggested in [5, 6]; their size may be smaller than λ/(2n), and they generate not photons but other bosonic particles – plasmons. ∗ Small sizes of spasers and DNLs are important for applications such as, for example, in chip-scale optical interconnects [7], but not only the small sizes are interesting features of DNLs and spasers. Many phenomena of laser physics, quantum optics, and plasmonics appear in these devices — the self-phasing of arrays of DNLs or spasers [8], superradiance and bistability [9, 10], local field effects, and thresholdless generation. * The possibility of laser generation of bosons different from photons has been pointed out, for example, in [11]. Manuscript submitted by the author in English first on October 28, 2012 and in final form on November 7, 2012. 1071-2836/12/3306-0559 c  2012 Springer Science+Business Media New York 559