The Onset of Lasing in Semiconductor Nanolasers

Nanolasers based on emerging dielectric cavities with deep sub-wavelength confinement of light offer a large light-matter coupling rate and near-unity spontaneous emission factor, $\beta$. These features call for reconsidering the standard approach to identifying the lasing threshold. Here, a new threshold definition is suggested, taking into account the recycling process of photons when $\beta$ is large. This threshold reduces to the classical balance between gain and loss in the limit of macroscopic lasers, but qualitative as well as quantitative differences emerge for nanolasers. In particular, this new threshold identifies the onset of a transition regime, where the quantum statistics of the emitted light evolve into the Poissonian statistics of a coherent state. It is shown that the threshold with photon recycling consistently marks the onset of the change in the second-order intensity correlation, $g^{(2)}(0)$, toward coherent laser light, irrespective of the laser size and down to the case of a single emitter. In contrast, other threshold definitions may well predict lasing in light-emitting diodes. An overview of different threshold definitions proposed in the literature is provided and their predictions are compared when going from macroscopic to microscopic lasers.