Lasers have a long history and their modeling has been considered as being a settled problem for several decades. The construction of ever smaller lasers has, however, opened new questions relative to the transition from the spontaneous to the stimulated emission regime. This transition is well described in "large-sized" lasers by models based on macroscopic averages and predicts the existence of a threshold point (in the thermodynamic limit). This point is known to lose meaning as the cavity size shrinks.
Photon statistics has played a crucial role in the characterization of the coherence buildup of the electromagnetic field through threshold. In the 1960's and 1970's intensive work showed that the coherence buildup takes place through a succession of states for the emitted photons which transform the thermal (incoherent) into the Poisson (coherent) statistical distribution, going through intermediate states describable in terms of statistical mixtures of incoherent and coherent photon fractions. The variable fraction of coherent versus incoherent photons is controlled by the pump parameter value in the (very narrow) transition region and is considered time-independent. At the time, all work was conducted in Class A lasers [1].
Our measurements show that this picture is too restrictive to match the experimental observations conducted in a mesoscale (i.e, very small-sized, but larger than a nanolaser) Class B laser [1]. Choosing a device sufficiently large to allow for a complete set of measurements (resolved time-traces), but small enough to possess a smooth transition region, we prove the existence of a nontrivial dynamics in the transition from incoherent to coherent emission, characterized by the presence of sharp intensity spikes [2]. These dynamics display autocorrelation values consistent with the gradual growth of coherence, but terminate in a deterministic (noisy) dynamics whose correlation properties may be considered at odds with coherent emission. When the only indicator is the autocorrelation function (e.g., when measuring the very weak output of a nanolaser) it is quite easy to mistake the excess (i.e., above the Poisson limit) value in the autocorrelation for imperfect electromagnetic field coherence. Instead, our experimental results show that [2]:
a. coherence is attained at pump values which are quite close to the point at which a nonnegligible photon flux is measured;
b. in Class B lasers the transition is dominated by dynamical spiking of the laser intensity, where short coherent pulses (for the moment indirectly inferred from the measurements) are separated by incoherent emission;
c. the picture corresponding to a time-independent superposition of incoherent and coherent photons instead holds for Class A devices, as confirmed by numerous authors (even recently in VECSEL devices);
d. in Class B devices, a regime of stochastically-induced coherent oscillations between field intensity and population inversion sets in and persists over a large range of pump parameters, which can be erroneously interpreted as imperfect coherence within the framework of Class A lasers photon statistics.
These results shed new light on the threshold transition for Class B lasers -- particularly important for meso- and nanoscale devices -- and suggest the need for an extension of the traditional photon statistics.
[1] J.R. Tredicce, F.T. Arecchi, G.L. Lippi, and G.P. Puccioni, J. Opt. Soc. Am. B 2, 173 (1984).
[2] T. Wang, G.P. Puccioni, and G.L. Lippi, Sci. Rep. 5, 15858 (2015).