  Nanolasers based on emerging dielectric cavities with deep sub-wavelength
confinement of light offer a large light-matter coupling rate and a near-unity
spontaneous emission factor, $\beta$. These features call for reconsidering the
standard approach to identifying the lasing threshold. Here, we suggest a new
threshold definition, taking into account the recycling process of photons when
$\beta$ is large. This threshold with photon recycling reduces to the classical
balance between gain and loss in the limit of macroscopic lasers, but
qualitative as well as quantitative differences emerge as $\beta$ approaches
unity. We analyze the evolution of the photon statistics with increasing
current by utilizing a standard Langevin approach and a more fundamental
stochastic simulation scheme. We show 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. These
results address the fundamental question of the transition to lasing all the
way from the macro- to the nanoscale and provide a unified overview of the
long-lasting debate on the lasing threshold.

Optics