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Nanophotonic components operate in the few-photon regime, thus their experimental characterization calls for photon-counting techniques, at least in the threshold region, and requires adequate laser models to interpret the observations.
While the photon statistics of (macroscopic) Class A [1] lasers is well understood and can be readily reconstructed from the zero-delay second order autocorrelation (g(2)(0)), the memory effects introduced by the slow material response of semiconductor-based devices (Class B [1]) and the sensitivity of nanolasers to spontaneous emission [2] require a more careful approach. The latter induces a spontaneous spiking dynamics [3], near threshold, resulting in values of g(2) larger than those expected even for a chaotic signal, and growing without bounds as the duration of the spikes decreases.
Currently available laser models appear unable to predict such a behaviour, due to an inadequate treatment of the contribution of spontaneous emission, and, since the Probability Density Function (PDF) collects into a statistical distribution the state of the system, its predictions fail when the dynamics is not reproduced by the model from which it is derived. Thus, contrary to the usual assumption, the validity of the photon statistics of macroscopic Class B devices [4] must be reconsidered as the cavity volume is reduced.
We investigate the influence of the cavity size on a commercial VCSEL microlaser with a moderate fraction of spontaneous emission coupled into the lasing mode (beta~0.0001), which represents a happy compromise between a large enough cavity size to detect the dynamics while capturing the self-spiking typical of very small lasers. The autocorrelation (g(2)(0)) is both computed from the intensity time series with a fast (10 GHz) photodetector and deduced from the measured coincidences in arrival times of a photon counting apparatus (TAC with 15 ps timing resolution) in Hanbury-Brown & Twiss (HBT) configuration. We observe values of g(2)(0) up to 2.2, which would produce exponentially decaying distributions if interpreted through the current models [4]. Instead, the experimental PDF, reconstructed from the time series, matches the generic distributions for class B lasers even for the maximum value of g(2)(0).
We therefore conclude that these two techniques cannot be considered as providing equivalent information if only the second order moment g(2) of the distribution is considered, and that new theoretical work is needed on the photon statistics of small-sized Class-B lasers.
References
[1] J. R. Tredicce, F. T. Arecchi, G. L. Lippi, and G. P. Puccioni, J. Opt. Soc. Am B2, 1, 173-183, 1985.
[2] G. P. Puccioni and G. L. Lippi, Opt. Express 23, 3, 2369-2374, 2015.
[3] T. Wang, G.P. Puccioni, and G.L. Lippi, Sci. Rep. 5, 15858 (2015).
[4] P. Paoli, A. Politi, and F.T. Arrecchi, Z. Physik B 71, 403-410, 1988.
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