Photon bursts at lasing onset and modelling issues in micro-VCSELs

Abstract

Spontaneous photon bursts are observed in the output collected from a mesoscale semiconductorbased laser near the lasing threshold. Their appearence is compared to predictions obtained from Laser Rate Equations and from a Stochastic Laser Simulator. While the latter is capable of predicting the observed large photon bursts, the photon numbers computed by the former produces a noisy trace well below the experimentally detectable limit. We explain the discrepancy between the two approaches on the basis of an incorrect accounting of the onset of stimulated emission by the Rate Equations, which instead are capable of complementing the physical description through topological considerations.PACS numbers:

“Amplified Spontaneous Emission” in Micro- and Nanolasers

“…The narrowness of the region in such devices where photon bursts may appear, due to the sharpness of the transition, may make direct measurements almost impossible even nowadays. The photon bursts observed in a microlaser [72,84] have an apparent duration of the order of τ b ≈ 0.4 ns. Although there may be bandwidth limitations which intervene in the measurement, this value agrees with time-delayed second-order autocorrelation measurements taken with a fast photocounting system (∼40 ps time jitter) [76].…”

“…While in itself there is no particular reason for preferring g (2) (0) > 2, its practical usefulness is clear, since it helps identifying a regime of photon bursts in experiments where g (2) (0) is the only easily accessible quantity. Whenever the statistics becomes subthermal it is impossible to distinguish between a regime with burst emission and a dynamically different one (photon bunched in a subthermal way, for instance, dynamical oscillations [72,86], or background effects [84]). This simple example immediately shows the limitations of the autocorrelation measurement in the identification of bursts and highlights the difficulties inherent in the presence of too large a number of pulses (fractional filling of the measurement interval T) and of the influence of background.…”

“…Figure 4 in [114] and Figure 5 in [115]); N.2 Photon bursts appear in the laser output for Class B lasers both at the micro-and nanoscale (cf. Figure 5 in the Supplementary Material of [72] and Figure 3a in [84]); N.3 Prediction of photon bursts in the laser output for semiconductor nanolaser in dynamical regimes between Classes A and B (cf. Figure 7 in [116]); N.4 Prediction of superthermal statistics (free-running, Quantum Well laser, Figure 7 in [119]); N.5 Prediction of superthermal statistics using a Gillespie algorithm in a model with pump blocking, suited to Quantum Dot modelling (cf.…”

“…While only a proper stochastic simulation is currently capable of reproducing the observed dynamics [84], a topological investigation of the phase space properties of the rate equations, with the added contribution of the average spontaneous emission, provides useful information. This is not surprising, given that the underlying topological structure on which the random walk takes place (e.g., [67,114]) is the same as the one of the stochastic laser simulators [83] (both derive from the semiclassical description of radiation [1]).…”

“…The origin of spontaneous spiking (photon bursts) in the transition from a purely spontaneous emission regime to the coherent one can be better understood from the analysis of the eigenvector [84]. Figure 7 shows the normalized component of the eigenvector which matches the photon number n (i.e., the ν component in Equation ( 12)) for the least stable of the two eigenvalues (Figure 4) for different values of β ranging from nano-to microlasers.…”